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Simulation and analysis of sediment resuspension observed in old Tampa Bay, Florida

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Title:
Simulation and analysis of sediment resuspension observed in old Tampa Bay, Florida
Creator:
Schoellhamer, David Henry
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English
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xvii, 215 leaves : ill., photos ; 29 cm.

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Subjects / Keywords:
Estuaries ( jstor )
Modeling ( jstor )
Sediment transport ( jstor )
Sediments ( jstor )
Shear stress ( jstor )
Shengs ( jstor )
Simulations ( jstor )
Turbulence ( jstor )
Velocity ( jstor )
Waves ( jstor )
Coastal and Oceanographic Engineering thesis Ph. D
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF
Old Tampa Bay ( local )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1993.
Bibliography:
Includes bibliographical references (leaves 196-214).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by David Henry Schoellhamer.

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University of Florida
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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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030045643 ( ALEPH )
29897677 ( OCLC )
AJX7109 ( NOTIS )

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SIMULATION AND ANALYSIS OF SEDIMENT RESUSPENSION
OBSERVED IN OLD TAMPA BAY, FLORIDA

















By

DAVID HENRY SCHOELLHAMER


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1993
























To Alicia V. Schoellhamer, 1920-1990















ACKNOWLEDGEMENTS

The support of my employer, the U.S. Geological Survey, while I

attended classes at the University of Florida is gratefully

acknowledged. My supervisors in Tampa, Carl Goodwin and Kathi Hammett,

were very cooperative in arranging my work schedule so I could complete

my classes, qualifying exams, and dissertation.

The Old Tampa Bay sediment resuspension data that was used in this

dissertation was collected as part of a study of sediment resuspension

and light attenuation in Tampa Bay that I conducted from 1987 to 1992

for the U.S. Geological Survey. The study was performed in cooperation

with the City of St. Petersburg, the City of Tampa, Hillsborough

County, Pinellas County, the Southwest Florida Water Management

District, and the Tampa Port Authority. Pliny Jewell and Victor

Levesque of the U.S. Geological Survey provided valuable assistance

with the data collection for the study.

I would like to thank my supervisory committee members, Drs.

Robert Dean, Dan Hanes, Ashish Mehta, Lou Motz, and Peter Sheng, and

former members Drs. Wayne Huber, Carl Goodwin, and Clay Montague. I

would especially like to thank Dr. Peter Sheng, who, as committee

chairman, guided this research.

Finally, the life-long support of my parents, Jack and Alicia, is

more than gratefully acknowledged.


















TABLE OF CONTENTS


page

ACKNOWLEDGEMENTS................................................ iii


LIST OF TABLES..................................................

LIST OF FIGURES...... ...................... .......... ............

KEY TO SYMBOLS ..................................................

ABSTRACT ... ......................... ............................

CHAPTERS

1 INTRODUCTION..............................................


Significance of Estuarine Sediments.......
Sediment Transport Processes.............
Initiation of Motion of Bed Sediments..
Bed Load Transport.....................
Erosion and Bottom Shear Stress........
Suspended Load Transport................
Flocculation and Aggregation............
Settling and Deposition.................
Other Bed and Near-bed Factors.........


Field Studies Related to Estuarine Sediment Transport.....
Numerical Models Applicable to
Estuarine Sediment Transport............................
Relation of this Research to Previous Studies.............

2 SEDIMENT RESUSPENSION DATA COLLECTION METHODOLOGY.........

Study Area ................................................
Sediment Resuspension Monitoring Sites....................
Old Tampa Bay Instrumentation Platform....................
Calibration and Output of Electromagnetic Current Meters..
Response Threshold and Biological Interference of
OBS Sensors.............................................
Water Sample Collection...................................
Instrument Deployment Strategies..........................

3 SEDIMENT RESUSPENSION DATA AND ANALYSIS...................

March 1990 Storm..........................................
November 1990 Storm.......................................
Tropical Storm Keith ......................................
Tropical Storm Marco ......................................


vi

viii

x

xvi


........ ....... 4
. 8
. .. .. 8
............... 15
. 1 6
..... ......... 24
. ......... .... 26
.. ...... ... .... 27
. 31
31









Implications for Numerical Modeling........................ 96

4 NUMERICAL MODEL.......................................... 98

Momentum and Transport Equations........................... 102
Turbulence Closure........................................ 106
Nondimensional Equations................................. 112
Steady State Conditions.................................. 116
Wave-Induced Pressure Gradients............................ 117
Bottom Shear Stress and Erosion ........................... 119
Suspended-Sediment Stratification......................... 122

5 NUMERICAL SIMULATIONS OF THE MARINE SURFACE LAYER
AND CRITICAL SHEAR STRESSES ON CONTINENTAL SHELVES...... 123

Simulation of Turbulence in the Marine Surface Layer...... 123
Critical Shear Stresses Observed on Continental Shelves... 126

6 OLD TAMPA BAY NUMERICAL SIMULATION RESULTS................ 138

Steady Flow Simulation................................. 138
Reproduction of Energy Spectra of Observed Currents....... 142
Simulated Shear Stresses.................................. 144
Old Tampa Bay Suspended-Sediment Simulation Procedure..... 154
Old Tampa Bay November 1990 Suspended-Sediment
Calibration Simulation ................... ............. 161
Old Tampa Bay March 1990 Suspended-Sediment
Validation Simulation .................................. 166
Old Tampa Bay March 1990 Suspended-Sediment
Improved Simulation.................................... 171
Old Tampa Bay November 1990 Sensitivity Simulations........ 175

7 SUMMARY AND CONCLUSIONS ................................... 181

APPENDICES

A OCM1D FINITE-DIFFERENCED EQUATIONS AND TURBULENCE
CLOSURE ALGORITHMS.... .................................... 188

Finite-Differenced Equations for Momentum and
Suspended Sediment...................................... 188
Turbulence Closure Algorithms............................... 192

REFERENCES...................................................... 196

BIOGRAPHICAL SKETCH........... ............. .................. 215















LIST OF TABLES


page

Table 1-1, Previous studies that are related to this research
and include an estuarine environment, wind waves,
field measurements of suspended-sediment
concentrations, or a numerical vertical sediment
transport model..................................... 50

3-1, Old Tampa Bay platform instrumentation deployments... 71

3-2, Old Tampa Bay platform data, March 8, 1990............ 75

3-3, Correlation coefficients for various wave properties
and bottom shear stresses with suspended-solids
concentrations at the Old Tampa Bay platform,
March 1990.......................................... 78

3-4, Old Tampa Bay platform data, November 30 -
December 1, 1990...................................... 86

3-5, Correlation coefficients for various wave properties
and bottom shear stresses with suspended-solids
concentrations at the Old Tampa Bay platform,
November 1990....................................... 88

4-1, Modifications made to the 1986 version of OCM1D
(Sheng 1986) for this research........................ 101

4-2, Comparison of the equilibrium closure and TKE
closure methods for turbulent transport............... 113

5-1, Mean current speed, maximum wave orbital velocity,
wave period, and critical shear stresses from a
wave-current model (Drake and Cacchione 1986) and
the OCM1D model...................................... 128

5-2, Mean current speed, maximum wave orbital velocity,
wave period, angle between the mean current and
waves, and critical shear stresses from a
wave-current model (Larsen et al. 1981) and
the OCM1D model...................................... 133

6-1, Total and grain shear stress distribution and
critical stresses, 1800 hours March 8, 1990........... 153

6-2, Old Tampa Bay suspended-sediment simulations......... 157









6-3, Values of the calibration coefficients determined by
other studies and determined for the November 1990
calibration simulation and the March 1990 improved
simulation........................................... 173

6-4, Mean percent differences of simulated suspended-solids
concentrations 70 and 183 cm above the bed caused by
20% changes in the calibration coefficients,
November 1990 sensitivity simulations................ 176















LIST OF FIGURES


page

Figure 1-1, Shields critical shear stress diagram................ 12

1-2, Roughness function B in terms of Reynolds number,
from Schlichting (1969).............................. 19

2-1, Old Tampa Bay study area............................ 53

2-2, Size distribution of bottom sediment at the
Old Tampa Bay platform .............................. 57

2-3, Old Tampa Bay platform............................... 58

2-4, Suspended-solids concentration and median OBS
sensor output 70 cm above the bed at the Old Tampa
Bay platform, March 1990 ............................ 67

3-1, Measured and calculated quantities at the Old Tampa
Bay platform, March 1990 .......................... 74

3-2, Measured and calculated quantities at the Old Tampa
Bay platform, November 1990 ......................... 85

3-3, Mean water depth, mean current speed, and maximum
bottom orbital velocity at the Old Tampa Bay
platform during tropical storm Keith,
November 1988...................................... 91

3-4, Wind speed, wind vector azimuth, and
suspended-solids concentration at the Old Tampa Bay
platform during tropical storm Marco, October 1990.. 95

5-1, Measured, simulated, and theoretical turbulent
dissipation in the marine surface layer, measurements
reported by Soloviev et. al (1988).................. 124

5-2, Extended Shields diagram for continental shelf
data, shear stresses from wave-current models (WC)
and OCM1D............................................ 130

6-1, Computational grid for 45 layers, 1.15 neighboring
layer height ratio, and a 399 cm domain height...... 140

6-2, Comparison of Reichardt and simulated velocity
profiles............................................. 141


viii









6-3, Comparison of turbulence macroscale from the
dynamic equation and the integral constraints....... 143

6-4, Raw energy spectra computed from measured and
simulated velocities, 1500 hours November 30, 1990.. 145

6-5, Spatial convergence of total and
grain shear stress.................................. 147

6-6, Maximum grain shear stress calculated by OCM1D and
from Engelund's experimental results................ 149

6-7, Simulated total and grain shear stresses,
1800 hours March 8, 1990 ........................... 150

6-8, Simulated grain shear stress,
1800 hours March 8, 1990............ .... ........... 152

6-9, Maximum total bottom shear stress from the
OCM1D model and the Grant and Madsen (1979)
wave-current model, November 1990 ................... 155

6-10, Simulated and measured suspended-solids
concentrations 70 cm above the bed,
November 1990 calibration simulation................ 162

6-11, Simulated and measured suspended-solids
concentrations 183 cm above the bed,
November 1990 calibration simulation................ 163

6-12, Simulated and measured suspended-solids
concentrations 24 cm above the bed,
March 1990 validation and improved simulations..... 168

6-13, Simulated and measured suspended-solids
concentrations 70 cm above the bed,
March 1990 validation and improved simulations..... 169

6-14, Simulated and measured suspended-solids
concentrations 183 cm above the bed,
March 1990 validation and improved simulations..... 170

6-15, Sensitivity of November 1990 calibration simulation
results to erosion rate exponent I ...... ........... 177

6-16, Sensitivity of November 1990 calibration simulation
results to erosion rate coefficient a.............. 178

6-17, Sensitivity of November 1990 calibration simulation
results to settling velocity ws.................... 180

A-l, Coordinate axes definition and grid structure for
program OCM1D........................................ 189















KEY TO SYMBOLS


A invariant constant for turbulence algorithm (0.75, eqn. 4-26)

Ab orbital amplitude just above the boundary layer (eqn. 1-14)

A eddy viscosity (eqn. 1-16)
nondimensional eddy viscosity (eqn. 4-42)

a wave amplitude (eqn. 1-12)
small reference elevation above the bed (eqn. 1-18)
Fourier series coefficient (eqn. 2-3)
invariant constant for turbulence algorithm (3, eqn. 4-23)

a corrected Fourier series coefficient (eqn. 2-9)
c
B roughness function (eqn. 1-5)

b intercept of line that fits a segment of fig. 1-2 (eqn. 1-6)
Fourier series coefficient (eqn. 2-3)
invariant constant for turbulence algorithm (0.125, eqn. 4-23)

b corrected Fourier series coefficient (eqn. 2-10)
c
C well-mixed suspended-sediment concentration (eqn. 1-19)

C coefficient for integral constraint on A (eqn. 4-32)
q
c mean suspended-sediment concentration (eqn. 1-15)
magnitude in frequency domain (eqn. 2-4)
nondimensional suspended-sediment concentration (eqn. 4-42)

ca suspended-sediment concentration at elevation a (eqn. 1-18)

c corrected magnitude in frequency domain (eqn. 2-7)

cm suspended-sediment mass concentration (eqn. 4-62)

c suspended-sediment concentration at upper boundary (eqn. 4-19)
nondimensional c (eqn. 4-52)

D rate of deposition (eqn. 1-19)

d particle diameter for which n percent of sediments are finer
n
d sediment particle diameter (eqn. 1-1)

E erosion rate (eqn. 1-3)









nondimensional erosion rate (eqn. 4-42)

E Ekman number (eqn. 4-43)

F Froude number (eqn. 4-43)
neighboring layer height ratio (eqn. 5-2)

f friction factor (eqn. 1-12)
Coriolis coefficient (eqn. 4-4)

G filter gain for current meter, function of w (eqn. 2-1)

g gravitational acceleration (fig. 1-1)

H elevation of model domain (eqn. 4-42)
nondimensional elevation of model domain (eqn. 4-42)

h water depth (eqn. 1-12)

i counter and exponent (eqn. 5-2)

K pressure transfer function (eqn. 4-60)
p
K eddy diffusivity (eqn. 1-16)
nondimensional eddy diffusivity (eqn. 4-42)

k wave number (eqn. 1-12)
molecular diffusion (eqn. 4-26)

kb bottom roughness (eqn. 1-14)

ks height of bottom roughness elements (eqn. 1-5)

M erosion rate constant (eqn. 1-3)

N number of data points for fast Fourier transform (eqn. 2-3)
Brunt-Vaisala frequency (eqn. 4-31)
number of layers (eqn. 5-2)

n counter (eqn. 2-3)

P Prandtl number (eqn. 4-43)

p pressure (eqn. 4-2)

p pressure at the water surface (eqn. 4-6)
nondimensional pressure at the water surface (eqn. 4-42)

Q nondimensional quantity (eqn. A-8)

q turbulent fluctuating velocity (eqn. 4-23)
nondimensional turbulent fluctuating velocity (eqn. 4-42)

R roughness Reynolds number u*ks/v (fig. 1-2)








R Reynolds number (eqn. 4-43)

R. Richardson number (eqn. A-11)

R horizontal Rossby number (eqn. 4-43)
x
R vertical Rossby number (eqn. 4-43)
z
R boundary Reynolds number U*ds/v (eqn. 1-1)

RC electronic filter time constant for current meter (eqn. 2-1)

s slope of line that fits a segment of fig. 1-2 (eqn. 1-6)
invariant constant for turbulence algorithm (1.8, eqn. 4-27)

T wave period (table 5-1)

t time (eqn. 1-15)
nondimensional time (eqn. 4-42)

U1/10 mean of the highest 1/10 ub (table 5-2)

U100 mean current speed 100 cm above bed (table 5-1)

U maximum wave orbital velocity 20 cm above bed (table 5-1)
w
U shear velocity (eqn. 1-1)

u horizontal velocity at elevation z (eqn. 1-5)
mean velocity of sediment particles (eqn. 1-15)
mean velocity component (eqn. 4-1)
nondimensional mean velocity component (eqn. 4-42)

ub maximum bottom orbital velocity (eqn. 1-11)

u, shear velocity (eqn. 1-5)

v mean horizontal velocity component (eqn. 4-4)
nondimensional mean velocity component (eqn. 4-42)

v invariant constant for turbulence algorithm (0.3, eqn. 4-23)

w mean vertical velocity component (eqn. 4-4)

w terminal settling velocity (eqn. 1-17)
s nondimensional settling velocity (eqn. 4-42)

x coordinate axis (eqn. 1-15)
nondimensional horizontal coordinate axis (eqn. 4-42)

y horizontal coordinate axis (eqn. 4-4)
nondimensional horizontal coordinate axis (eqn. 4-42)

Z Rouse number w /(fiu.) (eqn. 1-18)








z elevation above bed (eqn. 1-5)
vertical coordinate axis (eqn. 1-17)
vertical coordinate (eqn. 4-4, fig. A-l)

z vertical coordinate of velocity measurement (eqn. 4-61)
V
z nondimensional quantity u.z/v (eqn. 1-10)

z elevation with zero velocity (eqn. 1-9)
o
zo nondimensional quantity u.z /v (eqn. 1-10)

a erosion rate coefficient (eqn. 1-4)
invariant constant for turbulence algorithm (0.75, eqn. 4-26)

P K/A, the inverse of the turbulent Schmidt number (eqn. 1-16)

y specific weight of fluid (eqn. 1-2)

Ts specific weight of sediment (eqn. 1-2)

At time interval of data (eqn. 2-3)
nondimensional simulation time step (eqn. A-l)
simulation time step (eqn. 4-59)

Az1 height of bottom layer (eqn. 5-2)

ACTk nondimensional layer elevation (eqn. A-l)

AC-k nondimensional distance between grid points k and k-I (eqn. A-l)

AC+k nondimensional distance between grid points k and k-I (eqn. A-l)

Aw angular frequency increment 2r/(NAt) (eqn. 2-3)

6 Kronecker delta (eqn. 4-23)

6 distance for integral constraint on A (eqn. 4-32)
q
S phase (eqn. 2-4)
alternating tensor (eqn. 4-2)
energy dissipation rate (eqn. 5-1)

Sc corrected phase (eqn. 2-8)

S nondimensional quantity (eqn. 1-13)

7) erosion rate exponent (eqn. 1-4)

e production term (eqn. 4-3)
nondimensional production term (eqn. 4-42)

K von Karman's constant (eqn. 1-5)

A turbulence macroscale (eqn. 4-23)


xiii









nondimensional turbulence macroscale (eqn. 4-42)

A Taylor microscale (eqn. 4-28)

v kinematic viscosity (eqn. 1-1)
nondimensional kinematic viscosity (eqn. 4-42)

surface displacement from the mean water depth (eqn. 4-6)
nondimensional surface displacement (eqn. 4-42)

p fluid density (eqn. 1-1)
nondimensional fluid density (eqn. 4-42)

Po reference fluid density (eqn. 4-2)

ps sediment density (eqn. 4-62)

p water density (eqn. 4-62)

a nondimensional vertical coordinate (eqn. 4-42)

7 bottom shear stress (eqn. 1-3)

rb total bottom shear stress (table 5-1)

r critical shear stress for erosion (eqn. 1-3)
c
7r critical shear stress for deposition (eqn. 1-19)

'min minimum r that maintains sediment in suspension (eqn. 1-19)

7 bottom shear stress (eqn. 1-2)

"s grain shear stress (table 5-1)

w maximum bottom shear stress in oscillatory flow (eqn. 1-11)

w x component of wind shear stress at free surface (eqn. 4-14)
nondimensional x component of wind shear stress (eqn. 4-47)

7 y component of wind shear stress at free surface (eqn. 4-15)
WY nondimensional y component of wind shear stress (eqn. 4-48)

7 x component of total bottom shear stress (eqn. 4-20)
nondimensional x component of total shear stress (eqn. 4-53)

7 y component of total bottom shear stress (eqn. 4-21)
y nondimensional y component of total shear stress (eqn. 4-54)

,7 dimensionless shear stress (Shields parameter, eqn 1-2)

filter phase delay for current meter, a function of w (eqn. 2-2)
angle between the mean current and wave direction (table 5-2)

0 angular velocity of the Earth (eqn. 4-2)


xiv









u angular wave frequency (eqn. 1-12)
angular frequency of periodic input signal to filter (eqn. 2-1)


Subscripts:

k layer number (eqn. A-1)

r reference value (eqn. 4-42)


Superscripts:

n time step (eqn. A-1)

* nondimensional value (eqn. 4-42)

turbulent fluctuation


xv















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

SIMULATION AND ANALYSIS OF SEDIMENT RESUSPENSION
OBSERVED IN OLD TAMPA BAY, FLORIDA

By

DAVID HENRY SCHOELLHAMER

May 1993

Chairman: Y. Peter Sheng
Major Department: Coastal and Oceanographic Engineering

A comprehensive field and numerical modeling study was conducted

to improve the understanding and numerical modeling of sediment

resuspension and the vertical transport of resuspended sediment in the

shallow estuarine environment. Sediment resuspension was

intermittently monitored in Old Tampa Bay from 1988 to 1990. The data

indicate that net sediment resuspension was caused by depth-

transitional wind-waves that were generated by strong and sustained

winds associated with storm systems and not by tidal currents.

A vertical one-dimensional numerical model was modified and used

to help analyze the Old Tampa Bay sediment resuspension data and to

help determine significant sediment transport processes in Old Tampa

Bay. The model was modified to include viscous effects, multiple wave

frequencies, variable bottom roughness regimes, and spatially-averaged

grain shear stress. The model successfully simulated steady flow

profiles with laminar, transitional, and turbulent regions and

turbulent dissipation in the marine surface layer. Simulated shear








stresses (plotted on an extended Shields diagram) were in agreement

with observed critical conditions for sediment motion under combined

wave and current motion on the continental shelf. Energy spectra

produced from 1-Hz velocity data collected in Old Tampa Bay can be

reproduced by the model. Calibrated settling and erosion coefficients

for the model are reasonable compared to values from other studies.

Only the finer particles in the bed appear to be resuspended, and sand-

sized particles are probably intermittently transported as bed load.

Simulation results indicate that the settling velocity of resuspended

sediments was greater in November 1990 than March 1990, probably

because larger particles were eroded by larger shear stresses or there

was more fine material in the form of fecal pellets in November 1990.

Simulation results also indicate that the bottom sediments were more

erodible in March 1990 than November 1990. Reduced biological binding

of the fine bed sediments probably increased bottom sediment

erodibility in March 1990.


xvii















CHAPTER 1
INTRODUCTION

Estuaries are transition zones between riverine and marine

environments. Potential sources of sediment particles for an estuary

include rivers, net sediment flux from the marine environment, overland

runoff, and anthropogenic point sources. Sediment particles are

commonly trapped and deposited in the deeper parts of an estuary. The

bed sediment affects the overall health of an estuary in several ways.

Bed sediment, especially fine sediment, can be resuspended up into the

water column where it may reduce the amount of light penetrating the

water column, may act as a source for constituents adsorbed onto the

sediment, and may be transported to undesirable locations. The

reduction of light in the water column may adversely affect biological

communities. Adsorbed constituents that can be released to the water

column during suspension and possibly while on the bed include

nutrients which may contribute to eutrophication of the estuary, heavy

metals, pesticides, and organic carbons that may decrease the

productivity of the estuary. Resuspended sediment may be transported

throughout the estuary and spread the adverse effects and possibly

become deposited in undesirable locations, such as shipping channels,

turning basins, and marinas. Thus, the overall health of an estuarine

environment is partially dependent upon the resuspension, transport,

and deposition of sediment.

Numerical models can be used to study and predict sediment

dynamics in an estuary. An accurate numerical model must include









algorithms that represent significant hydrodynamic and sediment

transport processes which may be identified from comprehensive field

data. Governmental regulators could use a sediment model to help

predict the effect of proposed anthropogenic alterations to an estuary

on light attenuation, transport and fate of toxic substances, and

sedimentation. Potentially adverse alterations include increased

wastewater discharge, increased stormwater runoff, dredging, dredge

material disposal, and wetland destruction. Because sediment particles

are negatively buoyant and settle, accurate sediment models must

consider vertical sediment dynamics. Two obstacles, however, limit

application of sediment models. Field data are needed to calibrate and

validate estuarine sediment models, and the bottom boundary conditions

for the sediment must be specified.

Improved understanding and simulation of estuarine sediment

processes are dependent upon reliable field data. The importance of

the processes that potentially control sediment dynamics must be

understood and included in a realistic model. For example, if wind-

waves are an important sediment resuspension mechanism, then a model

that ignores water motions at wind-wave frequencies can not

realistically simulate estuarine sediment transport. Laboratory

studies can be used to improve understanding of sediment transport

process, but field conditions are often difficult to recreate in the

laboratory. Reconstruction of realistic sediment beds in a laboratory

is difficult, especially when the natural sediments are biologically

active. A field data collection program has far less control than

found in a laboratory, but the data and insights gained in the field

are directly applicable to the estuary being studied. Calibration is

the selection of model parameters that permit the model to accurately









simulate field data. Once selected, validation may be performed on an

independent data set to prove that the model algorithms and model

parameters can be used to make reliable predictions. Field data is

therefore required to develop a predictive model in which managers,

scientists, and the public can have confidence.

Sediment transport processes at the interface of the water column

and bottom sediments must be accurately simulated in a numerical model

because the bed is an omnipresent potential source and sink of

suspended sediment. A particle resting on the bed will move (erode)

when the lift force generated by the hydrodynamics is sufficiently

large. If a particle moves by rolling, sliding, or saltating

(jumping), then it contributes to the bed load. A mobilized particle

may also become suspended (or resuspended) in the water column.

Interaction of suspended particles may be caused by salt flocculation

of clay minerals and formation of large aggregates of organically bound

inorganic particles. Deposition is the process that returns particles

to the bed. The sedimentary processes of initiation of particle

motion, bed load, and deposition all occur at or near the interface of

the sediment bed and the water column. Other near-bed factors which

may affect hydrodynamics and sediment transport include bed forms,

armoring, porous beds, suspended-sediment stratification, and

biological activity.

The purpose of this research was to improve the understanding and

numerical modeling of sediment resuspension and the vertical transport

of resuspended sediment in the shallow estuarine environment. Field

data and a numerical model were used to accomplish this task. From

1988 to 1990, the author collected sediment resuspension data during

potential periods of resuspension in Old Tampa Bay, a shallow estuary









on the west-central coast of Florida. These field data were analyzed

by the author to determine the sediment resuspension mechanisms in Old

Tampa Bay. The author modified and used a vertical one-dimensional

model to simulate the Old Tampa Bay data and other data. The numerical

model was used as a tool to help analyze the Old Tampa Bay data and to

help determine significant sediment transport processes in Old Tampa

Bay.

The remainder of this chapter discusses existing literature on the

significance of estuarine sediments, sediment transport processes,

field studies related to estuarine sediment transport, numerical models

applicable to estuarine sediment transport, and the relation between

previous studies and this research. The data collection methodology

is discussed in chapter 2, and the data are presented and analyzed in

chapter 3. The numerical model is described in chapter 4. Numerical

simulations of the marine surface layer and critical shear stresses on

continental shelves were conducted to test modifications made to the

model during this research, and these simulation results are presented

and discussed in chapter 5. Simulations of suspended-solids

concentrations in Old Tampa Bay are presented and discussed in chapter

6. Conclusions of this study are summarized in chapter 7.

Significance of Estuarine Sediments

Bottom sediments are an omnipresent factor that affect the water

quality and biological productivity of an estuary. Potential sources

of sediment particles for an estuary include rivers, net sediment flux

from the marine environment, overland runoff, and anthropogenic point

sources. Sediment particles are commonly trapped and deposited in the

deeper or vegetated parts of the estuary. Bed sediments provide the

substrate for benthic organisms, seagrasses, and marshes, and chemical






5


exchange processes occur between the bed sediments and the water

column. Bed sediments, especially fine sediments, can be resuspended

up into the water column where they may 1) increase nutrient

concentrations, 2) transport trace metals, 3) influence the mortality,

life cycle, food supply, and photosynthesis of estuarine species, and

4) may move and settle in ports or marshes.

Bed sediments chemically interact with the overlying water column

and benthic biological communities. Diffusive fluxes between the bed

sediments and water column commonly remove dissolved oxygen from the

water column (Hinton and Whittemore 1991, Svensson and Rahm 1991) and

recycle nutrients to the water column (Callender and Hammond 1982,

Hammond et al. 1985, Simon 1988, Ullman and Aller 1989). In addition,

sediment geochemistry in seagrass beds determines the limiting nutrient

for seagrass growth (Short 1987).

The release of nutrients from sediments to the water column is

enhanced during resuspension events. Increased nutrient concentrations

in the water column that were caused by resuspension events have been

observed by Gabrielson and Lukatelich (1985) during wind related

sediment resuspension events in the Peel-Harvey estuarine system in

Australia, by Fanning et al. (1982) during storms on the continental

shelf of the Gulf of Mexico, and by Schwing et al. (1990) after

destabilization of bottom sediments by a seiche in Monterey Bay,

California. Grant and Bathmann (1987) found that bacterial mats

deposit sulfur on surficial bottom sediments and that resuspension is

an important mechanism for returning sulfur to the water column.

Phytoplankton and organic detritus resting on the bottom can also be

resuspended and impact estuarine productivity (Roman and Tenore 1978,

Gabrielson and Lukatelich 1985). The supply of Radon 222, a tracer, to









the water column from resuspension flux and diffusion flux is about the

same in the Hudson River estuary (Hammond et al. 1977). Simon (1989)

estimates that one resuspension event in the Potomac River that lasts

minutes can add as much ammonium to the water column as the diffusive

flux can in 5 to 1000 days, depending upon the site. Laboratory

experiments show that typical water column concentrations of

particulate nutrients would double in a few hours during a resuspension

event (Wainright 1990) and that biological growth is increased when

resuspended material is added to microcosms (Wainright 1987).

In addition to nutrients, trace metals and other contaminants may

be adsorbed to sediment particles and these contaminants are

detrimental to the biological health of many estuaries. For example,

metals are partitioned between adsorbed and dissolved phases, so the

transport of metals is related to sediment transport (Dolan and Bierman

1982, Li et al. 1984, Horowitz 1985). In South San Francisco Bay,

availability of trace metals may be a factor that limits growth of some

phytoplankton species, sorption processes influence dissolved

concentrations of metals, and sorption processes vary among specific

metals (Kuwabara et al. 1989). Sediment concentrations of trace

metals, PCBs, pesticides, or polynuclear aromatic hydrocarbons exceed

the median concentration associated with biological effects in

estuaries in Alaska, California, Connecticut, Florida, Hawaii,

Maryland, Massachusetts, New Jersey, New York, Oregon, Texas, and

Washington (Long and Morgan 1990).

The mortality, food supply, and life cycle of some estuarine

species may be affected by suspended sediments and sediment transport

processes. For species restricted to the benthos, mortality may be

increased by resuspension or burial and sediment transport may regulate









the food supply to both suspension and deposit feeders (Nowell et al.

1987). Eggs, cysts, and spores of many zooplankton and phytoplankton

species reside in bottom sediments and erosion may inject them into the

water column where they may hatch. Circumstantial evidence indicates

that this process may contribute to red tide outbreaks (Nowell et al.

1987). Sellner et al. (1987) found that increased suspended-sediment

concentrations reduced the survival rate of newborn larval copepods in

Chesapeake Bay. In addition, development and reproduction of survivors

was inhibited.

Suspended sediments reduce the sunlight available for

photosynthesis. Smaller particles are more efficient light attenuators

(Baker and Lavelle 1984, Campbell and Spinard 1987). McPherson and

Miller (1987) found that non-chlorophyll suspended material is the most

important component of light attenuation in Charlotte Harbor, Florida.

Inorganic suspended material is the dominant cause of light attenuation

in several New Zealand estuaries (Vant 1990) and sediment resuspension

by tidal currents and wind waves is an important cause of attenuation

(Vant 1991). In the coastal waters of northwest Africa, light

attenuation is greatest in nearshore waters where sediment

concentrations are greatest, compared to offshore waters, and nearshore

light attenuation reduces phytoplankton growth (Smith 1982). The

reduction of light in the water column reduces seagrass photosynthesis

and the maximum depth at which seagrasses can grow (Dennison 1987).

Resuspended sediments may move throughout the estuary, depending

upon the circulation, and, in addition to possibly spreading the

adverse effects already mentioned, may deposit in ports or marshes.

Large man-made basins that serve as ports and marinas are commonly

depositional environments that require costly maintenance dredging









(Granat 1987, Kobayashi 1987, Headland 1991). Estuarine sediments may

also deposit in marshes where vegetation and benthic algae impede water

motion and resuspension and enhance deposition, formation, and

maintenance of an important habitat (Ward et al. 1984, Krone 1985, Huh

et al. 1991).

Sediment Transport Processes

Sediment transport processes differ somewhat depending on whether

the sediment is noncohesive or cohesive. Noncohesive sediment

particles do not interact electro-chemically with other particles, and

cohesive sediment particles interact electro-chemically with other

cohesive particles. Sediments with a diameter larger than 20 am are

generally noncohesive. Thus, gravel, sand, and coarse silts are

noncohesive. Cohesion increases as particle size decreases below 20 im

(Migniot 1968), and clay minerals are generally cohesive. Transport of

noncohesive sediments is controlled by the processes of initiation of

particle motion, bed load transport, suspended load transport, and

deposition. Cohesive sediments differ in that they are not transported

as bed load, and interparticle electro-chemical forces may cause

flocculation in brackish estuarine waters. Both cohesive and

noncohesive suspended inorganic particles may adhere to large

organically bound aggregates that can deposit rapidly in an estuary.

Bed and near-bed factors that may affect hydrodynamics and sediment

transport include bed forms, bed armoring, suspended-sediment

stratification, fluid-mud, porous beds, and biological activity.

Initiation of Motion of Bed Sediments

The horizontal transport of noncohesive sediment as bed load and

suspended bed-material load is dependent upon the initiation of motion

of stationary particles in the sediment bed. Particles that roll,









slide, or saltate along or near the bed are part of the bed load, and

particles that are lifted into suspension are part of the suspended

load. Initiation of particle motion has been reviewed by the Task

Committee on Preparation of Sedimentation Manual (1966), Vanoni (1975),

Miller et al. (1977), Simons and Senturk (1977), and Lavelle and

Mofjeld (1987a, 1987b).

A noncohesive particle lying on a sediment bed, for which fluid is

flowing above, will be acted upon by the hydrodynamic forces of lift

and drag in addition to gravity and normal forces from adjacent

touching particles. Vanoni (1975, pp. 92-93), Simons and Senturk

(1977, pp. 400-407), Yalin (1977), and Wiberg and Smith (1987) describe

the forces acting on a bed particle in detail. The formulation of the

hydrodynamic forces will differ depending on whether the flow over the

particle is laminar or turbulent and whether the bed is composed of

uniform or heterogeneous particles. If the hydrodynamic forces exceed

a threshold or critical value, then the particle will move. Particle

motion may also be initiated by organisms that disturb the bottom

sediments and by trawling in coastal waters (Churchill 1989).

Because the exact geometry, size, and shape of every sediment

particle in a bed can not be determined, practical analysis of the

problem of initiation of particle motion requires assuming that the bed

is a continuum of particles instead of a large quantity of discrete

particles. Noncohesive sediment particles are usually assumed to be

spherical. The particle sizes (measured by sediment particle diameter

d ) that are present in an actual bed will vary vertically and
s
horizontally, but it is commonly represented as one or more sizes for

which a certain percentage N of the bed material is finer (denoted as









dN). The physical properties of the sediment particles at a fixed

location also will vary with time as particles are transported.

In addition to sediment particle properties, the flow field will

vary spatially and temporally. The shear force exerted by the flow on

the bed is commonly used to indicate the magnitude of the hydrodynamic

force on the bed. Because most natural flows are turbulent and

turbulent flows fluctuate in space and time, the bottom shear stress at

a fixed point will vary about the mean bottom shear stress. The bottom

shear stress will also vary spatially, especially if bed forms are

present. For example, for three-dimensional ripples, Ikeda and Asaeda

(1983) found that sediment is eroded from the side slopes of

longitudinally trailing ridges by lee side eddies and that sediment

entrainment is correlated with intermittent bursts of the lee side

eddy.

If the bed is assumed to be a continuum of particles, the

inception of particle motion is a stochastic rather than a

deterministic process because the particle sizes and bottom shear

stress vary spatially and temporally (He and Han 1982). Usually, the

existence of particle motion is determined by assuming a threshold

shear stress or threshold velocity. Definitions of threshold have been

categorized by Lavelle and Mofjeld (1987a) as those based on sediment

flux in a flume, visual flume observations (Kramer 1935, White 1970,

Mantz 1977), erosion rate experiments for cohesive sediments

(Partheniades 1965, Ariathurai and Arulanandan 1978, Sheng and Lick

1979, Kelly and Gularte 1981, Parchure and Mehta 1985), and field

measurements in marine environments (Sternberg 1971, Wimbush and Lesht

1979, Lesht et al. 1980, Larsen et al. 1981). Because of the

stochastic nature of the inception of particle motion problem, however,








some particle motion will still occur below the threshold values

(Einstein 1941, 1966, Taylor and Vanoni 1972, Vanoni 1975, Christensen

1981, Lavelle and Mofjeld 1987a). The concept of threshold is useful

for practical problems (Simons and Senturk 1977 pp. 417-487, Blaisdell

et al. 1981, Blaisdell 1988) and when ability to observe particle

motion is limited in the field (Sternberg 1971, Wimbush and Lesht 1979,

Lesht et al. 1980). Threshold criteria should only be applied with the

knowledge that initiation of particle motion is a stochastic process.

The most common threshold criterion is probably that presented in

the Shields diagram as modified by Rouse (fig. 1-1) (Vanoni 1975 p. 96,

Simons and Senturk 1977 p. 410). The Shields threshold criterion was

determined by extrapolating measured transport rates of laboratory

experiments to the point of zero transport for fully developed

turbulent flows, noncohesive sediments, and flat beds. The abscissa is

the boundary Reynolds number

R* = U ds / V (1-1)

in which U is the shear velocity for which U = (To/p) where ro is

the bottom shear stress and p is the fluid density, and v is the

kinematic fluid viscosity. The curve for R. less than two was

extrapolated by Shields and is not based upon data. The ordinate is a

dimensionless shear stress or Shields parameter

0 (1-2)
(T7-T) d

in which ys is the specific weight of the sediment particle and 7 is

the specific weight of the fluid. The line on figure 1-1 indicates the

critical condition for sediment motion. If (R.,r.) is below the line,

then there is no sediment motion, and if (R*,r*) is above the line,

then there is sediment motion.







































0.U

0.5
0.4-- -
0.3

0.2 -


0 .2 1 11 1 "-- -- -- D O I I -- I-: : V ; ; ---- t 1 1 1 1
0.1- 10 ,000
0.08

0.03 -

0.0 -- -- -i
0.05
0.04
0.03


0.2 0.4 0.6 1.0 2 4 6 8 10 20 40 00100 200

BOUNDARY REYNOLDS NUMBER. R.--


500 1,000


Figure 1-1, Shields critical shear stress diagram, from Vanoni (1975).









Several modifications to the Shields diagram have been proposed

because the bottom shear stress is included on both axes of the

diagram, so an iterative procedure must be used to determine the

critical shear stress for a given particle. The Task Committee on

Preparation of Sedimentation Manual (1966) added the quantity

d s
s 0.5
s [ 0.1( 1) g d ]"

to the diagram in which g is the acceleration of gravity. Yalin

(1977), Bonnefille (see Vollmers 1987) and Gessler (1971) regrouped the

dimensionless variables to make the diagram easier to use.

The Shields diagram also has been modified to account for bed

forms and small boundary Reynolds numbers. Gessler (1971) adjusted

Shields diagram because some of Shields' flume experiments formed

ripples and small dunes that increased the critical shear values by 10

percent. Inman (1963) shows a second curve for rippled beds. Shields

diagram was extended for values of R, less than 2 by Miller et al.

(1977) (mostly with data from White (1970)) with an envelope

encompassing the data scatter and by Mantz (1977) with a power function

that lies inside the envelope (Larsen et al. 1981). The extended

Shields diagrams are applicable to noncohesive fine sands and silts.

Although the Shields diagram was developed for unidirectional

flows, it also may be applicable to the estuarine and marine

environments. Field observations in oscillatory flow environments have

been in good agreement with the Shields criterion (Davies 1985).

Madsen and Grant (1977) stated that Shields diagram is applicable to

locations with both waves and currents and good agreement with data in

such environments was observed by Drake and Cacchione (1986). Field

measurements in Puget Sound by Sternberg (1971) were in good agreement









with the Shields diagram modified to account for ripples presented by

Inman (1963). Larsen et al. (1981) found that the extended Shields

diagram was in good agreement with observed threshold grain motion for

oscillatory flows on a continental shelf.

Other threshold relations have been developed for noncohesive

sediments. Lane (1955) used field data to develop curves of critical

shear stress vs. mean particle diameter, which give higher critical

shear stresses than Shields' diagram. Sundborg (1956) developed a

threshold criterion based on particle size and mean velocity 1 meter

above the bed, and Inman (1949, 1963) developed a criterion that is

dependent on particle size and shear velocity, both of which agree with

Puget Sound data (Sternberg 1971). Wiberg and Smith (1987) derived a

critical shear stress equation for beds with uniform particle size that

corresponded closely to Shields' diagram. In addition, they also

derived a critical shear stress equation for heterogeneous beds that

was in good agreement with experimental data.

For cohesive sediment beds, the consolidation of the bed is an

important factor that helps determine whether and how the bed sediment

will move. When initially deposited, cohesive sediment beds are

unconsolidated high concentration suspensions (fluid-mud) and have

little shear strength. Consolidation is a time dependent function of

the overbearing pressure, particle size, and of the clay mineralogy

that dewaters, compresses, and strengthens the bed (Meade 1966,

Terzaghi and Peck 1967 p. 84, Hayter 1986). Therefore, there is no

general threshold of motion criterion for cohesive sediments such as

the Shields diagram for noncohesive sediments. Critical shear stresses

for various cohesive sediments and consolidation states have been

determined in the laboratory (Partheniades 1965, Ariathurai and









Arulanandan 1978, Sheng and Lick 1979, Thorn and Parsons 1980, Kelly

and Gularte 1981, Mehta et al. 1982) and the field (Gust and Morris

1989). Three modes of initial motion of cohesive sediments are re-

entrainment of unconsolidated high concentration suspensions, surface

erosion of individual particles and flocs, and bulk erosion (also

called mass erosion) which is the sudden failure of the upper part of

the bed (Krone 1986, Mehta et al. 1989a).

Bed Load Transport

If a particle moves by rolling, sliding, or saltating (jumping),

then it contributes to the bed load. Determining whether a particle

that is not in contact with the bed is contributing to the bed load or

suspended load can be difficult (Einstein 1950, Bagnold 1966, Murphy

and Aguirre 1985). Bed load usually is composed of sand-sized and

coarser particles. Fine sediments (silts and clays) are usually

immediately suspended upon initiation of motion and are not transported

as bed load.

Calculation and measurement of bed load are difficult. Reviews of

equations for calculating bed load have been presented by Vanoni (1975,

pp. 168-172), Simons and Senturk (1977, pp. 508-543), Yalin (1977),

Gomez and Church (1989) (for gravel beds only), Ludwick (1989), and

Stevens and Yang (1989). Bed load transport equations were compared by

van Rijn (1984a), who concluded that predicted bed load transport rates

are accurate only within a factor of 2. Gomez and Church (1989)

assessed bed load equations for gravel beds and determined that none of

the reviewed equations consistently performed well. Carson (1987)

evaluated several factors used to estimate bed load in alluvial

channels and determined that the grain component of the bed shear

stress (shear stress corrected for sidewalls and bed forms) is a better









predictor of bed load than mean velocity, stream power, and unit stream

power. The bed load transport rate is related to the grain component

of the bed shear stress so this quantity should be used in bed load

formulas when bed forms are present (Wiberg and Smith 1989). Field

measurements of bed load are discussed by Emmett (1980), Edwards and

Glysson (1988), and Ludwick (1989), but bed load is difficult to

measure because any device placed near the bed may disturb the flow and

the rate of bed load transport.

Erosion and Bottom Shear Stress

The rate at which particle motion is initiated is an important

quantity for studies and numerical models of sediment transport. van

Rijn (1984b) developed a sediment pick-up function (mass per unit area

per unit time) by utilizing a mechanical device (a sediment lift) at

the bottom of a flume to supply erodible noncohesive particles and

compared the developed sediment pick-up function to the sediment pick-

up functions by Einstein (1950), Yalin (1977), Nagakawa and Tsujimoto

(1980), de Ruiter (1982), and Fernandez-Luque (see van Rijn 1984b).

Bed load and suspended load transport rates calculated with the

developed sediment pick-up function compared well with field and

laboratory data (van Rijn 1986b). Noncohesive particles that are

picked up are initially saltating and will either contribute to the bed

load or suspended load (Murphy and Aguirre 1985).

Quantification of the erosion of cohesive sediments is difficult

because of the lack of understanding of erosion mechanisms and the

numerous factors involved. Thus, the erosion relationships that have

been developed are simple relationships that contain coefficients that

must be determined in the laboratory or field. Assuming that the rate









of surface erosion is proportional to the nondimensional excess shear

gives (Ariathurai and Arulanandan 1978)

E = M 1 (1-3)
c
in which E is the surface erosion rate in mass per unit area per unit

time, M is an erosion rate constant defined as 'the increase in the

rate of erosion for an increase in the interface fluid shear by an

amount equal to the critical shear stress of that soil' (Ariathurai and
-2 -1
Arulanandan 1978) that has a range of values from 0.003 g cm min to
-2 -1
0.03 g cm min r is the bottom shear stress, and r is the critical

shear stress for erosion. For shear stresses less than the critical

value, no surface erosion occurs. Equation 1-3 was developed using

data from placed beds with uniform shear strength which is not

representative of cohesive beds in nature (Mehta et al. 1982). Erosion

functions by Mehta et al. (1982) and Parchure and Mehta (1985) were

determined using more realistic laboratory sediment bed conditions.

Equation 1-3 has been applied in numerical models of cohesive

sedimentation (Ariathurai and Krone 1976, Thomas and McAnally 1985,

Sheng et al. 1990b, Uncles and Stephens 1989). Because equation 1-3 is

an empirical erosion formula, it is not limited to cohesive sediments,

and it has been used to simulate transport of noncohesive suspended

sediments in the lower Mississippi River (Schoellhamer and Curwick

1986).

A general erosion equation is determined by setting the erosion

rate equal to a power of the excess shear stress

E = a Irl1 (1-4)

in which a and q are constants that are determined by calibration.

Values of a have been found to range from 1.9x10 to 3.7x106, for 7









in dynes/cm2, and n has been found to range from 0.23 to 10 (Lavelle et

al. 1984). Lavelle et al. (1984) used equation 1-4 to simulate erosion

as a stochastic process (Lavelle and Mofjeld 1987a).

The erosion rate is dependent upon the shear stress applied to the

bed by the flowing water and the bottom shear stress from the near-bed

velocity. Schlichting (1969) gave velocity profile equations for

turbulent flow in the near-wall region for hydraulically smooth, rough

and transitional cases. Given a measured or simulated velocity

profile, these equations can be used to calculate the bottom shear

stress. In general, the velocity distribution is
u 1
S 1= In(z/k ) + B (1-5)
u K S

in which u* is the shear velocity for which r = p u2, the velocity u is

at an elevation z above the bed, K is von Karman's constant (0.4), k

is the height of the bottom roughness elements, and B is a roughness

function that has the form
u k u. k
B = s log _Vs + b = s In -- s + b (1-6)
v 2.3 v
in which u.ks/v is a roughness Reynolds number (R), and s and b are the

slope and intercept of a line that fits a segment of the data presented

in figure 1-2 (Schlichting 1969 fig. 20.21), which is a plot of B vs.

log R developed from laboratory data. The boundary is smooth for R <

5, rough for R > 70, and transitional for intermediate values of R.

For a smooth wall, s = 5.75 and b 5.5, and equations 1-5 and 1-6 can

be written as
S= 1 In (9.03 z u. / v) (1-7)
u* K

For a rough wall s = 0.0 and b = 8.5 and equations 1-5 and 1-6 can be

written as
u = In (30 z / ks) (1-8)
u K S






19
















11 i '


_* ** .
B






smi--- transition -- -- complete rough
6

02 0.4a a6 oe ZO .2 1. Z.6 1.8 Z 22 Z. 2s Z 3.0 32
















Figure 1-2, Roughness function B in terms of Reynolds number, from
Schlichting (1969).









for which the elevation with zero velocity is z oks/30. Equations 1-5

and 1-6 can be combined to derive a general expression for the

elevation with zero velocity

z = k R"s/23 e-b (1-9)
o s
For transitional flow regimes, figure 1-2 and equations 1-5 and 1-6

must be applied in an iterative manner.

If the velocity used to calculate the bottom shear stress is from

the near-bed region of a hydraulically smooth (R < 5) or transitional

flow (5 < R < 70), the velocity profile may not be logarithmic near the

bed and a different velocity profile equation is applicable. Reichardt

(see Wiberg and Smith 1987) developed a velocity distribution equation

that gives a linear profile for elevations much smaller than the top of

the viscous sublayer, a logarithmic profile for elevations much larger

than the top of the viscous sublayer, and a smooth and accurate

transition between the two regions. This velocity distribution is
u+
u = [ ln(l+xz )
+ + +
+ -z /11.6 z -0.33z
(In(z ) + ln()) (1 e /11.6 e-0 ) ]

(1-10)
+ +
in which the nondimensional quantities z = u z/v and z = uzo/v.

The bottom roughness is dependent upon grain size in the bed and

bed forms. The bottom roughness element that controls the resistance

in the region of the water column adjacent to the bed is the grain

roughness and above this region the roughness is controlled by larger

roughness elements such as ripples, dunes, or surface irregularities

caused by bioturbation (Smith and McLean 1977). The grain roughness is

normally related to the bed sediment size distribution.









Two types of shear stresses, the total shear stress and the grain

shear stress, can be considered. The total shear stress is the shear

stress exerted on the flow by all of the bottom roughness elements.

The grain shear stress is the spatially-averaged (over a bed form

wavelength) shear stress exerted on the sediment particles in the bed

by the flow. The grain shear stress is less than the total shear

stress. Sediment motion is dependent upon the grain shear stress

(Vanoni 1977, McLean 1991).

If the height and wavelength of the bed forms are constant, then

the matching elevation at which the velocities from the two regions are

equal can be calculated based on the bed form geometry (Smith and

McLean 1977). Smith and McLean (1977) measured velocity profiles at

several positions on dunes in the Columbia River and showed that the

spatially-averaged (or "zero-order") velocity profile could be

constructed from equation 1-5. The zero-order velocity profile

averages near-bed velocity variations caused by the bed forms and the

resulting total shear stress and grain shear stress are spatially-

averaged values. Expressions for the bottom roughness due to bed forms

have been developed by van Rijn (1984c) for steady flow in alluvial

channels and by Grant and Madsen (1982) for oscillatory flow.

For an oscillatory flow, a simple expression for the maximum

bottom shear stress is (Jonnson 1967)
Pf
w 2 ub lub (1-11)
in which f is a friction factor and
gak (1-12)
Ub = w cosh(kh)
is the maximum bottom orbital velocity from linear wave theory, where a

is the wave amplitude, k is the wave number, w is the angular wave

frequency, and h is the water depth. Shallow-water waves are assumed









to be present for kh < w/10 and deep-water waves are present for kh > n

(Dean and Dalrymple 1984). Equations and diagrams for the friction

factor f as a function of the wave properties and bottom roughness have

been determined empirically (Jonsson 1967, Kamphius 1975). For waves

in the absence of a mean current and for rough turbulent flow, Grant

and Madsen (1979, 1982) determined that the friction factor is given by

f = 0.08 / [Ker2(2fr) + Kei2(2TF)] (1-13)

in which Ker and Kei are Kelvin functions of zero order and

kb w 2
S= 30 ub f (1-14)

in which kb is the bottom roughness. The friction factor appears on

both sides of equation 1-13, so the equation must be solved

iteratively. Equation 1-13 is valid for rough turbulent flow for which

Ab/kb > 1 where Ab=ub/w is the orbital amplitude just above the

boundary layer. Bottom stress in oscillatory boundary layers (e.g.

Jonsson and Carlsen 1976) has also been computed with turbulent

boundary layer models (Sheng 1984, Sheng and Villaret 1989).

A potentially important resuspension mechanism in estuaries is the

nonlinear interaction of a wave field and a mean current that can

increase the shear stress on the bed to a value greater than the sum of

the wave only and current only shear stresses. Grant and Madsen (1979)

developed a model to estimate the bed shear stress when waves and

current are present. The model is based on the assumption of rough

turbulent flow that is wave dominated. They also developed a model

that includes ripple formation and the effect of ripples on the bed

shear stress (Grant and Madsen 1982). Weaknesses of the Grant and

Madsen models include the introduction of a fictitious reference

velocity at an unknown level, a rather arbitrarily estimated thickness









of the wave boundary layer, and the model being valid only for wave

dominant cases (Christoffersen and Jonsson 1985). The Grant and Madsen

models also assume that 1) the thickness of the logarithmic layer is

constant, which is not correct when waves are present (Sheng 1984), 2)

the wave field can be represented by a single wave period and wave

height, and 3) the eddy viscosity is linear and time invariant.

Cacchione et al. (1987) found that the shear stress and bottom

roughness estimated by the moveable bed model were in good agreement

with estimates from measured velocity profiles, but no bottom

photographs were available to check the estimated bed form geometry.

Drake et al. (1992) took bottom photographs and found that the moveable

bed model overestimated the size of bottom ripples. Larsen et al.

(1981) present a simpler solution for the model formulation by Grant

and Madsen (1979) that is applicable to smooth, transitional, and rough

bottom roughness regimes and the shear stress at the observed threshold

of motion of noncohesive sediments observed in the field was in good

agreement with Shields diagram. The results of the Larsen et al.

(1981) model and the Grant and Madsen (1979) model are virtually

identical for rough bottoms. Simpler wave-current models that compare

well with laboratory data have also been developed by Christoffersen

and Jonsson (1985) for wave and current dominated cases and by Sleath

(1991) for wave-dominated cases and rough beds. All of the above

models consider wave-averaged bottom stresses by invoking some sort of

a priori parameterization of wave-current interaction.

Wave-current interaction in bottom boundary layers has also been

studied without such a priori parameterization. Sheng (1984) used a

Reynolds stress turbulence model to simulate the detailed dynamics of

the boundary layer over the wave cycle by using a small time step









(1/100 of the wave cycle) and specifying the mean and orbital currents

at the outer edge of the boundary layer. The results were then

averaged over the wave cycle to produce wave-averaged stresses. Sheng

(1984) found that the model of Grant and Madsen (1979) generally

overestimated the wave-averaged stress and apparent roughness height.

Suspended Load Transport

Suspended sediment is transported by the flow in the water column.

The Reynolds time-averaged equation for three-dimensional sediment

transport, written in tensor notation, is (Vanoni 1975)
au:c'
8c + c = (1-15)
at j ax. ax.

in which c is the mean suspended-sediment concentration, u is the mean

velocity of the sediment particles, c' is the turbulent fluctuation of

sediment concentration about the mean, u' is the turbulent fluctuating

velocity of sediment particles, t is time, and x is the coordinate

axis. The first term in equation 1-15 represents the time rate of

change of sediment concentration, the second term represents the

advection and settling of particles, and the term on the right hand

side represents the turbulent dispersion of particles. The second

order correlation of velocity fluctuation and concentration fluctuation

is often represented as the product of the mean concentration gradient

and an eddy diffusivity K such that (Vanoni 1975)
ac
u!c' = K x (1-16)
1 v. ax.
i 1
The eddy diffusivity is often assumed to be proportional to the eddy

viscosity A (K =A v) which is often assumed to be related to mean flow

variables (Fischer et al. 1979) or to have a particular distribution

(Vanoni 1975, Fischer et al. 1979). Eddy diffusivity also can be









calculated with an advanced turbulence closure algorithm (Sheng 1986a,

Celik and Rodi 1988, Sheng and Villaret 1989).

An analytic expression for the vertical distribution of suspended

sediment in an open channel can be derived from equations 1-15 and 1-

16. Assuming that lateral and longitudinal variations are small and

that the mean vertical water velocity is small, equation 1-15 reduces

to the vertical conservation of mass equation for sediment
ac a
at az (WC w'c') (1-17)

in which w is the terminal settling velocity of sediment particles and

z is the vertical coordinate axis (Vanoni 1975). The first term within

the parenthesis is the settling flux of sediment and the second term is

the vertical flux of sediment (usually upward) caused by turbulence.

For steady flow and a parabolic distribution of the eddy diffusivity,

equations 1-16 and 1-17 can be used to derive the Rouse equation
( h-z a )Z (1-18)
a z h-a
in which z is the elevation above the bed, ca is the suspended-sediment

concentration at a usually small reference elevation a above the bed,

and the exponent Z is the Rouse number equal to w s/(cu ) (Vanoni

1975). Equation 1-18 gives a suspended sediment distribution that is

greatest near the bed, as is expected due to the negative buoyancy of

sediment particles. In addition, the vertical gradient of suspended-

sediment concentration is greatest near the bed. The water velocity is

small near the bed compared to the vertically-averaged velocity, so the

dissimilar distributions of suspended sediment and velocity must be

considered when calculating the suspended load in a river (Schoellhamer

1986, McLean 1991).









Flocculation and Aggregation

Salt flocculation of clay minerals and formation of large

organically bound aggregates of inorganic particles may occur in the

water column, especially in estuaries. Clay minerals transported to

estuaries by rivers encounter high cation concentrations that reduce

repulsive forces that prevent flocculation in freshwater. Particle

cohesion begins at salinities of 0.6 to 2.4 ppt, depending on the clay

mineralogy, and increases with salinity up to about 10 ppt, although

the rate of increase is small for salinities greater than 3 ppt (Krone

1962, Mehta 1986). Seawater has salinity of about 34 ppt.

Flocculation has been observed for clay concentrations as low as 50

mg/L (Ozturgut and Lavelle 1986). As a floc grows, the density,

settling velocity, and shear strength of the floc decrease (Krone

1986). Turbulence may break up relatively weak flocs (Krank 1984).

Meade (1972) states that salt flocculation has been overemphasized in

the literature while biological agglomeration by filter feeding

organisms has not received enough attention.

Suspended material in estuaries and oceans is commonly found in

the form of large aggregates (length scale 0.5 mm or larger), often

called marine snow (Wells and Shanks 1987). In the ocean, large

aggregates are primarily biogenic material (Fowler and Knauer 1986),

but estuarine aggregates are primarily inorganic particles attached to

organic material (Eisma 1986). The primary collision mechanism that

forms large aggregates is differential settling, not Brownian motion or

fluid shear (Hawley 1982, Eisma 1986). Aggregation by organisms may

also be important in estuaries (Meade 1972, Krank 1984, Eisma 1986).

Large aggregates have been observed to remain intact in currents as

much as 50 cm/s in estuaries (Wells 1989), but large aggregates tend to









break apart when sampled (Shanks and Trent 1980, Krank 1984, Eisma

1986, Fowler and Knauer 1986). Sampling procedures are limited to in

situ settling columns (Shanks and Trent 1980, Gibbs 1985, Fowler and

Knauer 1986) and photography (Krank 1984, Eisma 1986, Wells and Shanks

1987, Wells 1989). Eisma (1986) and Dyer (1989) state that the size of

the aggregates is limited by the turbulence microscale, which is the

size of the smallest turbulent eddies. The density of large aggregates

decreases with increasing size and the settling velocity and porosity

increases with increasing size (McCave 1975, Hawley 1982, Gibbs 1985).

Settling and Deposition

Particles that are part of the bed or suspended load may settle

through the water column and deposit on the bed. A noncohesive

particle falling in quiescent fluid is affected by the forces of

gravity, buoyancy, and drag. The terminal settling velocity for a

sphere in quiescent fluid is given by Stokes law and Rubey's equation,

which are presented by Vanoni (1975) and Simons and Senturk (1977). A

nonspherical particle, which is common in nature, may have a different

terminal settling velocity. A shape factor defined by Alger and Simons

(1968) can be used to predict settling velocity and settling behavior

of nonspherical particles and shells (Mehta et al. 1980). Terminal

settling velocity equations are for a single particle, but high

concentrations of noncohesive particles, which are most likely to occur

near the bed, may hinder settling and decrease the terminal settling

velocity (Vanoni 1975, Simons and Senturk 1977). The size of suspended

particles tends to decrease with elevation above the bed, so assuming a

single suspended particle size with a single settling velocity may not

be appropriate (McLean 1991).









Deposition of suspended sediments in natural hydrologic systems is

complicated by turbulence. The effective settling velocity of a

particle settling in a vertically oscillating flow will be less than

the terminal settling velocity for the particle in quiescent fluid

because of nonlinear modification of the drag force (Hwang 1990) or

vortex trapping (Nielson 1984). As a particle settles toward the bed,

the turbulence intensity generally increases and, thus, the probability

increases that a turbulent eddy will carry the particle either upward

or downward. The turbulence intensity will decrease very near the bed

and vanish in the viscous sublayer adjacent to the bed. If a particle

passes through the high turbulence zone near the bed, it can then

deposit on the bed. Li and Shen (1975) and Bechteler and Farber (1985)

presented random walk models that stochastically simulate particle

settling. Turbulence, however, is not an independent variable.

Density stratification by suspended sediments can dampen turbulence

(Sheng and Villaret 1989) and reduce the transport capacity of the flow

(McLean 1991).

Because turbulent intensity and the vertical gradient of sediment

concentration are greatest near the bed, near-bed hydrodynamic

processes determine deposition rates. Sheng (1986c) derived a

deposition velocity formula by considering the resistances that

sediment particles experience in various near-bed layers including the

logarithmic layer, vegetation canopy, laminar sublayer, and biochemical

effects. Numerical suspended-sediment transport models that solve

equation 1-15 generally have finer vertical grid resolution closer to

the bed and represent the bottom boundary condition either by setting

the net upward sediment flux equal to an erosion rate minus a

deposition rate (Sheng and Lick 1979, Schoellhamer 1988, Sheng et al.









1990a), by estimating a near-bed sediment concentration (van Rijn

1986a, Celik and Rodi 1988, Schoellhamer 1988), or by setting a net

erosion or deposition flux which is dependent on the bottom shear

stress (Thomas and McAnally, 1985).

Estimates of sediment deposition rates in estuaries have been made

with sediment traps and acoustic devices. Interpretation of sediment

trap data is difficult, but sediment traps have been used to estimate

deposition rates (Oviatt and Nixon 1975, Gabrielson and Lukatelich

1985). Bedford et al. (1987) used an acoustic transceiver to measure

near-bed suspended-sediment concentration profiles and calculated

deposition and erosion fluxes over a 3.5 hour period and a tidal cycle

at one site in Long Island Sound.

Large aggregates control settling and are an important mechanism

for transporting material to the bottom of oceans (McCave 1975, Shanks

and Trent 1980, Hawley 1982, Fowler and Knauer 1986) and estuaries

(Wells and Shanks 1987, Dyer 1989). Fowler and Knauer (1986) give a

minimum range of large aggregate settling velocities of 1 to 1000

m/day. Shanks and Trent (1980) measured settling velocities of large

aggregates in Monterey Bay, California, and the northeastern Atlantic

Ocean and found that the range of settling velocities was 43 to 95

m/day.

The settling velocity of depositing cohesive sediments is

dependent upon the sediment concentration. Krone (1962) measured

settling velocities of San Francisco Bay sediment in still water and

determined that the median settling velocity was proportional to the

concentration to the 4/3 power. This is a typical result for settling

column experiments with cohesive sediments (Mehta 1986), probably

because differential settling is the dominant collision mechanism









(Farley and Morel 1986). In estuaries, however, collisions caused by

velocity gradients are most important because they form the strongest

aggregates (Krone 1986). Ross (1988, also in Mehta 1989) conducted a

settling column experiment and found that the settling velocity of

Tampa Bay mud increased as the concentration increased up to about 1

g/L, the settling velocity was about constant (about 0.32 mm/s or 27

m/day) for concentrations from about 1 to 10 g/L, and the settling

velocity decreased as the concentration increased above 10 g/L due to

hindered settling.

Deposition of flocs of cohesive sediments may be prevented by the

turbulent boundary layer above the bed in which flocs may be broken

apart and lifted up into the water column. Krone (1962) conducted

deposition experiments in a recirculating flume from which he

determined that the rate of deposition of cohesive sediment from a

vertically mixed flow is

D = C s (1 /rr), r < cr (1-19)

in which C is the vertically well-mixed suspended-sediment

concentration and r is the critical shear stress for deposition that
cr
must be determined by analyzing time series of concentration and shear

stress measured in the laboratory or field. Laboratory experiments

indicate that r is less than r the critical shear stress for
cr c
erosion. If r > rcr no deposition occurs, and if r < cr, equation 1-

19 will eventually deposit all of the sediment in suspension.

Laboratory experiments by Mehta and Partheniades (1975), however,

showed that a constant fraction of the original suspension will be

maintained in suspension indefinitely for cr > > min where r m is

a minimum shear stress below which all of the suspended sediment will

deposit. Equation 1-19 is an empirical formula for deposition that









does not include the near-bed hydrodynamic processes that determine

deposition rates. Equation 1-19 has been used to simulate noncohesive

suspended-sediment transport in the lower Mississippi River

(Schoellhamer and Curwick 1986) in addition to cohesive sediment

transport (Ariathurai and Krone 1976, Thomas and McAnally 1985, Uncles

and Stephens 1989).

Other Bed and Near-bed Factors

Many bed and near-bed factors may affect hydrodynamics and

sediment transport. These factors include bed forms, bed armoring,

suspended-sediment stratification, fluid-mud, and porous beds. Some of

these factors (bed forms, bed armoring, suspended-sediment

stratification, and fluid-mud) are the result of sediment transport and

affect the hydrodynamics, which, in turn, affect the sediment

transport. Biological activity also affects sediment transport.

One consequence of noncohesive sediment transport can be the

formation of bed forms in riverine (Kennedy 1969, Vanoni 1975, Simons

and Senturk 1977, Yalin 1977) and coastal (Boothroyd 1985)

environments. Bed forms such as ripples and dunes do not occur in

cohesive sediment beds. Bed forms increase the bottom roughness of

open channels compared to flat bed conditions in which the only

roughness elements are the bed sediment particles. Because some of the

total bottom shear stress is caused by the bed forms, the shear stress

applied to the particles will decrease, so the total (grain and form)

critical shear stress for initiation of particle motion will increase

(Vanoni 1975, McLean 1991). On the upstream face of a dune, the grain

shear increases from zero at the reattachment point to a maximum at the

crest (Shen et al. 1990). van Rijn (1984c) used flume and field data

to develop and verify a methodology to predict bed form dimensions and









effective hydraulic roughness for steady flow in alluvial channels.

For oscillating flows, Grant and Madsen (1982) present empirical

relations for bed ripple geometry and an expression for the bottom

roughness. Drake et al. (1992), however, found that the Grant and

Madsen empirical relations overestimated ripple height on the Northern

California continental shelf.

An armored or paved bed has finer particles removed from the bed

surface so that only coarser noncohesive particles remain at the

surface thus preventing erosion of finer particles below (Simons and

Senturk 1977, Sutherland 1987). For equilibrium conditions, Jain

(1990) defines an armored bed as having a coarse surface layer that is

inactive (or immobile) and a paved bed as having a coarse surface layer

that is actively eroding and depositing (or mobile). For

nonequilibrium or degrading conditions, the particle-size distribution

of the surficial bottom sediments coarsens and the erosion rate

decreases with time. Therefore, near-bed sediment transport may be

dependent upon the armoring process, especially in alluvial channels.

Dawdy and Vanoni (1986) review several bed armoring and pavement

studies and predictive algorithms. More recently, bed armoring

algorithms have been presented by Karim and Holly (1986) and Park and

Jain (1987).

Near-bed suspended-sediment stratification will affect the

hydrodynamics and, therefore, affect sediment transport processes at

the bed. As previously mentioned, high near-bed sediment

concentrations may hinder settling of particles. Several authors have

found that sediment-laden flows reduced near-bed turbulence intensity

or bottom shear stress in steady and uniform open-channel flows (Vanoni

and Nomicos 1960, Itakura and Kishi 1980, Lau 1983, Julien and Lan









1988, Xingkui and Ning 1989). West and Oduyemi (1989) measured

turbulence and near-bed density stratification in an estuary and found

that density stratification damped turbulence. Flume experiments by

Vanoni and Nomicos (1960), however, indicated that the effect of bed

forms on the total bottom shear stress is much greater than the effect

of suspended sediment. Parker and Coleman (1986) found that suspended

sediments may either increase or decrease near-bed turbulence intensity

and bottom shear stress (discussed by Julien and Lan (1988)). Near-bed

stratification in sediment-laden flows may reduce near-bed turbulent

shear stresses and, therefore, reduce erosion rates (Sheng and Villaret

1989) and the sediment-transport capacity of the flow (McLean 1991).

Costa and Mehta (1990) collected hydrodynamic and suspended sediment

data in a high energy coastal environment and found a hysteresis in the

relationship between suspended-sediment concentration and the flow

velocity, with higher concentrations for accelerating flows, due to

near-bed density stratification.

An extreme case of near-bed suspended-sediment stratification is

the formation of an unconsolidated fluid-mud by cohesive sediments

above a consolidated bed in estuarine and near-shore environments. In

this situation, the water column is composed of two layers--a thin

dense non-Newtonian fluid underlying a Newtonian fluid. The fluid-mud

may interact with the overlying fluid. Surface waves cause mud waves

to form in the fluid-mud and the fluid-mud acts to attenuate (dampen)

surface waves (Suhayda 1986, Wells and Kemp 1986, Mehta 1991, Jiang and

Mehta 1992). Suhayda, Mehta, and Jiang and Mehta developed models to

simulate the interaction of the two fluids. Wells and Kemp also point

out that the formation of mud waves can produce significant

reentrainment of the fluid-mud.









The bed is commonly assumed to be an impermeable boundary but

water exchange between the bed and water column may advect sediment and

ripples may enhance water exchange at the bed/water column interface.

In an alluvial river water may exchange between the river and pore

space of the alluvium (Bencala et al. 1984) and this water exchange may

transport fine sediments by advection to and from the relatively coarse

alluvium (Jobson and Carey 1989). Thus, advection may be an important

transport process at the bed/water interface for fine, noncohesive

sediments in an alluvial channel. For oscillatory flows over porous

beds in coastal environments, the total water exchange across the

bed/water column interface averaged over the wave period is

significantly greater for rippled beds than for flat beds (Shum 1992).

Benthic biological communities may influence sediment-transport

processes, especially in biologically abundant estuaries. Erosion

rates may be decreased by microbial films and benthic algae that

stabilize sandy sediments (Gabrielson and Lukatelich 1985, Grant et al.

1986, Meadows et al. 1990) and cohesive sediments (Montague 1986).

Tracks made by motile bivalves, however, reduced the critical shear

velocity of fine sandy sediments in a laboratory flume by 20 percent

(Nowell et al. 1981). Fecal mounds from polychaetes and a deposit-

feeding bivalve in a laboratory flume had a higher critical shear

velocity than ambient cohesionless sediments and were transported as

bed load (Nowell et al. 1981). Sediments that have been bound by

secretions from benthic invertebrates may settle more slowly than

unbound particles when resuspended (Meadows et al. 1990). Seagrasses

reduce bottom orbital velocities of wind-waves and thus reduce erosion

and increase deposition (Ward et al. 1984). Biological effects

frequently are ignored in sediment-transport studies because biological









activity is difficult to quantify in the field, difficult to reproduce

in a laboratory, and difficult to incorporate into a numerical model.

Field Studies Related to Estuarine Sediment Transport

Field studies of estuarine sediment transport are often conducted

to determine the mechanisms that control sediment transport processes,

such as resuspension and horizontal transport. Data is collected by in

situ instrumentation, water sample collection and analysis, and/or

bottom sediment sampling and observation. Statistical analysis, time

series analysis, and numerical process models are used to analyze the

data. Field studies provide less control than laboratory studies, but

they are more applicable because of the difficulty recreating natural

conditions in the laboratory. For numerical studies, an initial or

concurrent field study may indicate the processes that must be included

in the numerical model in order to accurately simulate sediment

transport and a field study will provide data for calibration and

validation of the numerical model. Sediment resuspension mechanisms

are often the focus of estuarine field studies because the bottom of

the estuary is an omnipresent potential source of suspended sediment

and many potential sediment resuspension mechanisms are present in the

estuarine environment. The potential sediment resuspension mechanisms

include tidal currents, wind waves, wave/current interactions, seiches,

trawling, and vessel traffic. Many of these potential mechanisms are

also present on the continental shelf and in large lakes, so some

relevant field studies in these environments will also be mentioned in

this section.

The mean current in estuaries and on the continental shelf may

resuspend bottom sediments. Wimbush and Lesht (1979) deployed a tripod

with current meters and a bottom camera at a site with a bottom









sediment of medium sands in the deep (710 meters) Florida Straits and

estimated the critical velocity for ripple formation. Lavelle et al.

(1984) deployed a current meter and transmissometer 5 meters above a

fine sediment bottom in 200 meters of water in Puget Sound. They

observed that tidal currents resuspended bottom sediments and that the

erosion rate could be described with the shear stress power law given

by equation 1-4. Both of these studies were conducted in deep water

where wave motion was not observed. Bohlen (1987) deployed an

instrument array that included an electromagnetic current meter and

transmissometers for monitoring suspended-solids concentrations in 12

meters of water in Chesapeake Bay. Spectral analysis of the suspended-

solids concentration showed variation at tidal frequencies, including a

spring/neap variation. Roman and Tenore (1978) collected and analyzed

water samples over several tidal cycles in Buzzards Bay, Massachusetts,

and observed resuspension of organic carbon and chlorophyll-a at a site

with a muddy bottom in 13 meters of water by tidal currents that was

significant enough to potentially affect estuarine productivity. They

did not address resuspension by wind waves, possibly because the data

may contain a fair weather bias due to the manual collection of water

samples and the lack of in situ instrumentation. Costa and Mehta

(1990) observed resuspension by tidal currents in Hangshou Bay, China,

a high energy tidal environment.

Wind waves may resuspend bottom sediments in relatively shallow

water. Anderson (1972) collected water samples in a tidal lagoon with

fine sediments and found that wave heights of only a few centimeters

resuspended bottom sediments in water depths of 40 to 150 cm. Water

samples and sediment traps were used by Ward et al. (1984) to determine

that shallow water sites (less than 2 meters) in Chesapeake Bay with









seagrasses attenuate wave motion and reduce resuspension compared to

sites without seagrasses. Gabrielson and Lukatelich (1985) found that

sedimentation rates calculated from sediment traps deployed in the

Peel-Harvey estuarine system were temporally correlated with the

strength and duration of wind events and spatially correlated with wind

direction and fetch. Kenney (1985) deployed sediment traps in Lake

Manitoba at a depth of 4.2 meters and found that resuspension of bottom

sediments during wind events stratified the water column. Lavelle et

al. (1978) deployed a current meter and turbidimeter 1 meter above the

medium sand bed of Long Island Sound at an average depth of 10.5

meters. Wind waves during a storm resuspended bottom sediments and

tidal currents did not cause resuspension. An empirical relationship

between suspended sediment concentration and wave orbital velocity in

Long Island Sound was developed by Lesht et al. (1980). In addition to

resuspension by tidal currents in Chesapeake Bay discussed previously,

root-mean-squared velocity fluctuations and suspended-solids

concentrations increased when the wind was blowing up the longitudinal

axis of Chesapeake Bay (Bohlen 1987). Davies (1985) deployed a

tetrahedra containing electromagnetic current meters and a video camera

in 4 to 10 meters of water in Start Bay, England, and found that the

observed threshold of sediment motion in oscillatory flow was in good

agreement with Shields diagram (fig. 1-1). Sheng et al. (1990b)

collected synoptic suspended sediment data and deployed anemometers,

pressure transducers, electromagnetic current meters, and optical

backscatterance suspended-solids sensors from several platforms and

piles over two one-month periods in Lake Okeechobee, Florida. It was

found that wind waves associated with the diurnal lake breeze

resuspended fine sediments and this field data were used to calibrate









and validate three-dimensional and vertical one-dimensional numerical

sediment transport models (Sheng et al. 1990b, Sheng et al. 1992).

Mehta (1991) also collected data and applied a vertical one-dimensional

model to study fluid-mud and sediment resuspension by wind waves in

Lake Okeechobee. Perjup (1986) deployed an instrument tower in about 2

meters of water in the Ho Bugt estuary, Denmark, from which water

velocity, suspended-solids concentration, salinity, depth, wind speed,

and wind direction were measured. Perjup found that the suspended-

solids concentration did not correlate with mean water velocity but was

correlated to parameters containing wind speed and onshore wind

direction and inversely correlated with salinity, which was well-

correlated with water depth. These results indicate that resuspension

was caused by onshore wind waves, especially at low tide when the near-

bed orbital wave motion can be greatest.

As mentioned previously, the nonlinear interaction of waves and

current can significantly increase the bottom shear stress and thus it

may be an important sediment resuspension mechanism. Drake and

Cacchione (1986) used data from Norton Sound, Alaska, and the northern

California continental shelf to calculate the grain shear stress with a

modified version of the fixed bed wave/current interaction model of

Grant and Madsen (1979). The observed resuspension threshold was in

good agreement with Shield's diagram (fig. 1-1). Cacchione et al.

(1987) and Drake et al. (1992) compared field data collected on the

northern California continental shelf (water depth 85 meters) and

results of the moveable bed wave/current interaction model of Grant and

Madsen (1982) and found good agreement for bottom shear stress but not

bed form geometry. The high bottom stresses caused by wave/current

interaction during winter storms were a major factor controlling the









distribution of surficial sediment on the northern California

continental shelf. Measurements were made with a tripod containing

electromagnetic current meters, a pressure transducer, a nephelometer

(for measuring light scattering which can be calibrated to suspended

solids), and a camera (Cacchione and Drake 1979).

Estuaries contain abundant fisheries and they are convenient sites

for ports, so trawling and commercial vessels are potential sediment

resuspension mechanisms. Churchill (1989) reviewed several sets of

hydrodynamic and sediment data from the middle Atlantic Bight and

determined that sediment resuspension by trawling is a significant

source of suspended sediments. Schoellhamer (1991b) found that during

the departure and arrival of a cruise ship at the Port of St.

Petersburg the suspended-solids concentration increased almost an order

of magnitude due to the maneuvering of the vessel. The resuspended

sediments settled within 1 to 2 hours once the cruise ship either

docked or departed.

In partially-mixed and well-mixed estuaries, the maximum

suspended-solids concentration is often present in brackish waters and

is greater than concentrations found elsewhere in the estuary (Uncles

and Stephens 1989). This feature is called a turbidity maximum and

field data collection programs and numerical models have been used to

determine the controlling mechanisms. Uncles and Stephens (1989)

collected water samples and data from an optical suspended-solids

sensor to measure salinity and suspended-solids concentrations during

twice monthly sampling trips that proceeded up the Tamar estuary,

England. These data were used with a longitudinal one-dimensional

model to determine that the location of the turbidity maximum is

associated with the location of the freshwater/saltwater interface and









that local resuspension, and perhaps gravitational circulation and

stratification, determined suspended-solids concentrations in the

turbidity maximum. West and Oduyemi (1989) deployed electromagnetic

current meters and suspended-solids sensors on a bed frame in the Tamar

estuary and observed that near-bed stratification by suspended sediment

reduced the turbulence intensity. Hamblin (1989) collected vertical

profiles of velocity, salinity, and suspended-solids concentrations

from a vessel anchored at several stations near the turbidity maximum

in the upper Saint Lawrence estuary. These data showed that local

resuspension by the mean current controlled the suspended-solids

concentrations at the measurement sites and that a landward flux of

sediment near the bed is maintained by ebb-flood asymmetry and a

reduction in vertical mixing during flood tide caused by the salt

wedge. A vertical one-dimensional sediment transport model was

developed with these data. Grabemann and Krause (1989) analyzed time

series of long-term salinity, current meter, and optical transmittance

sensor data collected in the Weser River estuary to determine that

tidally controlled resuspension and deposition is the dominant process

in the turbidity maximum and that gravitational circulation is a long-

term source and sink of particles. An intensive two-week experiment on

the Weser River estuary included the deployment of instrumentation to

measure velocity, salinity, and suspended-solids concentration at

several locations and similar measurements were taken from vessels

(Lang et al. 1989). These data showed that there was a close

relationship between suspended-sediment concentration and near-bed

velocity gradient and stratification and the data was used to develop a

three-dimensional numerical model.









Most of the field studies discussed so far have focused on tidal

transport processes and vertical sediment transport processes, but

field studies have also been conducted to quantify subtidal horizontal

sediment transport. Powell et al. (1989) collected water samples in

South San Francisco Bay and observed that during spring runoff fresh

water and suspended sediment from the Sacramento River entered South

San Francisco Bay. Wells and Kim (1991) used vibracores, surficial

sediment data, and vertical profiles of velocity, salinity, and

suspended sediment concentration collected during monthly sampling

trips from several sites in the Neuse River estuary, North Carolina, to

describe long-term sedimentation patterns. In Puget Sound, Baker

(1984) collected suspended-solids concentration data with a

transmissometer at several sites during several sampling trips to help

determine that gravitational circulation and surface and bottom sources

of particles control the distribution and transport of suspended

solids.

Sample collection for the preceding studies was generally

performed by collecting water samples and/or collecting pressure,

velocity, and suspended solids concentration data from conventional

sensors. Alternative methods of data collection have been utilized to

collect data on estuarine sediment transport processes. Rubin and

McCulloch (1979) used side scan sonar to determine the shape of

bedforms in central San Francisco Bay, which indicate near-bed

circulation patterns and sediment transport directions. Bedford et al.

(1987) used an acoustic transceiver to sample the sediment

concentration in 1 cm bins in the bottom 70 cm of the water column over

a 3.5 hour period and a tidal cycle at a site in Long Island Sound.

This device provides much better resolution of the near bed sediment









concentration profile than is available from optical instrumentation,

but calibration is difficult due to sensitivity to the particle size

distribution. Resuspension fluxes were calculated and were found to be

best correlated with the squared velocity fluctuation (horizontal and

vertical) due to wind waves and turbulence about the mean velocity.

Portable flumes that are deployed on the bottom of the estuary have

been used to study the erosion of in situ sediments under controlled

conditions. For example, Young and Southard (1978) deployed a sea

floor flume in Buzzards Bay, Massachusetts, and observed that the in

situ critical shear velocity was one-half the value found in laboratory

experiments due to bioturbation. Laboratory and sea flume values for

the critical shear velocity also differed in Puget Sound (Gust and

Morris 1989). To estimate the residence time of fine particles

introduced at the water surface in Puget Sound (11-16 days), Lavelle et

al. (1991) used vertical profiles of radioactive isotope activities and

a sorption model.

Due to practical limitations, it is very difficult to collect

synoptic samples throughout a large water body by conventional means,

but remote sensing from aircraft and satellites can be used to

synoptically determine suspended-solids concentrations near the water

surface in large water bodies. The advantage of remote sensing is that

a measurement of an entire estuary can be made instantly but the

disadvantages are that remote measurements must be calibrated with

suspended-solids concentrations, sampling times and locations are

limited by the satellite orbit, clouds and other weather may degrade or

prevent satellite observation, and resolution may be limited. Sheng

and Lick (1979) used remote-sensing data and field data to produce the

near-surface suspended-sediment concentrations in the western basin of









Lake Erie, which were then used to provide initial conditions and

validation for a numerical sediment transport model of Lake Erie. Huh

et al. (1991) used remote sensing to help determine that storms 1)

produce landward sediment transport along coastal Louisiana and 2) help

build marshes. In Mobile Bay, remote sensing has shown rapid changes

in sediment concentrations due to high river inflow and wind-induced

sediment resuspension (Stumpf 1991).

Numerical Models Applicable to Estuarine Sediment Transport

Numerical models can be used to simulate or predict estuarine

sediment transport, resuspension events, sedimentation rates, adsorbed

constituent transport, and light availability. Transport processes are

dependent upon hydrodynamics, so sediment transport models require an

accurate hydrodynamic model. Deposition, erosion, and density

stratification caused by suspended sediments may affect the

hydrodynamics, so a coupled hydrodynamic and sediment transport model

may be required. Many numerical models of suspended sediment transport

have been developed for steady riverine flows (for example van Rijn

1986a, Celik and Rodi 1988, Schoellhamer 1988), but they are not

applicable to estuaries because of the unsteady motions of tidal waves,

seiches, and wind waves. Some riverine models are stochastic or random

walk models that use Lagrangian particles to represent suspended

sediment (Alonso 1981, Bechteler and Farber 1985). The random walk

approach may be applicable to estuarine sediment transport. Mehta et

al. (1989b) reviewed estuarine applications of primarily cohesive

sediment transport models, and they discussed simulation of the bed and

zero-, one-, two-, and three-dimensional models. A similar outline

will be followed herein. Some estuarine sediment transport processes

are also present on the continental shelf and in large lakes, so some









relevant numerical models for these environments will also be discussed

in this section.

The properties of the sediment bed may vary with time and depth

below the interface with the water column, especially for cohesive

sediments. Bed properties such as density and shear strength may vary

with distance below the top of the sediment bed, the elevation of which

may vary during a tidal cycle. In order for a numerical sediment

transport model to account for these temporal and spatial variations,

the bed could be divided into layers with different properties, and

new layers could be added during deposition and existing layers could

be removed by erosion. Properties such as layer density, thickness,

and shear strength can vary temporally and spatially in the simulated

estuarine bed (Thomas and McAnally 1985, Hayter 1986, Sheng 1991).

If the spatial variation of suspended-sediment concentration can

be ignored, then only the temporal variation of suspended-sediment

concentrations needs to be considered. This type of modeling is

referred to as zero-dimensional and is equivalent to assuming that the

study area is well-mixed. Krone (1985) used a zero-dimensional model

to simulate and predict deposition in a marsh. Amos and Tee (1989)

simulated the Cumberland Basin in the Bay of Fundy as a well-mixed

water body in order to calculate sediment fluxes at the mouth of the

Basin. Because the distribution of sediment sources in an estuary is

likely to be nonuniform and because the settling property of sediment

increases concentrations deeper in the water column, the assumption

that the spatial variation of suspended sediment is negligible is

generally poor.

The longitudinal variation of suspended sediment in an estuary can

be simulated with horizontal one-dimensional models. Cross sectional









variations are averaged transversely and vertically, so if the

suspended-sediment concentration varies significantly in the cross

section, one-dimensional model may not be applicable. Uncles and

Stephens (1989) used a longitudinal one-dimensional model to describe

the magnitude and location of the turbidity maximum in the Tamar

estuary. Equations 1-3 and 1-19 were used to simulate deposition and

erosion and the coefficients in the equations were selected by

calibration with measured suspended-sediment concentrations. Hayter et

al. (1985) predicted shoaling rates in the Hooghly River estuary,

India, with a longitudinal one-dimensional model that was calibrated

with measured channel dredged material volumes.

The vertical profile of suspended sediment at a given location in

an estuary can be simulated with a vertical one-dimensional model.

These models are applicable when horizontal gradients of suspended-

sediment concentration can be neglected. Weisman et al. (1987)

simulated a depositional tidal lagoon with a series of vertical layers

for which vertical dispersion was neglected and the simulated shoaling

rate was reasonable compared to shoaling rates estimated with

radioactive isotopes. Teeter (1986) developed a vertical transport

model that uses a Richardson number dependent parabolic eddy

diffusivity to include the effect of density stratification. Hamblin

(1989) used this model to simulate vertical mixing of suspended

sediment at a site in the upper St. Lawrence estuary were suspended-

sediment concentrations were observed to depend upon local

resuspension. Field data were used to determine the erosion function

and particle settling velocity. Costa and Mehta (1990) also applied a

Richardson number dependent model to simulate vertical sediment

transport in Hangzhou Bay, China. Steady state vertical profiles of









near-bed suspended sediment in the Florida Straits were estimated with

a model by Adams and Weatherly (1981) that used three sediment size

classes. Velocity data but no suspended-sediment concentration data

were collected to calibrate the model. Sheng and Villaret (1989) used a

vertical one-dimensional model (OCMlD, which is presented in detail and

utilized later) with a simplified second-order turbulence closure model

to determine vertical profiles of velocity and suspended-sediment

concentration and the erosion rate of bottom sediments for laboratory

experiments. They found that near-bed stratification by high

suspended-sediment concentrations reduces turbulence intensity and

erosion rates. The same basic model was used to determine erosion

rates of sediments from measured suspended-sediment concentrations from

Lake Okeechobee and was successfully applied to simulate the dynamics

of the vertical structure of suspended-sediment concentration over

several 3-day and 1-week periods (Sheng et al. 1990b, Sheng 1991, Sheng

et al. 1992).

Vertical hydrodynamic models have also been developed for

estuarine applications. OCM1D has been used to simulate storm-induced

currents in Grand Bank (Sheng 1986b) and in the Atlantic Ocean during

the passage of hurricane Josephine (Sheng and Chiu 1986). Davies et

al. (1988) used a one-dimensional vertical hydrodynamic model to

simulate the interaction of waves and a mean current. This model

achieves turbulence closure with a dynamic equation for turbulence

energy and turbulence scaling relations for the mixing length and eddy

viscosity, but results were not compared to data. A vertical

hydrodynamic model with complete second order turbulence closure model

(i.e., Reynolds stress model) was used by Sheng (1984) to simulate the









development and evolution of the logarithmic wave boundary layer for

laboratory and field data.

The horizontal transport of sediment in an estuary has been

simulated with depth-averaged two-dimensional models. Ariathurai and

Krone (1976) developed a two-dimensional finite element model for

simulating cohesive sediment transport in estuaries. Erosion and

deposition were simulated with equations 1-3 and 1-19. This model is

included in the U.S. Army Corps of Engineers TABS-2 modeling system for

estuarine hydrodynamics and sedimentation (Thomas and McAnally 1985)

which has been applied to several estuaries (Heltzel 1985, Granat 1987,

Hauck 1991). Heltzel (1985) and Granat (1987) used physical model

results for the simulated hydrodynamic boundary conditions and the

validation of simulated hydrodynamics and measured shoaling rates

(instead of measured suspended-sediment concentrations) were used to

calibrate sediment simulations. For San Francisco Bay (Hauck 1991),

hydrodynamic simulations were in agreement with measured data but

sediment simulations did not successfully reproduce field data,

possibly because simulated settling velocities for cohesive sediment

were not dependent upon the concentration, poor simulation of wave

action and related shear stress, and only one grain size for cohesive

sediments was simulated.

Depth-averaging may not be appropriate for estuarine hydrodynamic

and sediment transport models. Density stratification and

gravitational circulation are three-dimensional flow features in

estuaries that can not be simulated by a depth-averaged model.

Sediment resuspension may be dependent upon the bottom shear stress but

depth-averaged models do not calculate the vertical velocity profile

and therefore empirical relations must be used to calculate the bottom









shear stress instead of equation 1-5. Because of the settling property

of sediment, sediment concentrations are usually much higher near the

bed than up in the water column, so depth-averaging may not be

appropriate. For example, in an open channel, the near-bed region

contains the largest suspended-sediment concentrations but the smallest

velocities, so the depth-averaged longitudinal velocity of suspended

sediment is less than the depth-averaged water velocity (Schoellhamer

1986). Downing et al. (1985) combined an analytic vertical one-

dimensional sediment model with linear eddy viscosity and diffusivity,

the Grant and Madsen (1979) wave-current model, and a horizontal two-

dimensional sediment transport model and obtained reasonable simulation

results based on a comparison with field data from the Sagavonirktok

River Delta in Alaska.

Three-dimensional models permit vertical discretization for

simulation of vertical suspended sediment profiles and density

stratification in addition to vertically variable horizontal transport

by tidal currents, wind-induced circulation, and gravitational

circulation. Sheng and Lick (1979) used vertical two- and three-

dimensional circulation and sediment transport models and a wave-

hindcasting model, in addition to remote-sensing data, to simulate

wind-wave sediment resuspension and transport in Lake Erie. Laboratory

experiments were used to determine settling velocity, critical shear

stress, and erosion rates which were a bilinear function of the excess

shear stress. Wang et al. (1987) used a three-dimensional hydrodynamic

and sediment transport model to simulate sediment transport in Kachemak

Bay, Alaska, but field data were not included in the study. A three-

dimensional hydrodynamic and sediment transport model of the turbidity

maximum in the Weser estuary, Germany, by Lang et al. (1989) was able









to reproduce some of the features present in measured suspended-

sediment concentrations. Hayter and Pakala (1989) applied a three-

dimensional model of estuarine hydrodynamics, sediment transport, and

contaminant transport to the Sampit River in South Carolina but field

data was not available to validate the model. Sheng (1991) and Sheng

et al. (1992) collected field data and successfully applied a three-

dimensional model of hydrodynamics, fine sediment transport, and

contaminant transport to study phosphorus dynamics in Lake Okeechobee,

Florida. A preliminary simulation of three-dimensional sediment

transport in Tampa Bay was performed by Sheng et al. (1992).

Relation of this Research to Previous Studies

The purpose of this research was to improve the understanding and

numerical modeling of sediment resuspension and the vertical transport

of resuspended sediment in the shallow estuarine environment and this

was accomplished by combining three important elements of previous

studies that have not been previously combined. These three elements

are: 1) resuspension by wind-waves in a shallow estuary, 2) field

measurements of suspended-sediment concentrations, and 3) a vertical

sediment transport model. Estuarine sediments and their transport are

important because they may reduce the amount of light penetrating the

water column, may act as a source for adsorbed constituents, and may be

transported to undesirable locations. Estuaries are also biologically

active, and this activity may affect sediment transport. Wind waves

are an important resuspension mechanism in many estuaries (table 1-1),

and they are shown to be an important resuspension mechanism in Old

Tampa Bay in chapter 3. Field measurements of sediment concentrations

are needed to understand estuarine sediment transport processes and to

develop accurate numerical models. Resuspension from the bed and









Table 1-1, Previous studies that are related to this research and
include an estuarine environment, wind waves, field measurements of
suspended-sediment concentrations, or a numerical vertical sediment
transport model.


Estuarine Wind Field Vertical
Environment waves cone. sed. model

Adams and Weatherly (1981) N N N Y
Amos and Tee (1989) Y N Y N
Anderson (1972) Y Y Y N
Baker (1984) Y N Y N
Bedford et al. (1987) Y N Y N
Bohlen (1987) Y N Y N
Cacchione et al. (1987) N Y Y N
Churchill (1989) N N Y N
Costa and Mehta (1990) Y N Y Y
Davies (1985) Y Y N N
Davies et al. (1988) Y Y N N
Downing et al. (1985) Y Y Y N
Drake and Cacchione (1986) N Y Y N
Drake et al. (1992) N Y Y N
Gabrielson and Lukatelich (1985) Y Y N N
Hamblin (1989) Y N Y Y
Hauck (1991) Y Y Y N
Hayter and Pakala (1989) Y N N Y
Kenney (1985) N Y N N
Lang et al. (1989) Y N Y Y
Lavelle et al. (1978) Y Y Y N
Lavelle et al. (1984) Y N Y N
Lavelle et al. (1991) Y N Y Y
Lesht et al. (1980) Y Y Y N
Mehta (1991) N Y Y Y
Perjup (1986) Y Y Y N
Powell et al. (1989) Y N Y N
Roman and Tenore (1978) Y N Y N
Schoellhamer (1991b) Y N Y N
Sheng (1991) N Y Y Y
Sheng and Lick (1979) N Y Y Y
Sheng and Villaret (1989) N N N Y
Sheng et al. (1990b) N Y Y Y
Sheng et al. (1992) N Y Y Y
Stumpf (1991) Y Y N N
Teeter (1986) N N N Y
Uncles and Stephens (1989) Y N Y N
Wang et al. (1987) Y N N Y
Ward et al. (1984) Y Y Y N
Weisman et al. (1987) Y N N Y
Wells and Kim (1991) Y N Y N
West and Oduyemi (1989) Y N Y N









settling of suspended sediment exemplify the importance of simulating

the vertical axis in a numerical sediment transport model.

None of the field and numerical model studies described previously

include estuarine wind-wave resuspension, field measurements of

suspended-sediment concentration, and a vertical sediment transport

model (table 1-1). Studies that include almost all of the elements

include those by Hamblin (1989), Costa and Mehta (1990), Sheng et al.

(1990b), Mehta (1991), and Sheng et al. (1992). Hamblin studied

resuspension by tidal currents near a turbidity maximum, Costa and

Mehta studied resuspension by tidal currents in a high tidal energy

environment, and Mehta and Sheng and his colleagues studied sediment

transport in a large shallow lake. This research used field

measurements of suspended-sediment concentration and a vertical

sediment transport model to study sediment resuspension by wind waves

in an estuary. The numerical model was used as a tool to help analyze

the Old Tampa Bay data and to help determine significant sediment

transport processes in Old Tampa Bay.















CHAPTER 2
SEDIMENT RESUSPENSION DATA COLLECTION METHODOLOGY

In 1987, the U.S. Geological Survey began a study to determine the

effect of fine sediment resuspension on light attenuation in Tampa Bay

and to determine the mechanisms that cause resuspension of fine

sediments. Light attenuation in the waters of Tampa Bay may adversely

affect benthic organisms, seagrasses, and fish and other marine

communities that are dependent upon the seagrasses. Resuspension of

sediment on the bottom of the bay may contribute to light attenuation,

and the mechanisms that cause sediment resuspension in Tampa Bay had

not previously been studied. The author was the project chief for the

study and his duties included project administration, project planning,

data collection, data analysis, presentation of project results at

meetings, and report preparation.

During the U.S. Geological Survey study, pressure, water velocity,

and suspended-solids concentration data were collected in Old Tampa

Bay, a subembayment of Tampa Bay, in order to observe sediment

resuspension events and to determine the hydrodynamic mechanisms that

cause sediment resuspension. In this research, sediment resuspension

data collected from Old Tampa Bay were simulated with a numerical model

of vertical one-dimensional hydrodynamics and sediment transport, and

the model results were analyzed.

Study Area

Tampa Bay is located on the west-central coast of Florida as shown

in figure 2-1. The estuary is Y-shaped, really large (about 1000
























































Figure 2-1, Old Tampa Bay study area.









km2), shallow (average depth 3.6 meters), vertically well-mixed,

microtidal (spring tide range about 1 meter), and warm (temperature

range from about 14 to 31 C in 1988 and 1989) (Goodwin 1987, Boler

1990). The northwest subembayment is called Old Tampa Bay and the

northeast subembayment is called Hillsborough Bay. These subembayments

are of most concern ecologically because seagrass loss is more common

and water-quality is probably more impacted by point and non-point

nutrient loading and by reduced tidal flushing (Lewis et al. 1985,

Goodwin 1987). The cities of Tampa, St. Petersburg, and Clearwater are

adjacent to the bay. The subtropical weather includes almost daily

thunderstorms during the summer, occasional storms from winter cold

fronts, and the possibility of tropical storms primarily during the

fall. The river inflow is small compared to the volume of the bay, and

the riverine flushing time, the bay volume divided by the combined

river discharge, is about 2 years (Goodwin 1987). Bottom sediments in

Old Tampa Bay are generally silty very fine sands in the deeper water

(4 meters) and fine sands in shallow water (less than 2 meters) near

the shoreline. Goodell and Gorsline (1961) found clay minerals only in

isolated portions of Old Tampa Bay, and the sedimentology has not

changed significantly since their study (Schoellhamer 1991a).

Sediment Resuspension Monitoring Sites

State variables in an estuary, such as water velocity, salinity,

and suspended-solids concentration, vary spatially and temporally.

Unfortunately, it is neither technically or economically feasible to

obtain complete spatial and temporal coverage when measuring these

variables, so a limited data collection network must be designed that

is representative of a large portion of the estuary. Therefore,

representative sites for resuspension monitoring were selected.









The most important site selection criterion was that a potential

site be at the center of a large area of homogeneous sediment. A

potential problem with monitoring sediment resuspension at one site is

the possibility that horizontal advection may transport suspended

sediment to the site and the resulting increase in suspended-solids

concentration may be mistaken for local resuspension. Selection of a

site in the center of a large homogeneous area of bed sediments reduces

the possibility that more erodible sediments will be transported to the

site and insures that the site is representative of a large fraction of

the bay bottom. Careful data analysis is required to identify the

source of an increase in suspended-solids concentration, and specific

data are discussed in chapter 3. Other criteria were 1) nearly uniform

residual currents over the homogeneous sediment bed, based upon a

depth-averaged two-dimensional barotropic hydrodynamic model by Goodwin

(1987), 2) site location far from ship channels for safety and

homogeneity of bottom sediments and currents, and 3) a secluded

location to reduce vandalism.

The size classification of the bottom sediments in upper Tampa Bay

(north of a line that extends approximately east from St. Petersburg)

were determined with a fathometer and grab samples in 1987 and 1988

(Schoellhamer 1991a). Finer sediments, which are more easily

suspended, are generally found in the deeper parts of the bay. The

fine inorganic bed sediments are commonly in the form of fecal pellets

and organically bound aggregates (Ross 1975). Coarser sediments found

closer to shore in shallower water may experience more wave activity,

however, and also are likely to be resuspended. Thus, selection of a

deeper site with finer sediments and a shallow site with coarser

sediments in Old Tampa Bay was desired.









In Old Tampa Bay, typical deep- and shallow- water sediment

resuspension monitoring sites were selected. A deep-water site

(average depth about 4 meters) was located in the approximate center of

a large area of silty-fine sand at latitude 27"57'01" N and longitude

82*37'55" W. The particle size distribution at this site is shown in

figure 2-2, and it has changed little from the 1950's to the 1980's

(Goodell and Gorsline 1961, Taylor and Saloman 1969, Schoellhamer

1991a). The mean particle diameter is 127 pm, and 16% of the material

is fine material (particle diameter less than 63 um). The density of

the bottom sediments is 2.68 g/cm3 and 2.7%, by weight, of the bottom

sediments are organic. A shallow-water site (average depth about 2

meters) was selected 3.0 km south-southwest of the deep-water site in

an area of fine sands on the estuarine shoal at latitude 27*55'30" N

and longitude 82*38'33" W. The mean particle diameter is 152 pm, and

the material is 1.5% fine sediment. A submersible instrument package

was used to collect hydrodynamic and sediment resuspension data at the

shallow-water site (Schoellhamer 1990), but only a single point

velocity was measured so the bottom roughness could not be determined.

Therefore, the data collected at the shallow-water site is not well-

suited for numerical modeling and only data collected at the platform

were utilized in this research.

Old Tampa Bay Instrumentation Platform

In June 1988, a platform was constructed at the Old Tampa Bay

deep-water site in order to support sediment resuspension monitoring

instrumentation (fig. 2-3). The platform consists of three vertical

pilings that are the apexes of a 3.7 m equilateral triangle

(Schoellhamer 1990, Levesque and Schoellhamer in press). The pilings

support a triangular galvanized expanded-steel deck approximately 2
































Z
I-
z
LLI
aC,
S40


0 I t i I II Il 1I I I I I I 1I
1000 100 10


GRAIN DIAMETER, IN MICRONS











Figure 2-2, Size distribution of bottom sediment at the Old Tampa Bay
platform.





























































Figure 2-3, Old Tampa Bay platform (Levesque and Schoellhamer,
manuscript in review).









meters (average) above the water surface. Water column instrument

sensors were mounted on movable horizontal aluminum arms that were 61-

cm-long and extended perpendicular to a vertical 610-cm-long, 10-cm-

diameter aluminum pipe that was fixed to the center of the steel deck.

The entire pipe structure resembled an inverted tree.

Several types of sensors were deployed from the platform. A

biaxial electromagnetic current meter was mounted at the end of each

horizontal arm, and an optical backscatterance (OBS) suspended-solids

sensor was mounted at the midpoint of each arm. In addition to a

current meter and an OBS sensor, one of the horizontal arms also

supported a pressure transducer for measuring water depth and wave

activity. Wind velocity was measured with a cup anemometer and a wind

vane that were mounted at the top of one platform pile, located about 3

meters above the steel deck. The sensor electronics, data recorder,

and associated power supplies were housed in an aluminum shelter

mounted at one corner of the steel deck. An underwater camera for

taking bottom photographs was not deployed because visibility was

usually insufficient, especially during resuspension events.

Resuspension monitoring instrumentation consisted of Marsh

McBirney Model 512 biaxial electromagnetic current meters, Downing and

Associates Instruments Model OBS-1P backscatterance sensors, and two

types of pressure transducers. The biaxial current meters have a 5.1-

cm-diameter sphere attached very near the end of a 20.3-cm-long metal

rod. The biaxial electromagnetic current meters measure water velocity

using the Faraday principle of electromagnetic induction, where a

conductor (water) moving in a magnetic field (induced by the current

sensor) produces a voltage that is proportional to the water velocity.

The OBS sensors are thumb-size, and they have an optical window at the









relative position of the thumbnail (Downing et al. 1981, Downing 1983).

The optical window is used to transmit an infrared pulse of light that

scatters or reflects off particles in the water up to a distance of

about 10 to 20 cm at angles up to 140' in front of the window. Some of

this scattered or reflected light returns to the optical window where a

receiver converts the backscattered light to an output voltage. For

well-sorted suspended material, the output voltage is proportional to

the suspended-solids concentration and turbidity in the water column.

The calibration of the OBS output to suspended-solids concentration

varies depending on the size and optical properties of the suspended

solids, so the OBS sensors must be calibrated either in the field or in

a laboratory with the same suspended material as is found in the field.

A laboratory evaluation by Ludwig and Hanes (1990) concluded that

instrument response to suspended mud was linear up to a concentration

of 3,000 to 4,000 mg/L, and they recommended that OBS sensors not be

used for the measurement of suspended sand in areas that concurrently

experience suspended mud. Originally, a Geokon vibrating-wire pressure

transducer was used at the platform-site and was eventually replaced

with a Druck strain-gage transducer for improved reliability and

increased sensitivity. Data acquisition, data storage, and sensor

timing were controlled by a Campbell Scientific CR10 data logger. A 5-

minute burst sample of the current meter outputs, OBS sensor outputs,

and the pressure transducer output was collected every hour during

deployments at the platform-site. The burst sample consisted of 1-

second data of all sensor outputs for the duration of the 5-minute

sampling interval. The burst sample was temporarily stored in the data

logger and following the end of the burst sample collection the data

was sent to an external data storage module.









The instruments were submerged continuously when initially

deployed in August 1988. Data was transmitted from the platform in Old

Tampa Bay to the U.S. Geological Survey office in Tampa by a modem and

a cellular phone. Every night, the platform data logger would turn on

a cellular telephone. At the same time, a shore-based personal

computer would automatically call the cellular phone through a modem,

establish communications with the data logger through a modem on the

platform, and issue commands for the data logger to transmit data that

were then stored by the shore-based personal computer. Approximately 2

hours were required to transmit data from 24 burst samples.

Transmission time and power requirements of the cellular phone required

the connection of a deep-cycle 12 volt battery to the solar panel on

the platform, which was accomplished in mid-October 1988. If the

weather conditions were poor during data transmission, the transmission

would fail and cause a loss of data. Both the platform and shore-based

modems used an error checking protocol to help insure accurate data

transmission.

In October 1988, analyses of the available data indicated that the

OBS sensors had fouled, and when the sensors were cleaned by SCUBA

equipped divers, large amounts of marine growth were observed on all of

the sensors. The output from the OBS sensors began to increase as the

sensors fouled, usually about 24 to 48 hours after cleaning, and the

current meters fouled in about seven days. The OBS sensors were coated

with an antifoulant for optical surfaces (Spinard 1987) that only

prevented barnacle growth on the optical surface. The cause of the

fouling was probably an algal slime that would grow on the face of the

sensors and affect their optical properties. In late 1988, when the

instruments were submerged continuously, cleaning dives were conducted









about every two weeks. Therefore, the OBS sensors were fouled most of

the time, and only data collected within 24 to 48 hours of cleaning

were reliable.

The sensor fouling caused by the continuously submerged system

proved to be impractical, and a modification was required, so the

vertical pipe that supported the instruments was attached to an A-frame

and pulley system in December 1988. The vertical pipe was suspended

from an A-frame steel-pipe structure secured to the steel deck that

allowed the vertical pipe to be raised above the water surface for

sensor cleaning and storage. Daily servicing visits to clean the

sensors were usually made when the sensors were deployed, so the

cellular phone and modem were removed from the platform and the data

storage module was exchanged daily during the servicing visits.

Flow around the platform pilings is a potential cause of sediment

resuspension that could affect suspended-solids concentrations at the

platform, so several steps were taken to reduce this possibility and to

determine that any local scour caused by the platform did not

significantly affect concentrations at the platform. Barnacles were

removed from the platform pilings on February 22, 1990, to reduce their

effect on the flow. Scour holes were not observed by divers at the

bases of the pilings, possibly due to bioturbation. The bottom of the

aluminum pipe that supported the instruments was about 20 cm above the

bed to reduce the possibility that it would cause local scour. Four

sets of water samples collected at the platform and 750 and 1500 meters

south-southwest of the platform on November 30, 1989, July 13, 1990,

October 12, 1990, and November 30, 1990, indicate that the average

concentration of suspended-solids at the platform was 6.9 mg/L greater

than the other sites. In March 1990, however, two water samples were









collected at the platform at the same time on 8 different occasions,

and the average concentration difference between concurrently collected

sample pairs was 7.1 mg/L. Thus, the higher observed platform

concentration is equivalent to the sample concentration variation.

Although only a few data points are available, these results indicate

that any local scour caused by the platform did not significantly

affect suspended-solids concentrations at the platform.

Calibration and Output of Electromagnetic Current Meters

The relationship between the output voltages of the

electromagnetic current meters and the water velocity must be known.

The electromagnetic current meters have two separate output voltages,

one for each velocity component, that are linearly related to the water

velocity components. Linear calibration equations are used to convert

output voltages from the meters to water velocities. After

construction and following any repairs, the manufacturer calibrated the

meters by adjusting the output voltages to match specifications. About

annually, the current meter calibrations were checked by the U.S.

Geological Survey hydraulics laboratory at the Stennis Space Center in

Mississippi. The calibration check generally agreed within 10% of the

manufacturers stated calibration values. All calibrations were for

steady flows. If a U.S. Geological Survey calibration was available,

then it was used; otherwise, the manufacturer's calibration was used.

A potential limitation of the electromagnetic current meters used

in this study is a reduction in the meter's output response to short

period water waves, such as wind-waves with 2 to 4 second periods

(frequencies 0.25 to 0.5 Hz). The current meter output response to

short period water waves is reduced by an electronic filter network

that is used to suppress a 60 Hertz carrier signal that is inherent in









the current meter design. At wind-wave frequencies of interest to this

study, the gain (output voltage) of the meters is reduced by the

electronic filter so that actual velocities are greater than the

recorded values.

The recorded velocities can be corrected for the electronic

filtering (Guza 1988). The output filter is an active RC

(resistor/capacitor) 2-pole filter, 6dB per octave rolloff, with a time

constant RC = 0.94 seconds for the meters used in this study. The

filter reduces the magnitude of output signal and the reduction

increases as the frequency of the input signal increases. For a

periodic input signal with angular frequency w, the gain of the filter

is

G(w) = [1 + (wRC)2]2 (2-1)

The filter also causes a phase delay of the output signal. The phase

delay, a negative number in radians, is
-1
4(w) = tan-1 [1/(wRC)] i/2 (2-2)

Equations 2-1 and 2-2 can be applied to correct the recorded data

in the frequency domain. The time series is converted to the frequency

domain via the fast Fourier transform (FFT), resulting in the series
N/2+1
a(l) + 2 2 a(n) cos[(n-l) Aw t] + b(n) sin[(n-l) Aw t] -
n=2
N/2+1
Z a(n) cos[(n-l) Am t] + b(n) sin[(n-l) Aw t] +
n=l
N
Z a(n) cos[(n-N-l) Aw t] + b(n) sin[(n-N-l) AM t] (2-3)
n=N/2+2
for which N is the number of data points, a power of 2, the angular

frequency increment Aw=2r/(NAt), At is the time interval of the data,

and the Fourier series coefficients a(2)=a(N), b(2)=-b(N), a(3)-a(N-l),

b(3)=-b(N-l), ., a(n)=a(N-n+2), b(n)=-b(N-n+2), ...








a(N/2)=a(N/2+2), b(N/2)=-b(N/2+2). The left hand side of the

is how the Fourier series is commonly presented and the right

is how the FFT algorithm represents the Fourier series, which

visually more complicated but computationally more efficient.

discrete frequency w is represented by a sine and cosine term

also be written as

a(n) cos(wt) + b(n) sin(wt) = c(n) cos(wt+e(n))

in which the magnitude is

c(n) = ( a(n)2 + b(n)2 )h

and the phase is

e(n) = tan-1 (b(n)/a(n))


equality

hand side

is

Each

that can



(2-4)



(2-5)



(2-6)


The corrected magnitude at the frequency w is

cc(n) = c(n)/G(w) (2-7)

and the corrected phase is

E (n) = e(n) + 4(w) (2-8)

The corrected Fourier series coefficients are

ac(n) = c c(n) cos[ c(n)] (2-9)

bc(n) = cc(n) sin[Ec(n)] (2-10)

The inverse FFT is then applied to the corrected Fourier coefficients

to determine the corrected velocity time series. Guza and Thornton

(1980) found that the significant wave height from pressure and

velocity sensors agreed within 20%, and similar agreement occurred

between pressure and corrected velocity data from platform sensors at

the same elevation in November 1990. Raw wave spectra from pressure

and corrected velocity data were also in good agreement, so the


corrected velocities seem to be reasonable.









Response Threshold and Biological Interference of OBS Sensors

Ambient suspended-solids concentrations were often below the

response threshold of the OBS sensors, and biological interference with

the sensors was a potential problem (Schoellhamer, manuscript to be

published in Marine Geology). The sediment load of the rivers that

flow into Tampa Bay is small and Tampa Bay is microtidal, so the

ambient suspended-solids concentrations are also small, about 10 to 50

mg/L. Due to the response threshold of OBS sensors, accurate

interpretation of OBS data may be difficult except during episodic

events that resuspend bottom sediments. Backscatterance from

phytoplankton may be detected when suspended-solids are at ambient

concentrations. The OBS sensor electronics were factory adjusted in

mid-1989 to improve their sensitivity, which diminished but did not

eliminate these problems. Laboratory calibrations of the OBS sensors

with bottom sediments from the platform site did not agree with the

suspended-solids concentrations of collected water samples, so the

sensors were calibrated with water sample data. The standard error of

an OBS sensor in Old Tampa Bay is 5.8 mg/L, based upon a set of 21 OBS

measurements and water samples collected from an elevation 70.1 cm

above the bed by an automatic water sampler during a storm in March

1990 (fig. 2-4). Shallow depths, high water temperatures, and

eutrophic conditions encouraged biological growth on the OBS sensors

that sometimes increased their output voltages and invalidated the

data, so daily cleaning were desirable.

Fish would sometimes interfere with the OBS sensors. During dives

and instrument cleaning, it was noted that fish would sometimes be

congregated around the instrumentation and occasionally would swim past

the OBS sensors. The infrared light pulse would reflect off the fish

























0 0
0
I o
0
0
0OO
oo

0 0


35 40 45 50 55 50 65

MEDIAN OBS OUTPUT, IN MILLIVOLTS


Figure 2-4,


Suspended-solids concentration and median OBS sensor output
70 cm above the bed at the Old Tampa Bay platform, March
1990 (Schoellhamer, manuscript to be published in Marine
Geology).


80
so

S 60


C-2
z
wp 40

LLI-

LU 20
n0
O









and produce a high spike (short-duration increase in output voltage)

during the burst sample collection. Usually no more than a few spikes

would occur during a burst, but they were large enough to significantly

affect the resulting mean value for the burst, so the median value

proved to be a simple and more appropriate measure of the OBS burst

average than the mean value. Regular sensor maintenance and careful

data analyses to identify spikes and fouling were used to minimize

abnormalities in OBS data.

Water Sample Collection

Water samples were collected manually and automatically at the

platform. The water samples were usually analyzed by the methods of

Fishman and Friedman (1989) to determine specific conductance,

turbidity, and concentrations of suspended-solids, volatile suspended-

solids, and dissolved chloride. At the Old Tampa Bay platform, point

water samples used for the calibration of the OBS sensors were

collected each day from each OBS sensor depth using a peristaltic pump

connected to tygon tubing that was attached at the end of a long pole

that was lowered to the desired depth.

A continuous water sample collection technique was required for

accurate suspended solids monitoring during storm events and nighttime.

An automatic water sampler was secured in one corner of the steel deck

of the Old Tampa Bay platform, beginning with deployments in March

1990. A SIGMAMOTOR Model 6601 automatic water sampler, connected to

nylon-reinforced teflon-tubing, collected an OBS calibration point

sample every hour at one OBS depth for the duration of most instrument

deployments. The water sampler was set to sample during the sensor on-

time.








Instrument Deployment Strategies

Sediment resuspension monitoring instrumentation was deployed

intermittently in Old Tampa Bay from 1988 to 1990. As mentioned

previously, instrumentation was continuously deployed from the Old

Tampa Bay platform in fall 1988. Analyses of the data indicated that

bottom sediment resuspension did not occur with normal or spring tidal

currents. Waves generated by strong winds were determined to be the

most likely sediment resuspension mechanism in Old Tampa Bay. In

Florida, the typical sources for strong winds are winter storm systems,

tropical storms, and summer thunderstorms. Therefore, in late 1989 and

1990, instrumentation was deployed in Old Tampa Bay before the

anticipated arrival of selected meteorological events. The automatic

water sampler was set up at the platform, the instruments were tested,

and the vertical pipe that supported the instruments was lowered into

the water and secured to the steel deck at the beginning of each

deployment. The submersible instrument package was also deployed at

the shallow-site shortly after the platform instrumentation was

deployed. Weather permitting, daily servicing trips were made to clean

sensors, retrieve data, and collect water samples. The vertical pipe

was secured out of the water, and the submersible instrument package

was recovered several days after being deployed.















CHAPTER 3
SEDIMENT RESUSPENSION DATA AND ANALYSIS

Data collected intermittently from 1988 to 1990 in Old Tampa Bay

shows that sediment resuspension coincided with wind-waves generated by

strong sustained winds associated with storm systems (Schoellhamer

1990, Schoellhamer and Levesque 1991, Schoellhamer manuscript in

review). Tidal currents were too weak to resuspend measurable

quantities of sediment at the Old Tampa Bay platform, but some bottom

sediment motion probably did occur because of the stochastic nature of

the process (Lavelle and Mofjeld 1987a). Suspended-solids

concentrations returned to ambient values within several (4 to 8) hours

as wave activity diminished.

Sediment resuspension data collected at the Old Tampa Bay platform

during storms in March 1990 and November 1990 were suitable for

numerical simulation, and these data and the analysis of these data by

Schoellhamer (manuscript in review) are presented in this chapter.

Instrumentation deployments at the Old Tampa Bay platform are

summarized in table 3-1. Platform data collected in March 1990 and

November 1990 were suitable for simulation because net sediment

resuspension occurred and both hydrodynamic and suspended-solids

concentration data were collected successfully. Several data sets were

collected during which the OBS sensors could not be calibrated,

sediment resuspension was not observed, or instruments malfunctioned.

Data collected during two tropical storms unfortunately were not

suitable for numerical simulation, but these data and the analysis of





71


Table 3-1.--Old Tampa Bay platform instrumentation deployments.


Instrumentation
deployment
dates

Fall 1988

Sept 20-21, 1989

Nov 28-30, 1989

March 8-10, 1990

July 11-13, 1990

Oct 9-12, 1990

Nov 28 -
Dec 3, 1990


Hydrodynamic
data
available


Suspended-solids
concentration
data available


Net sediment
resuspension
observed


Y Y








these data by Schoellhamer (manuscript in review) are presented and

compared to the March and November 1990 data. Hydrodynamic data, but

no suspended-solids concentration data, were collected successfully

during tropical storm Keith November 21-24, 1988. No hydrodynamic data

were collected successfully during tropical storm Marco in October

1990. The limited data collected during tropical storms Keith and

Marco indicate that tropical storms can resuspend more sediment than

winter storms can resuspend.

The bottom roughness at the Old Tampa Bay platform was determined

with equation 1-5 and velocity profiles collected during several

instrumentation deployments. Velocity profiles that were measured

during periods of small wave motion and during relatively strong flood

and ebb tides were used. Velocity data collected 183 cm above the bed

were not used because the values usually were not logarithmic compared

to velocities closer to the bed. Data collected before and immediately

after sediment resuspension events did not indicate that bottom

roughness changed significantly. Bottom photographs taken by divers

were not useful due to poor visibility. Divers observed that the bed

was nearly flat with some undulations, possibly from bioturbation, and

that there were no regular bed forms. Thus, bed load transport at the

platform probably was not significant, except possibly during major

sediment resuspension events. The bottom sediment included 16% fine

material, and it is possible that this was the material that was

observed in suspension and that the sandy material either did not move

or did not create ripples that significantly affected the data. The

analysis of the velocity data produced an optimal bottom roughness

equal to 0.3 cm, and the bottom roughness regime was usually

transitional between the rough and smooth limits. The total bottom









roughness is composed of contributions from form drag and grain

roughness, but only the roughness associated with the particles

determines particle motion (Vanoni 1975, McLean 1991). Spatially-

averaged grain shear stress can be calculated by collecting velocity

data within the flow layer adjacent to the bed that is influenced by

grain roughness or by applying empirical relationships based on ripple

geometry (Smith and McLean 1977). For this study, however, velocity

data could not be collected close enough to the bed to recognize

different bottom roughness scales, and no regular ripples were

observed. Therefore, in this chapter, the total shear stress

calculated with the total bottom roughness was used to determine the

sediment resuspension mechanisms at the platform. The spatially-

averaged grain shear stress was estimated by the numerical model that

is presented in chapter 4. For a given particle diameter, a calculated

total shear stress that is greater than a critical shear stress (such

as Shields critical shear stress, fig. 1-1) may not indicate that

motion will occur because not all of the total shear stress is acting

on the grains and biological activity may increase the critical shear

stress.

March 1990 Storm

Data were collected at the Old Tampa Bay platform after a cold

front moved through the Tampa Bay area on March 8, 1990. The high

pressure system behind the front generated 8- to 9-meter-per-second

sustained northeasterly winds from 1100 to 2100 hours on March 8 (fig.

3-1, table 3-2). Wave activity increased as a result of the sustained

northeasterly winds, providing favorable conditions for sediment

resuspension. Operational equipment at the platform consisted of

electromagnetic current meters at elevations of 70 and 183 cm above the
































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MARCH MARCH
8 1990 9


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MARCH
a


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MARCH
1990


Figure 3-1, Measured and calculated quantities at the Old Tampa
Bay platform, March 1990


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Table 3-2.--01d Tampa Bay platform data, March 8, 1990.


Hour Water
depth
___ (cm)

1400 402.4

1500 410.2

1600 409.8

1700 405.7

1800 399.1

1900 395.4

2000 398.1

2100 405.4

2200 413.9

2300 420.3


Mean current
(cm/s) at elev


70 cm

3.8

1.4

3.4

8.3

8.9

2.6

0.6

8.7

7.8

5.7


183 cm

4.7

1.3

4.8

9.6

9.5

2.7

4.2

10.0

8.7

7.0


Wind
speed
(m/s)

9.2

8.1

8.4

8.6

8.5

8.6

8.1

8.3

6.0

5.8


Wave
amp.
(cm)

38.2

30.8

30.0

26.4

27.7

30.8

21.6

26.2

24.8

14.0


Wave
period
(sec)

2.46/2.43

2.78/2.53

2.64/2.50

2.69/2.52

2.46/2.52

2.75/2.54

2.15/2.41

2.31/2.42

2.27/2.35

2.19/2.58


Suspended-solids
cone. (mg/L)
24 cm 70 cm 183 cm

54.0 42.0 44.0

66.0 47.9 44.0

58.0 47.9 49.1

74.0 51.5 47.8

98.0 68.2 59.3

86.0 67.0 63.2

71.9 62.2 52.9

53.9 45.6 44.0

44.0 43.2 40.1

42.0 42.0 36.3


Wave periods are maximum energy of the surface amplitude spectrum/zero
upcrossing period of the squared bottom orbital velocity spectrum.








bed and OBS sensors at 24, 70, and 183 cm above the bed. Water samples

were collected from 1500 March 8 to 1100 March 9 at a position 70 cm

above the bed using the automatic water sampler. In addition, discrete

water samples were manually collected during instrument on-time once

each day throughout the instrument deployment (March 8 10) at the

elevations of the OBS sensors and analyzed for suspended-solids

concentration. The discrete samples were used to calibrate the output

of the OBS sensors to suspended-solids concentration, and the automatic

samples validated the calibration of the OBS sensor 70 cm above the

bed. The suspended-solids concentrations (fig. 3-1) peaked at 1800

hours March 8, then decreased rapidly. No data was successfully

recorded before 1400 hours on March 8 because of a power supply

problem, but the suspended-solids concentrations for the first platform

measurement at 1400 hours were slightly greater than the upper limit of

the observed ambient concentrations (20 to 40 mg/L), which indicates

that only the initial resuspension was missed.

The temporal variation in the bottom shear stresses calculated

from the measured mean current with equation 1-5 did not correspond to

the temporal variation of the measured suspended-solids concentrations.

The mean current speeds measured 70 and 183 cm and the bottom shear

stresses calculated from the mean current speed 70 cm above the bed are

shown in figure 3-1. A bottom roughness of 0.3 cm was used. A small

ebb tide from 1600 hours to 1900 hours March 8 and a small flood time

from 1900 hours March 8 to 0100 hours March 9 had maximum speeds of

about 9 cm/s and increased the mean current bottom shear stress to

about 0.15 dynes/cm2, but these increases are not correlated with the

observed suspended-solids concentrations. A strong ebb tide at the

platform during a period of relatively little wave activity from 0200









to 0900 hours March 9 had maximum speeds of 12 to 16 cm/s and increased

the mean current bottom shear stress to 0.28 dynes/cm2, but apparently

did not resuspend bottom sediments. This total (grain and form) shear

stress is smaller than the Shields critical shear stress for the

platform sediment. The mean current during the morning of March 9 was

relatively large for the platform site, and the lack of a corresponding

increase in suspended-solids concentration indicates that the tidal

currents did not generate enough shear stress to resuspend bottom

sediments at the platform site. The suspended-solids concentrations

did not correlate with mean current bottom shear stress (r=-0.4, table

3-3).

Horizontal advection is not a likely cause of the observed

increase in suspended-solids concentration because the tidal excursion

was within the large area of homogeneous sediments that surrounded the

platform and sediments further upcurrent were probably not resuspended.

The tidal excursion of the small ebb tide from 1600 to 1900 hours

(about 750 meters) was within the large area of silty very fine sands

that surrounded the platform. The ebb tidal flow was from the

northwest to the southeast at the platform, so the most likely source

of resuspended sediment for transport to the platform during an ebb

tide was resuspension in relatively shallow water 1500 meters northwest

of the platform and within 500 meters of the southern side of the

Courtney Campbell Causeway. The wind was from the northeast, however,

so wind waves were not approaching the southern side of the causeway,

and resuspension was unlikely.

Wave properties were calculated using spectral analysis. Usually,

buoy acceleration or pressure data are used to calculate the energy

spectrum, but the pressure transducer was only partially responding to









Table 3-3.--Correlation coefficients for various wave properties and
bottom shear stresses with suspended-solids concentrations at the Old
Tampa Bay platform, March 1990.


Shear stress: mean current only

Shear stress: wave only (Kamphius 1975)

Shear stress: wave only
(Grant and Madsen 1979 and 1982)

Shear stress wave-current
(Grant and Madsen 1979)

Wave amplitude

Bottom orbital velocity

Square of bottom orbital velocity


Elevation of measured
suspended-solids concentration

24 cm 70 cm 183 cm

-0.29 -0.41 -0.52

0.74 0.61 0.70


0.73

0.73


0.73

0.74

0.69


0.59

0.59


0.66

0.61

0.58


0.68

0.67


0.78

0.70

0.66









the changes in pressure from wave activity, so the velocity component

pairs measured by the lowest current meter were used to calculate the

energy spectra after correcting the raw data for the electronic output

filter of the electromagnetic current meters as described in chapter 2.

The wave energy was located almost exclusively at wave periods from 2

to 3 seconds, and the maximum energy period of the surface amplitude

spectrum was selected to represent the wave period. The zero-

upcrossing period of the squared bottom orbital velocity spectrum

(square root of the second moment divided by the zero moment), however,

is probably more indicative of wave periods that affect the bottom

shear stress. Table 3-2 indicates that these periods are similar, and

the interpretations that result from this analysis are not affected by

this difference. For narrow banded spectra such as these, the

significant wave amplitude is twice the square root of the area under

the wave spectrum (Ochi 1990). Significant wave amplitudes calculated

with data from the current meter 70 cm above the bed (fig. 3-1)

corresponded with the wind speed and decreased after 2200 hours March

8. The wave amplitude was somewhat correlated with the suspended-

solids concentrations (r=0.7, table 3-3). The waves during the storm

(1400 to 2100 hours) were transitional between the deep-water and

shallow-water limits, but as the wind diminished the waves became deep-

water waves. The maximum orbital particle velocities calculated from

linear wave theory based upon the significant wave amplitude were close

to measured values, so the calculated wave properties appeared to be

reasonable. The bottom orbital velocity (fig. 3-1) decreased in

conjunction with the wind speed. Note that only a single wave

amplitude and period are considered, whereas realistically, there are

many periods and amplitudes present in the wave field. Thus, the









results of the spectral analysis were used to provide approximate wave

data in a consistent manner.

The bottom orbital velocities corresponded with the observed

suspended-solids concentrations. The bottom orbital velocities were

9.8 to 16 cm/s until 1900 hours March 8 and during this time the

suspended-solids concentrations increased from slightly greater than

ambient values to the maximum values measured during the deployment.

After 1900 hours March 8, the waves were deep-water waves, the bottom

orbital velocities were less than 7 cm/s, and the suspended-solids

concentrations decreased to ambient values in the early morning of

March 9. Thus, resuspension seems to have occurred during the period

of greatest wave activity, and the resuspended sediments settled as the

wave action diminished. The bottom orbital velocity and squared bottom

orbital velocity were somewhat correlated with suspended-solids

concentrations (r=0.7, table 3-3).

The calculated bottom orbital velocity and estimated maximum

bottom shear stress were more dependent on the water depth and wave

period than the wave amplitude. The bottom orbital velocity increases

with increasing wave amplitude, increasing wave period, and decreasing

mean water depth. A sensitivity analysis was performed to investigate

the relative importance of wave amplitude, wave period, and mean water

depth on the bottom orbital velocity calculation for this data set.

Typical storm values for this data set are a significant wave amplitude

of 30 cm, a maximum energy period of 2.6 seconds, and a water depth of

400 cm. A 10% increase in wave amplitude, a 10% increase in wave

period, and a 10% decrease in water depth, increase the bottom orbital

velocity 10, 29, and 25%, respectively. The bottom orbital velocity

during resuspension at the Old Tampa Bay platform was more sensitive to








wave period and mean water depth than wave amplitude because the waves

are depth transitional. The maximum bottom shear stress is

proportional to the square of the maximum bottom orbital velocity (eqn.

1-11), so an error in the estimated bottom orbital velocity may

severely degrade the estimated bottom shear stress. For example,

assuming that the wave friction factor is unchanged, if a 10%

overestimate of the wave period produces a 29% overestimate of the

maximum bottom orbital velocity, then the maximum bottom shear stress

will be overestimated by 66%.

The maximum bottom shear stresses estimated for wave motion only

are much greater than the bottom shear stresses estimated for the mean

current only and correspond to the suspended-solids concentrations.

Equation 1-11 and friction coefficients determined empirically

(Kamphius 1975) and theoretically (eqn. 1-13, Grant and Madsen 1979,

1982) were used to estimate the maximum bottom shear stress for the

observed bottom roughness (fig. 3-1). The estimated bottom shear

stress considering wave motion only is much greater than the estimated

bottom shear stress considering the mean current only. The greatest

wave shear stress occurred during the period of sediment resuspension

on March 8 and the wave shear stress is somewhat correlated with

suspended-solids concentration (r=0.7, table 3-3).

Poor knowledge of the behavior of the wave friction factor for

regime transitional waves may account for the differences between the

results of the two methods for calculating the wave only bottom shear

stress (fig. 3-1). The waves were transitional between the laminar

(smooth bottom) and fully turbulent (rough bottom) flow regimes.

Kamphius (1975) states that the data used to determine the friction

factors for regime transitional waves are poorly ordered and that the









resulting values should be used with caution. Grant and Madsen (1979)

state that their approach is applicable to regime transitional waves

but fully rough turbulent flow has previously been assumed (Drake and

Cacchione 1986, Drake et al. 1992, Cacchione et al. 1987, Grant and

Madsen 1979 and 1982, Signell et al. 1990).

The maximum wave-current bottom shear stresses were estimated with

the Grant and Madsen (1979) model (fig. 3-1). Estimated maximum bottom

shear stresses were greatest from 1400 to 1900 hours during which time

the suspended-solids concentration increased. This qualitative

behavior and the correlation coefficient with suspended-solids

concentration for the wave-current bottom shear stress (r=0.7, table 3-

3) are virtually identical to that for the maximum bottom shear

stresses estimated considering wave motion only.

Compared to the bottom shear stress estimated by the Grant and

Madsen model for wave motion only (eqns. 1-11 and 1-13) and the sum of

this wave shear stress and the mean current shear stress (eqn. 1-5),

consideration of wave-current interaction slightly increases the

estimated bottom shear stress, but this increase is smaller than the

uncertainty associated with the wave friction factor. During the

period of greatest wave activity from 1400 to 1900 hours, the maximum

bottom shear stresses estimated with the wave-current model were 9%

greater than those estimated considering waves only (eqns. 1-11 and 1-

13) and 6% greater than the sum of the mean current (eqn. 1-5) and wave

only shear stresses. The maximum wave bottom shear stress during this

period calculated with the friction factor diagram by Kamphius (1975)

is 44% greater than the shear stress calculated with the friction

factor of equation 1-13. Therefore, for this data set, the estimated

maximum bottom shear stress seems to be more sensitive to the selected









estimation procedure than the possible effect of wave-current

interaction.

Because the waves at the platform are depth transitional, the

bottom orbital velocity and estimated wave bottom shear stress are also

sensitive to the wave period and water depth and errors in these

quantities can produce large errors in the wave bottom shear stress, as

discussed previously. A similar sensitivity analysis of the wave-

current model using a water depth of 400 cm, wave period of 2.6

seconds, wave amplitude of 30 cm, an angle between the wave and current

of 150 degrees, a 0.3 cm bottom roughness, and a mean velocity of 10

cm/s at an elevation 70 cm above the bed indicates that a 10% increase

in wave amplitude, a 10% increase in wave period, and a 10% decrease in

water depth, increases the maximum wave-current bottom shear stress 14,

39, and 37%, respectively. The maximum wave-current bottom shear

stress was relatively insensitive to 10% changes in mean velocity (4%),

angle (0.4%), and bottom roughness (4%). Selection of a representative

wave period from a measured wave spectrum is probably the most likely

source of inaccuracy.

The sediment resuspension observed on March 8, 1990, at the Old

Tampa Bay platform was caused by increased wave motion associated with

strong and sustained northeasterly wind. The bottom shear stresses

estimated by considering the mean current only were much less than the

maximum bottom shear stresses estimated by considering wave motion

only. Wave-current interaction may have contributed to the bottom

shear stress, but this difference is not as significant as the

differences associated with the selected wave period and the selected

procedure used to calculate the wave friction factor. The period of

the largest estimated wave and wave-current shear stresses corresponds




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FILES



SIMULATION AND ANALYSIS OF SEDIMENT RESUSPENSION
OBSERVED IN OLD TAMPA BAY, FLORIDA
By
DAVID HENRY SCHOELLHAMER
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1993

To Alicia V. Schoellhamer, 1920-1990

ACKNOWLEDGEMENTS
The support of my employer, the U.S. Geological Survey, while I
attended classes at the University of Florida is gratefully
acknowledged. My supervisors in Tampa, Carl Goodwin and Kathi Hammett,
were very cooperative in arranging my work schedule so I could complete
my classes, qualifying exams, and dissertation.
The Old Tampa Bay sediment resuspension data that was used in this
dissertation was collected as part of a study of sediment resuspension
and light attenuation in Tampa Bay that I conducted from 1987 to 1992
for the U.S. Geological Survey. The study was performed in cooperation
with the City of St. Petersburg, the City of Tampa, Hillsborough
County, Pinellas County, the Southwest Florida Water Management
District, and the Tampa Port Authority. Pliny Jewell and Victor
Levesque of the U.S. Geological Survey provided valuable assistance
with the data collection for the study.
I would like to thank my supervisory committee members, Drs.
Robert Dean, Dan Hanes, Ashish Mehta, Lou Motz, and Peter Sheng, and
former members Drs. Wayne Huber, Carl Goodwin, and Clay Montague. I
would especially like to thank Dr. Peter Sheng, who, as committee
chairman, guided this research.
Finally, the life-long support of my parents, Jack and Alicia, is
more than gratefully acknowledged.
iii

TABLE OF CONTENTS
Rage
ACKNOWLEDGEMENTS iii
LIST OF TABLES vi
LIST OF FIGURES viii
KEY TO SYMBOLS x
ABSTRACT xvi
CHAPTERS
1 INTRODUCTION 1
Significance of Estuarine Sediments 4
Sediment Transport Processes 8
Initiation of Motion of Bed Sediments 8
Bed Load Transport 15
Erosion and Bottom Shear Stress 16
Suspended Load Transport 24
Flocculation and Aggregation 26
Settling and Deposition 27
Other Bed and Near-bed Factors 31
Field Studies Related to Estuarine Sediment Transport 35
Numerical Models Applicable to
Estuarine Sediment Transport 43
Relation of this Research to Previous Studies 49
2 SEDIMENT RESUSPENSION DATA COLLECTION METHODOLOGY 52
Study Area 52
Sediment Resuspension Monitoring Sites 54
Old Tampa Bay Instrumentation Platform 56
Calibration and Output of Electromagnetic Current Meters.. 63
Response Threshold and Biological Interference of
OBS Sensors 66
Water Sample Collection 68
Instrument Deployment Strategies 69
3 SEDIMENT RESUSPENSION DATA AND ANALYSIS 70
March 1990 Storm 73
November 1990 Storm 84
Tropical Storm Keith 90
Tropical Storm Marco 94
IV

Implications for Numerical Modeling 96
4 NUMERICAL MODEL 98
Momentum and Transport Equations 102
Turbulence Closure 106
Nondimensional Equations 112
Steady State Conditions 116
Wave-Induced Pressure Gradients 117
Bottom Shear Stress and Erosion 119
Suspended-Sediment Stratification 122
5 NUMERICAL SIMULATIONS OF THE MARINE SURFACE LAYER
AND CRITICAL SHEAR STRESSES ON CONTINENTAL SHELVES 123
Simulation of Turbulence in the Marine Surface Layer 123
Critical Shear Stresses Observed on Continental Shelves... 126
6 OLD TAMPA BAY NUMERICAL SIMULATION RESULTS 138
Steady Flow Simulation 138
Reproduction of Energy Spectra of Observed Currents 142
Simulated Shear Stresses 144
Old Tampa Bay Suspended-Sediment Simulation Procedure 154
Old Tampa Bay November 1990 Suspended-Sediment
Calibration Simulation 161
Old Tampa Bay March 1990 Suspended-Sediment
Validation Simulation 166
Old Tampa Bay March 1990 Suspended-Sediment
Improved Simulation 171
Old Tampa Bay November 1990 Sensitivity Simulations 175
7 SUMMARY AND CONCLUSIONS 181
APPENDICES
A 0CM1D FINITE-DIFFERENCED EQUATIONS AND TURBULENCE
CLOSURE ALGORITHMS 188
Finite-Differenced Equations for Momentum and
Suspended Sediment 188
Turbulence Closure Algorithms 192
REFERENCES 196
BIOGRAPHICAL SKETCH 215
v

LIST OF TABLES
page
Table 1-1, Previous studies that are related to this research
and include an estuarine environment, wind waves,
field measurements of suspended-sediment
concentrations, or a numerical vertical sediment
transport model 50
3-1, Old Tampa Bay platform instrumentation deployments... 71
3-2, Old Tampa Bay platform data, March 8, 1990 75
3-3, Correlation coefficients for various wave properties
and bottom shear stresses with suspended-solids
concentrations at the Old Tampa Bay platform,
March 1990 78
3-4, Old Tampa Bay platform data, November 30 -
December 1, 1990 86
3-5, Correlation coefficients for various wave properties
and bottom shear stresses with suspended-solids
concentrations at the Old Tampa Bay platform,
November 1990 88
4-1, Modifications made to the 1986 version of 0CM1D
(Sheng 1986) for this research 101
4-2, Comparison of the equilibrium closure and TKE
closure methods for turbulent transport 113
5-1, Mean current speed, maximum wave orbital velocity,
wave period, and critical shear stresses from a
wave-current model (Drake and Cacchione 1986) and
the 0CM1D model 128
5-2, Mean current speed, maximum wave orbital velocity,
wave period, angle between the mean current and
waves, and critical shear stresses from a
wave-current model (Larsen et al. 1981) and
the 0CM1D model 133
6-1, Total and grain shear stress distribution and
critical stresses, 1800 hours March 8, 1990 153
6-2, Old Tampa Bay suspended-sediment simulations 157
vi

6-3, Values of the calibration coefficients determined by
other studies and determined for the November 1990
calibration simulation and the March 1990 improved
simulation 173
6-4, Mean percent differences of simulated suspended-solids
concentrations 70 and 183 cm above the bed caused by
20% changes in the calibration coefficients,
November 1990 sensitivity simulations 176
Vll

LIST OF FIGURES
pase
Figure 1-1, Shields critical shear stress diagram 12
1-2, Roughness function B in terms of Reynolds number,
from Schlichting (1969) 19
2-1, Old Tampa Bay study area 53
2-2, Size distribution of bottom sediment at the
Old Tampa Bay platform 57
2-3, Old Tampa Bay platform 58
2-4, Suspended-solids concentration and median OBS
sensor output 70 cm above the bed at the Old Tampa
Bay platform, March 1990 67
3-1, Measured and calculated quantities at the Old Tampa
Bay platform, March 1990 74
3-2, Measured and calculated quantities at the Old Tampa
Bay platform, November 1990 85
3-3, Mean water depth, mean current speed, and maximum
bottom orbital velocity at the Old Tampa Bay
platform during tropical storm Keith,
November 1988 91
3-4, Wind speed, wind vector azimuth, and
suspended-solids concentration at the Old Tampa Bay
platform during tropical storm Marco, October 1990.. 95
5-1, Measured, simulated, and theoretical turbulent
dissipation in the marine surface layer, measurements
reported by Soloviev et. al (1988) 124
5-2, Extended Shields diagram for continental shelf
data, shear stresses from wave-current models (WC)
and 0CM1D 130
6-1, Computational grid for 45 layers, 1.15 neighboring
layer height ratio, and a 399 cm domain height 140
6-2, Comparison of Reichardt and simulated velocity
profiles 141
viii

6-3, Comparison of turbulence macroscale from the
dynamic equation and the integral constraints 143
6-4, Raw energy spectra computed from measured and
simulated velocities, 1500 hours November 30, 1990.. 145
6-5, Spatial convergence of total and
grain shear stress 147
6-6, Maximum grain shear stress calculated by 0CM1D and
from Engelund's experimental results 149
6-7, Simulated total and grain shear stresses,
1800 hours March 8, 1990 150
6-8, Simulated grain shear stress,
1800 hours March 8, 1990 152
6-9, Maximum total bottom shear stress from the
0CM1D model and the Grant and Madsen (1979)
wave-current model, November 1990 155
6-10, Simulated and measured suspended-solids
concentrations 70 cm above the bed,
November 1990 calibration simulation 162
6-11, Simulated and measured suspended-solids
concentrations 183 cm above the bed,
November 1990 calibration simulation 163
6-12, Simulated and measured suspended-solids
concentrations 24 cm above the bed,
March 1990 validation and improved simulations 168
6-13, Simulated and measured suspended-solids
concentrations 70 cm above the bed,
March 1990 validation and improved simulations 169
6-14, Simulated and measured suspended-solids
concentrations 183 cm above the bed,
March 1990 validation and improved simulations 170
6-15, Sensitivity of November 1990 calibration simulation
results to erosion rate exponent r¡ 177
6-16, Sensitivity of November 1990 calibration simulation
results to erosion rate coefficient a 178
6-17, Sensitivity of November 1990 calibration simulation
results to settling velocity w^ 180
A-l, Coordinate axes definition and grid structure for
program 0CM1D 189
IX

KEY TO SYMBOLS
A invariant constant for turbulence algorithm (0.75, eqn. 4-26)
orbital amplitude just above the boundary layer (eqn. 1-14)
A eddy viscosity (eqn. 1-16)
nondimensional eddy viscosity (eqn. 4-42)
a wave amplitude (eqn. 1-12)
small reference elevation above the bed (eqn. 1-18)
Fourier series coefficient (eqn. 2-3)
invariant constant for turbulence algorithm (3, eqn. 4-23)
ac corrected Fourier series coefficient (eqn. 2-9)
B roughness function (eqn. 1-5)
b intercept of line that fits a segment of fig. 1-2 (eqn. 1-6)
Fourier series coefficient (eqn. 2-3)
invariant constant for turbulence algorithm (0.125, eqn. 4-23)
bc corrected Fourier series coefficient (eqn. 2-10)
C well-mixed suspended-sediment concentration (eqn. 1-19)
coefficient for integral constraint on A (eqn. 4-32)
c mean suspended-sediment concentration (eqn. 1-15)
magnitude in frequency domain (eqn. 2-4)
nondimensional suspended-sediment concentration (eqn. 4-42)
c suspended-sediment concentration at elevation a (eqn. 1-18)
cL
cc corrected magnitude in frequency domain (eqn. 2-7)
c suspended-sediment mass concentration (eqn. 4-62)
m
c suspended-sediment concentration at upper boundary (eqn. 4-19)
nondimensional c^ (eqn. 4-52)
D rate of deposition (eqn. 1-19)
d^ particle diameter for which n percent of sediments are finer
dg sediment particle diameter (eqn. 1-1)
E erosion rate (eqn. 1-3)
x

nondimensional erosion rate (eqn. 4-42)
Ekman number (eqn. 4-43)
Froude number (eqn. 4-43)
neighboring layer height ratio (eqn. 5-2)
friction factor (eqn. 1-12)
Coriolis coefficient (eqn. 4-4)
filter gain for current meter, function of w (eqn. 2-1)
gravitational acceleration (fig. 1-1)
elevation of model domain (eqn. 4-42)
nondimensional elevation of model domain (eqn. 4-42)
water depth (eqn. 1-12)
counter and exponent (eqn. 5-2)
pressure transfer function (eqn. 4-60)
eddy diffusivity (eqn. 1-16)
nondimensional eddy diffusivity (eqn. 4-42)
wave number (eqn. 1-12)
molecular diffusion (eqn. 4-26)
bottom roughness (eqn. 1-14)
height of bottom roughness elements (eqn. 1-5)
erosion rate constant (eqn. 1-3)
number of data points for fast Fourier transform (eqn. 2-3)
Brunt-Vaisala frequency (eqn. 4-31)
number of layers (eqn. 5-2)
counter (eqn. 2-3)
Prandtl number (eqn. 4-43)
pressure (eqn. 4-2)
pressure at the water surface (eqn. 4-6)
nondimensional pressure at the water surface (eqn. 4-42)
nondimensional quantity (eqn. A-8)
turbulent fluctuating velocity (eqn. 4-23)
nondimensional turbulent fluctuating velocity (eqn. 4-42)
roughness Reynolds number u^ks/j/ (fig. 1-2)

Reynolds number (eqn. 4-43)
R^ Richardson number (eqn. A-ll)
R^ horizontal Rossby number (eqn. 4-43)
R^ vertical Rossby number (eqn. 4-43)
R_u boundary Reynolds number U^d /j/ (eqn. 1-1)
RC electronic filter time constant for current meter (eqn. 2-1)
s slope of line that fits a segment of fig. 1-2 (eqn. 1-6)
invariant constant for turbulence algorithm (1.8, eqn. 4-27)
T wave period (table 5-1)
t time (eqn. 1-15)
nondimensional time (eqn. 4-42)
Ui/io mean of the highest 1/10 u^ (table 5-2)
mean current speed 100 cm above bed (table 5-1)
maximum wave orbital velocity 20 cm above bed (table 5-1)
shear velocity (eqn. 1-1)
u horizontal velocity at elevation z (eqn. 1-5)
mean velocity of sediment particles (eqn. 1-15)
mean velocity component (eqn. 4-1)
nondimensional mean velocity component (eqn. 4-42)
u^ maximum bottom orbital velocity (eqn. 1-11)
u_,_ shear velocity (eqn. 1-5)
v mean horizontal velocity component (eqn. 4-4)
nondimensional mean velocity component (eqn. 4-42)
v^ invariant constant for turbulence algorithm (0.3, eqn. 4-23)
w mean vertical velocity component (eqn. 4-4)
w terminal settling velocity (eqn. 1-17)
nondimensional settling velocity (eqn. 4-42)
x coordinate axis (eqn. 1-15)
nondimensional horizontal coordinate axis (eqn. 4-42)
y horizontal coordinate axis (eqn. 4-4)
nondimensional horizontal coordinate axis (eqn. 4-42)
Z Rouse number w /(/J/cu ) (eqn. 1-18)
s ^r
Xll

z elevation above bed (eqn. 1-5)
vertical coordinate axis (eqn. 1-17)
vertical coordinate (eqn. 4-4, fig. A-l)
z^ vertical coordinate of velocity measurement (eqn. 4-61)
z+ nondimensional quantity u_,_z/V (eqn. 1-10)
zq elevation with zero velocity (eqn. 1-9)
z+ nondimensional quantity u,z /v (eqn. 1-10)
o J * o
a erosion rate coefficient (eqn. 1-4)
invariant constant for turbulence algorithm (0.75, eqn. 4-26)
p K/A, the inverse of the turbulent Schmidt number (eqn. 1-16)
7 specific weight of fluid (eqn. 1-2)
7g specific weight of sediment (eqn. 1-2)
At time interval of data (eqn. 2-3)
nondimensional simulation time step (eqn. A-l)
simulation time step (eqn. 4-59)
Az^ height of bottom layer (eqn. 5-2)
Act^ nondimensional layer elevation (eqn. A-l)
Act k nondimensional distance between grid points k and k-1 (eqn. A-l)
Acr+k nondimensional distance between grid points k and k-1 (eqn. A-l)
Aw angular frequency increment 27r/(NAt) (eqn. 2-3)
6 Kronecker delta (eqn. 4-23)
distance for integral constraint on A (eqn. 4-32)
e phase (eqn. 2-4)
alternating tensor (eqn. 4-2)
energy dissipation rate (eqn. 5-1)
tc corrected phase (eqn. 2-8)
f nondimensional quantity (eqn. 1-13)
r¡ erosion rate exponent (eqn. 1-4)
0 production term (eqn. 4-3)
nondimensional production term (eqn. 4-42)
k von Karman's constant (eqn. 1-5)
A turbulence macroscale (eqn. 4-23)
xiii

nondiraensional turbulence macroscale (eqn. 4-42)
Taylor microscale (eqn. 4-28)
kinematic viscosity (eqn. 1-1)
nondimensional kinematic viscosity (eqn. 4-42)
surface displacement from the mean water depth (eqn. 4-6)
nondimensional surface displacement (eqn. 4-42)
fluid density (eqn. 1-1)
nondimensional fluid density (eqn. 4-42)
reference fluid density (eqn. 4-2)
sediment density (eqn. 4-62)
water density (eqn. 4-62)
nondimensional vertical coordinate (eqn. 4-42)
bottom shear stress (eqn. 1-3)
total bottom shear stress (table 5-1)
critical shear stress for erosion (eqn. 1-3)
critical shear stress for deposition (eqn. 1-19)
minimum r that maintains sediment in suspension (eqn. 1-19)
bottom shear stress (eqn. 1-2)
grain shear stress (table 5-1)
maximum bottom shear stress in oscillatory flow (eqn. 1-11)
x component of wind shear stress at free surface (eqn. 4-14)
nondimensional x component of wind shear stress (eqn. 4-47)
y component of wind shear stress at free surface (eqn. 4-15)
nondimensional y component of wind shear stress (eqn. 4-48)
x component of total bottom shear stress (eqn. 4-20)
nondimensional x component of total shear stress (eqn. 4-53)
y component of total bottom shear stress (eqn. 4-21)
nondimensional y component of total shear stress (eqn. 4-54)
dimensionless shear stress (Shields parameter, eqn 1-2)
filter phase delay for current meter, a function of w (eqn. 2-2)
angle between the mean current and wave direction (table 5-2)
angular velocity of the Earth (eqn. 4-2)
xiv

angular wave frequency (eqn. 1-12)
angular frequency of periodic input signal to filter (eqn. 2-1)
to
Subscripts:
k layer number (eqn. A-l)
r reference value (eqn. 4-42)
Superscripts:
n time step (eqn. A-l)
* nondimensional value (eqn. 4-42)
' turbulent fluctuation
xv

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
SIMULATION AND ANALYSIS OF SEDIMENT RESUSPENSION
OBSERVED IN OLD TAMPA BAY, FLORIDA
By
DAVID HENRY SCHOELLHAMER
May 1993
Chairman: Y. Peter Sheng
Major Department: Coastal and Oceanographic Engineering
A comprehensive field and numerical modeling study was conducted
to improve the understanding and numerical modeling of sediment
resuspension and the vertical transport of resuspended sediment in the
shallow estuarine environment. Sediment resuspension was
intermittently monitored in Old Tampa Bay from 1988 to 1990. The data
indicate that net sediment resuspension was caused by depth-
transitional wind-waves that were generated by strong and sustained
winds associated with storm systems and not by tidal currents.
A vertical one - dimensional numerical model was modified and used
to help analyze the Old Tampa Bay sediment resuspension data and to
help determine significant sediment transport processes in Old Tampa
Bay. The model was modified to include viscous effects, multiple wave
frequencies, variable bottom roughness regimes, and spatially-averaged
grain shear stress. The model successfully simulated steady flow
profiles with laminar, transitional, and turbulent regions and
turbulent dissipation in the marine surface layer. Simulated shear
xvi

stresses (plotted on an extended Shields diagram) were in agreement
with observed critical conditions for sediment motion under combined
wave and current motion on the continental shelf. Energy spectra
produced from 1-Hz velocity data collected in Old Tampa Bay can be
reproduced by the model. Calibrated settling and erosion coefficients
for the model are reasonable compared to values from other studies.
Only the finer particles in the bed appear to be resuspended, and sand¬
sized particles are probably intermittently transported as bed load.
Simulation results indicate that the settling velocity of resuspended
sediments was greater in November 1990 than March 1990, probably
because larger particles were eroded by larger shear stresses or there
was more fine material in the form of fecal pellets in November 1990.
Simulation results also indicate that the bottom sediments were more
erodible in March 1990 than November 1990. Reduced biological binding
of the fine bed sediments probably increased bottom sediment
erodibility in March 1990.
xvix

CHAPTER 1
INTRODUCTION
Estuaries are transition zones between riverine and marine
environments. Potential sources of sediment particles for an estuary
include rivers, net sediment flux from the marine environment, overland
runoff, and anthropogenic point sources. Sediment particles are
commonly trapped and deposited in the deeper parts of an estuary. The
bed sediment affects the overall health of an estuary in several ways.
Bed sediment, especially fine sediment, can be resuspended up into the
water column where it may reduce the amount of light penetrating the
water column, may act as a source for constituents adsorbed onto the
sediment, and may be transported to undesirable locations. The
reduction of light in the water column may adversely affect biological
communities. Adsorbed constituents that can be released to the water
column during suspension and possibly while on the bed include
nutrients which may contribute to eutrophication of the estuary, heavy
metals, pesticides, and organic carbons that may decrease the
productivity of the estuary. Resuspended sediment may be transported
throughout the estuary and spread the adverse effects and possibly
become deposited in undesirable locations, such as shipping channels,
turning basins, and marinas. Thus, the overall health of an estuarine
environment is partially dependent upon the resuspension, transport,
and deposition of sediment.
Numerical models can be used to study and predict sediment
dynamics in an estuary. An accurate numerical model must include
1

2
algorithms that represent significant hydrodynamic and sediment
transport processes which may be identified from comprehensive field
data. Governmental regulators could use a sediment model to help
predict the effect of proposed anthropogenic alterations to an estuary
on light attenuation, transport and fate of toxic substances, and
sedimentation. Potentially adverse alterations include increased
wastewater discharge, increased stormwater runoff, dredging, dredge
material disposal, and wetland destruction. Because sediment particles
are negatively buoyant and settle, accurate sediment models must
consider vertical sediment dynamics. Two obstacles, however, limit
application of sediment models. Field data are needed to calibrate and
validate estuarine sediment models, and the bottom boundary conditions
for the sediment must be specified.
Improved understanding and simulation of estuarine sediment
processes are dependent upon reliable field data. The importance of
the processes that potentially control sediment dynamics must be
understood and included in a realistic model. For example, if wind-
waves are an important sediment resuspension mechanism, then a model
that ignores water motions at wind-wave frequencies can not
realistically simulate estuarine sediment transport. Laboratory
studies can be used to improve understanding of sediment transport
process, but field conditions are often difficult to recreate in the
laboratory. Reconstruction of realistic sediment beds in a laboratory
is difficult, especially when the natural sediments are biologically
active. A field data collection program has far less control than
found in a laboratory, but the data and insights gained in the field
are directly applicable to the estuary being studied. Calibration is
the selection of model parameters that permit the model to accurately

3
simulate field data. Once selected, validation may be performed on an
independent data set to prove that the model algorithms and model
parameters can be used to make reliable predictions. Field data is
therefore required to develop a predictive model in which managers,
scientists, and the public can have confidence.
Sediment transport processes at the interface of the water column
and bottom sediments must be accurately simulated in a numerical model
because the bed is an omnipresent potential source and sink of
suspended sediment. A particle resting on the bed will move (erode)
when the lift force generated by the hydrodynamics is sufficiently
large. If a particle moves by rolling, sliding, or saltating
(jumping), then it contributes to the bed load. A mobilized particle
may also become suspended (or resuspended) in the water column.
Interaction of suspended particles may be caused by salt flocculation
of clay minerals and formation of large aggregates of organically bound
inorganic particles. Deposition is the process that returns particles
to the bed. The sedimentary processes of initiation of particle
motion, bed load, and deposition all occur at or near the interface of
the sediment bed and the water column. Other near-bed factors which
may affect hydrodynamics and sediment transport include bed forms,
armoring, porous beds, suspended-sediment stratification, and
biological activity.
The purpose of this research was to improve the understanding and
numerical modeling of sediment resuspension and the vertical transport
of resuspended sediment in the shallow estuarine environment. Field
data and a numerical model were used to accomplish this task. From
1988 to 1990, the author collected sediment resuspension data during
potential periods of resuspension in Old Tampa Bay, a shallow estuary

4
on the west-central coast of Florida. These field data were analyzed
by the author to determine the sediment resuspension mechanisms in Old
Tampa Bay. The author modified and used a vertical one-dimensional
model to simulate the Old Tampa Bay data and other data. The numerical
model was used as a tool to help analyze the Old Tampa Bay data and to
help determine significant sediment transport processes in Old Tampa
Bay.
The remainder of this chapter discusses existing literature on the
significance of estuarine sediments, sediment transport processes,
field studies related to estuarine sediment transport, numerical models
applicable to estuarine sediment transport, and the relation between
previous studies and this research. The data collection methodology
is discussed in chapter 2, and the data are presented and analyzed in
chapter 3. The numerical model is described in chapter 4. Numerical
simulations of the marine surface layer and critical shear stresses on
continental shelves were conducted to test modifications made to the
model during this research, and these simulation results are presented
and discussed in chapter 5. Simulations of suspended-solids
concentrations in Old Tampa Bay are presented and discussed in chapter
6. Conclusions of this study are summarized in chapter 7.
Significance of Estuarine Sediments
Bottom sediments are an omnipresent factor that affect the water
quality and biological productivity of an estuary. Potential sources
of sediment particles for an estuary include rivers, net sediment flux
from the marine environment, overland runoff, and anthropogenic point
sources. Sediment particles are commonly trapped and deposited in the
deeper or vegetated parts of the estuary. Bed sediments provide the
substrate for benthic organisms, seagrasses, and marshes, and chemical

5
exchange processes occur between the bed sediments and the water
column. Bed sediments, especially fine sediments, can be resuspended
up into the water column where they may 1) increase nutrient
concentrations, 2) transport trace metals, 3) influence the mortality,
life cycle, food supply, and photosynthesis of estuarine species, and
4) may move and settle in ports or marshes.
Bed sediments chemically interact with the overlying water column
and benthic biological communities. Diffusive fluxes between the bed
sediments and water column commonly remove dissolved oxygen from the
water column (Hinton and Whittemore 1991, Svensson and Rahm 1991) and
recycle nutrients to the water column (Callender and Hammond 1982,
Hammond et al. 1985, Simon 1988, Ullman and Aller 1989). In addition,
sediment geochemistry in seagrass beds determines the limiting nutrient
for seagrass growth (Short 1987).
The release of nutrients from sediments to the water column is
enhanced during resuspension events. Increased nutrient concentrations
in the water column that were caused by resuspension events have been
observed by Gabrielson and Lukatelich (1985) during wind related
sediment resuspension events in the Peel-Harvey estuarine system in
Australia, by Fanning et al. (1982) during storms on the continental
shelf of the Gulf of Mexico, and by Schwing et al. (1990) after
destabilization of bottom sediments by a seiche in Monterey Bay,
California. Grant and Bathmann (1987) found that bacterial mats
deposit sulfur on surficial bottom sediments and that resuspension is
an important mechanism for returning sulfur to the water column.
Phytoplankton and organic detritus resting on the bottom can also be
resuspended and impact estuarine productivity (Roman and Tenore 1978,
Gabrielson and Lukatelich 1985). The supply of Radon 222, a tracer, to

6
the water column from resuspension flux and diffusion flux is about the
same in the Hudson River estuary (Hammond et al. 1977). Simon (1989)
estimates that one resuspension event in the Potomac River that lasts
minutes can add as much ammonium to the water column as the diffusive
flux can in 5 to 1000 days, depending upon the site. Laboratory
experiments show that typical water column concentrations of
particulate nutrients would double in a few hours during a resuspension
event (Wainright 1990) and that biological growth is increased when
resuspended material is added to microcosms (Wainright 1987) .
In addition to nutrients, trace metals and other contaminants may
be adsorbed to sediment particles and these contaminants are
detrimental to the biological health of many estuaries. For example,
metals are partitioned between adsorbed and dissolved phases, so the
transport of metals is related to sediment transport (Dolan and Bierman
1982, Li et al. 1984, Horowitz 1985). In South San Francisco Bay,
availability of trace metals may be a factor that limits growth of some
phytoplankton species, sorption processes influence dissolved
concentrations of metals, and sorption processes vary among specific
metals (Kuwabara et al. 1989). Sediment concentrations of trace
metals, PCBs, pesticides, or polynuclear aromatic hydrocarbons exceed
the median concentration associated with biological effects in
estuaries in Alaska, California, Connecticut, Florida, Hawaii,
Maryland, Massachusetts, New Jersey, New York, Oregon, Texas, and
Washington (Long and Morgan 1990).
The mortality, food supply, and life cycle of some estuarine
species may be affected by suspended sediments and sediment transport
processes. For species restricted to the benthos, mortality may be
increased by resuspension or burial and sediment transport may regulate

7
the food supply to both suspension and deposit feeders (Nowell et al.
1987). Eggs, cysts, and spores of many zooplankton and phytoplankton
species reside in bottom sediments and erosion may inject them into the
water column where they may hatch. Circumstantial evidence indicates
that this process may contribute to red tide outbreaks (Nowell et al.
1987). Sellner et al. (1987) found that increased suspended-sediment
concentrations reduced the survival rate of newborn larval copepods in
Chesapeake Bay. In addition, development and reproduction of survivors
was inhibited.
Suspended sediments reduce the sunlight available for
photosynthesis. Smaller particles are more efficient light attenuators
(Baker and Lavelle 1984, Campbell and Spinard 1987). McPherson and
Miller (1987) found that non-chlorophyll suspended material is the most
important component of light attenuation in Charlotte Harbor, Florida.
Inorganic suspended material is the dominant cause of light attenuation
in several New Zealand estuaries (Vant 1990) and sediment resuspension
by tidal currents and wind waves is an important cause of attenuation
(Vant 1991). In the coastal waters of northwest Africa, light
attenuation is greatest in nearshore waters where sediment
concentrations are greatest, compared to offshore waters, and nearshore
light attenuation reduces phytoplankton growth (Smith 1982). The
reduction of light in the water column reduces seagrass photosynthesis
and the maximum depth at which seagrasses can grow (Dennison 1987) .
Resuspended sediments may move throughout the estuary, depending
upon the circulation, and, in addition to possibly spreading the
adverse effects already mentioned, may deposit in ports or marshes.
Large man-made basins that serve as ports and marinas are commonly
depositional environments that require costly maintenance dredging

8
(Granat 1987, Kobayashi 1987, Headland 1991). Estuarine sediments may
also deposit in marshes where vegetation and benthic algae impede water
motion and resuspension and enhance deposition, formation, and
maintenance of an important habitat (Ward et al. 1984, Krone 1985, Huh
et al. 1991) .
Sediment Transport Processes
Sediment transport processes differ somewhat depending on whether
the sediment is noncohesive or cohesive. Noncohesive sediment
particles do not interact electro - chemically with other particles, and
cohesive sediment particles interact electro-chemically with other
cohesive particles. Sediments with a diameter larger than 20 ¡im are
generally noncohesive. Thus, gravel, sand, and coarse silts are
noncohesive. Cohesion increases as particle size decreases below 20 fim
(Migniot 1968), and clay minerals are generally cohesive. Transport of
noncohesive sediments is controlled by the processes of initiation of
particle motion, bed load transport, suspended load transport, and
deposition. Cohesive sediments differ in that they are not transported
as bed load, and interparticle electro-chemical forces may cause
flocculation in brackish estuarine waters. Both cohesive and
noncohesive suspended inorganic particles may adhere to large
organically bound aggregates that can deposit rapidly in an estuary.
Bed and near-bed factors that may affect hydrodynamics and sediment
transport include bed forms, bed armoring, suspended-sediment
stratification, fluid-mud, porous beds, and biological activity.
Initiation of Motion of Bed Sediments
The horizontal transport of noncohesive sediment as bed load and
suspended bed-material load is dependent upon the initiation of motion
of stationary particles in the sediment bed. Particles that roll,

9
slide, or sáltate along or near the bed are part of the bed load, and
particles that are lifted into suspension are part of the suspended
load. Initiation of particle motion has been reviewed by the Task
Committee on Preparation of Sedimentation Manual (1966) , Vanoni (1975) ,
Miller et al. (1977), Simons and Senturk (1977), and Lavelle and
Mofjeld (1987a, 1987b).
A noncohesive particle lying on a sediment bed, for which fluid is
flowing above, will be acted upon by the hydrodynamic forces of lift
and drag in addition to gravity and normal forces from adjacent
touching particles. Vanoni (1975, pp. 92-93), Simons and Senturk
(1977, pp. 400-407), Yalin (1977), and Wiberg and Smith (1987) describe
the forces acting on a bed particle in detail. The formulation of the
hydrodynamic forces will differ depending on whether the flow over the
particle is laminar or turbulent and whether the bed is composed of
uniform or heterogeneous particles. If the hydrodynamic forces exceed
a threshold or critical value, then the particle will move. Particle
motion may also be initiated by organisms that disturb the bottom
sediments and by trawling in coastal waters (Churchill 1989) .
Because the exact geometry, size, and shape of every sediment
particle in a bed can not be determined, practical analysis of the
problem of initiation of particle motion requires assuming that the bed
is a continuum of particles instead of a large quantity of discrete
particles. Noncohesive sediment particles are usually assumed to be
spherical. The particle sizes (measured by sediment particle diameter
dg) that are present in an actual bed will vary vertically and
horizontally, but it is commonly represented as one or more sizes for
which a certain percentage N of the bed material is finer (denoted as

10
d^j) . The physical properties of the sediment particles at a fixed
location also will vary with time as particles are transported.
In addition to sediment particle properties, the flow field will
vary spatially and temporally. The shear force exerted by the flow on
the bed is commonly used to indicate the magnitude of the hydrodynamic
force on the bed. Because most natural flows are turbulent and
turbulent flows fluctuate in space and time, the bottom shear stress at
a fixed point will vary about the mean bottom shear stress. The bottom
shear stress will also vary spatially, especially if bed forms are
present. For example, for three-dimensional ripples, Ikeda and Asaeda
(1983) found that sediment is eroded from the side slopes of
longitudinally trailing ridges by lee side eddies and that sediment
entrainment is correlated with intermittent bursts of the lee side
eddy.
If the bed is assumed to be a continuum of particles, the
inception of particle motion is a stochastic rather than a
deterministic process because the particle sizes and bottom shear
stress vary spatially and temporally (He and Han 1982). Usually, the
existence of particle motion is determined by assuming a threshold
shear stress or threshold velocity. Definitions of threshold have been
categorized by Lavelle and Mofjeld (1987a) as those based on sediment
flux in a flume, visual flume observations (Kramer 1935, White 1970,
Mantz 1977), erosion rate experiments for cohesive sediments
(Partheniades 1965, Ariathurai and Arulanandan 1978, Sheng and Lick
1979, Kelly and Guiarte 1981, Parchure and Mehta 1985), and field
measurements in marine environments (Sternberg 1971, Wimbush and Lesht
1979, Lesht et al. 1980, Larsen et al. 1981). Because of the
stochastic nature of the inception of particle motion problem, however,

11
some particle motion will still occur below the threshold values
(Einstein 1941, 1966, Taylor and Vanoni 1972, Vanoni 1975, Christensen
1981, Lavelle and Mofjeld 1987a). The concept of threshold is useful
for practical problems (Simons and Senturk 1977 pp. 417-487, Blaisdell
et al. 1981, Blaisdell 1988) and when ability to observe particle
motion is limited in the field (Sternberg 1971, Wimbush and Lesht 1979,
Lesht et al. 1980). Threshold criteria should only be applied with the
knowledge that initiation of particle motion is a stochastic process.
The most common threshold criterion is probably that presented in
the Shields diagram as modified by Rouse (fig. 1-1) (Vanoni 1975 p. 96,
Simons and Senturk 1977 p. 410). The Shields threshold criterion was
determined by extrapolating measured transport rates of laboratory
experiments to the point of zero transport for fully developed
turbulent flows, noncohesive sediments, and flat beds. The abscissa is
the boundary Reynolds number
R* “ u* ds / " d-D
y2
in which U, is the shear velocity for which U, = (t / p) where r is
* J ' o o
the bottom shear stress and p is the fluid density, and v is the
kinematic fluid viscosity. The curve for R^ less than two was
extrapolated by Shields and is not based upon data. The ordinate is a
dimensionless shear stress or Shields parameter
* (7s'7) ds
(1-2)
in which 7s is the specific weight of the sediment particle and 7 is
the specific weight of the fluid. The line on figure 1-1 indicates the
critical condition for sediment motion. If (R^.r^) is below the line,
then there is no sediment motion, and if (R t^) is above the line,
then there is sediment motion.

DIMENSIONLESS SHEAR STRESS,
12
0.2 0 4 0.6 t.O 2 4 6 8 10 20 40 60 100 200 500 1,000
BOUNDARY REYNOLDS NUMBER,
Figure 1-1
Shields critical shear stress diagram, from Vanoni (1975).

13
Several modifications to the Shields diagram have been proposed
because the bottom shear stress is included on both axes of the
diagram, so an iterative procedure must be used to determine the
critical shear stress for a given particle. The Task Committee on
Preparation of Sedimentation Manual (1966) added the quantity
d _s n c
— [ 0.1 ( - 1) g d ]
u 1 7 b s
to the diagram in which g is the acceleration of gravity. Yalin
(1977), Bonnefille (see Vollmers 1987) and Gessler (1971) regrouped the
dimensionless variables to make the diagram easier to use.
The Shields diagram also has been modified to account for bed
forms and small boundary Reynolds numbers. Gessler (1971) adjusted
Shields diagram because some of Shields' flume experiments formed
ripples and small dunes that increased the critical shear values by 10
percent. Inman (1963) shows a second curve for rippled beds. Shields
diagram was extended for values of less than 2 by Miller et al.
(1977) (mostly with data from White (1970)) with an envelope
encompassing the data scatter and by Mantz (1977) with a power function
that lies inside the envelope (Larsen et al. 1981). The extended
Shields diagrams are applicable to noncohesive fine sands and silts.
Although the Shields diagram was developed for unidirectional
flows, it also may be applicable to the estuarine and marine
environments. Field observations in oscillatory flow environments have
been in good agreement with the Shields criterion (Davies 1985) .
Madsen and Grant (1977) stated that Shields diagram is applicable to
locations with both waves and currents and good agreement with data in
such environments was observed by Drake and Cacchione (1986). Field
measurements in Puget Sound by Sternberg (1971) were in good agreement

14
with the Shields diagram modified to account for ripples presented by
Inman (1963). Larsen et al. (1981) found that the extended Shields
diagram was in good agreement with observed threshold grain motion for
oscillatory flows on a continental shelf.
Other threshold relations have been developed for noncohesive
sediments. Lane (1955) used field data to develop curves of critical
shear stress vs. mean particle diameter, which give higher critical
shear stresses than Shields' diagram. Sundborg (1956) developed a
threshold criterion based on particle size and mean velocity 1 meter
above the bed, and Inman (1949, 1963) developed a criterion that is
dependent on particle size and shear velocity, both of which agree with
Puget Sound data (Sternberg 1971). Wiberg and Smith (1987) derived a
critical shear stress equation for beds with uniform particle size that
corresponded closely to Shields' diagram. In addition, they also
derived a critical shear stress equation for heterogeneous beds that
was in good agreement with experimental data.
For cohesive sediment beds, the consolidation of the bed is an
important factor that helps determine whether and how the bed sediment
will move. When initially deposited, cohesive sediment beds are
unconsolidated high concentration suspensions (fluid-mud) and have
little shear strength. Consolidation is a time dependent function of
the overbearing pressure, particle size, and of the clay mineralogy
that dewaters, compresses, and strengthens the bed (Meade 1966,
Terzaghi and Peck 1967 p. 84, Hayter 1986). Therefore, there is no
general threshold of motion criterion for cohesive sediments such as
the Shields diagram for noncohesive sediments. Critical shear stresses
for various cohesive sediments and consolidation states have been
determined in the laboratory (Partheniades 1965, Ariathurai and

15
Arulanandan 1978, Sheng and Lick 1979, Thorn and Parsons 1980, Kelly
and Guiarte 1981, Mehta et al. 1982) and the field (Gust and Morris
1989). Three modes of initial motion of cohesive sediments are re¬
entrainment of unconsolidated high concentration suspensions, surface
erosion of individual particles and floes, and bulk erosion (also
called mass erosion) which is the sudden failure of the upper part of
the bed (Krone 1986, Mehta et al. 1989a).
Bed Load Transport
If a particle moves by rolling, sliding, or saltating (jumping),
then it contributes to the bed load. Determining whether a particle
that is not in contact with the bed is contributing to the bed load or
suspended load can be difficult (Einstein 1950, Bagnold 1966, Murphy
and Aguirre 1985) . Bed load usually is composed of sand-sized and
coarser particles. Fine sediments (silts and clays) are usually
immediately suspended upon initiation of motion and are not transported
as bed load.
Calculation and measurement of bed load are difficult. Reviews of
equations for calculating bed load have been presented by Vanoni (1975,
pp. 168-172), Simons and Senturk (1977, pp. 508-543), Yalin (1977),
Gomez and Church (1989) (for gravel beds only), Ludwick (1989), and
Stevens and Yang (1989) . Bed load transport equations were compared by
van Rijn (1984a), who concluded that predicted bed load transport rates
are accurate only within a factor of 2. Gomez and Church (1989)
assessed bed load equations for gravel beds and determined that none of
the reviewed equations consistently performed well. Carson (1987)
evaluated several factors used to estimate bed load in alluvial
channels and determined that the grain component of the bed shear
stress (shear stress corrected for sidewalls and bed forms) is a better

16
predictor of bed load than mean velocity, stream power, and unit stream
power. The bed load transport rate is related to the grain component
of the bed shear stress so this quantity should be used in bed load
formulas when bed forms are present (Wiberg and Smith 1989). Field
measurements of bed load are discussed by Emmett (1980), Edwards and
Glysson (1988), and Ludwick (1989), but bed load is difficult to
measure because any device placed near the bed may disturb the flow and
the rate of bed load transport.
Erosion and Bottom Shear Stress
The rate at which particle motion is initiated is an important
quantity for studies and numerical models of sediment transport, van
Rijn (1984b) developed a sediment pick-up function (mass per unit area
per unit time) by utilizing a mechanical device (a sediment lift) at
the bottom of a flume to supply erodible noncohesive particles and
compared the developed sediment pick-up function to the sediment pick¬
up functions by Einstein (1950), Yalin (1977), Nagakawa and Tsujimoto
(1980), de Ruiter (1982), and Fernandez-Luque (see van Rijn 1984b).
Bed load and suspended load transport rates calculated with the
developed sediment pick-up function compared well with field and
laboratory data (van Rijn 1986b). Noncohesive particles that are
picked up are initially saltating and will either contribute to the bed
load or suspended load (Murphy and Aguirre 1985) .
Quantification of the erosion of cohesive sediments is difficult
because of the lack of understanding of erosion mechanisms and the
numerous factors involved. Thus, the erosion relationships that have
been developed are simple relationships that contain coefficients that
must be determined in the laboratory or field. Assuming that the rate

17
of surface erosion is proportional to the
gives (Ariathurai and Arulanandan 1978)
E = M
r
nondimensional
excess
shear
(1-3)
c
in which E is the surface erosion rate in mass per unit area per unit
time, M is an erosion rate constant defined as 'the increase in the
rate of erosion for an increase in the interface fluid shear by an
amount equal to the critical shear stress of that soil' (Ariathurai and
-2 -1
Arulanandan 1978) that has a range of values from 0.003 g cm min to
-2 -1
0.03 g cm min , r is the bottom shear stress, and is the critical
shear stress for erosion. For shear stresses less than the critical
value, no surface erosion occurs. Equation 1-3 was developed using
data from placed beds with uniform shear strength which is not
representative of cohesive beds in nature (Mehta et al. 1982). Erosion
functions by Mehta et al. (1982) and Parchure and Mehta (1985) were
determined using more realistic laboratory sediment bed conditions.
Equation 1-3 has been applied in numerical models of cohesive
sedimentation (Ariathurai and Krone 1976, Thomas and McAnally 1985,
Sheng et al. 1990b, Uncles and Stephens 1989). Because equation 1-3 is
an empirical erosion formula, it is not limited to cohesive sediments,
and it has been used to simulate transport of noncohesive suspended
sediments in the lower Mississippi River (Schoellhamer and Curwick
1986) .
A general erosion equation is determined by setting the erosion
rate equal to a power of the excess shear stress
E = q |r|^ (1-4)
in which a and r¡ are constants that are determined by calibration.
Values of a have been found to range from 1.9x10 ^ to 3.7x10 ^, for t

18
in dynes/cm2, and r¡ has been found to range from 0.23 to 10 (Lavelle et
al. 1984). Lavelle et al. (1984) used equation 1-4 to simulate erosion
as a stochastic process (Lavelle and Mofjeld 1987a).
The erosion rate is dependent upon the shear stress applied to the
bed by the flowing water and the bottom shear stress from the near-bed
velocity. Schlichting (1969) gave velocity profile equations for
turbulent flow in the near-wall region for hydraulically smooth, rough
and transitional cases. Given a measured or simu.ated velocity
profile, these equations can be used to calculate the bottom shear
stress. In general, the velocity distribution is
— = - ln(z/k ) + B (1-5)
U . K S
•k
in which u^_ is the shear velocity for which t = p u2, the velocity u is
at an elevation z above the bed, k. is von Karman’s constant (0.4), kg
is the height of the bottom roughness elements, and B is a roughness
function that has the form
u , k u k
B = s log ——- + b = 7T In ——- + b (1-6)
in which u¡,„ks/i' is a roughness Reynolds number (R) , and s and b are the
slope and intercept of a line that fits a segment of the data presented
in figure 1-2 (Schlichting 1969 fig. 20.21), which is a plot of B vs.
log R developed from laboratory data. The boundary is smooth for R <
5, rough for R > 70, and transitional for intermediate values of R.
For a smooth wall, s = 5.75 and b = 5.5, and equations 1-5 and 1-6 can
be written as
i In (9.03 z u* / v) (1-7)
â– k
For a rough wall s = 0.0 and b = 8.5 and equations 1-5 and 1-6 can be
written as
In (30 z / k )
UL /Í S
(1-8)

19
5
02 OA 0.6 0.8 7.0 1.2 7A 1.6 1.8 ZB 22 ZA ZB ZB 10 32
/„ v' ks
l09 -p—
Figure 1-2, Roughness function B in terms of Reynolds number, from
Schlichting (1969).

20
for which the elevation with zero velocity is ZQ=ks/30. Equations 1-5
and 1-6 can be combined to derive a general expression for the
elevation with zero velocity
z = k r-ks/2-3 e'Kb (1-9)
o s
For transitional flow regimes, figure 1-2 and equations 1-5 and 1-6
must be applied in an iterative manner.
If the velocity used to calculate the bottom shear stress is from
the near-bed region of a hydraulically smooth (R < 5) or transitional
flow (5 < R < 70), the velocity profile may not be logarithmic near the
bed and a different velocity profile equation is applicable. Reichardt
(see Wiberg and Smith 1987) developed a velocity distribution equation
that gives a linear profile for elevations much smaller than the top of
the viscous sublayer, a logarithmic profile for elevations much larger
than the top of the viscous sublayer, and a smooth and accurate
transition between the two regions. This velocity distribution is
u* +
u = ~ [ ln(l+/cz )
(ln(zQ) + ln(/c)) (1 - e
â– z+/11.6
z+ -0.33z+. ,
e ) ]
11.6
(1-10)
in which the nondimensional quantities z = u^z/u and zq — u^z^/v.
The bottom roughness is dependent upon grain size in the bed and
bed forms. The bottom roughness element that controls the resistance
in the region of the water column adjacent to the bed is the grain
roughness and above this region the roughness is controlled by larger
roughness elements such as ripples, dunes, or surface irregularities
caused by bioturbation (Smith and McLean 1977). The grain roughness is
normally related to the bed sediment size distribution.

21
Two types of shear stresses, the total shear stress and the grain
shear stress, can be considered. The total shear stress is the shear
stress exerted on the flow by all of the bottom roughness elements.
The grain shear stress is the spatially-averaged (over a bed form
wavelength) shear stress exerted on the sediment particles in the bed
by the flow. The grain shear stress is less than the total shear
stress. Sediment motion is dependent upon the grain shear stress
(Vanoni 1977, McLean 1991).
If the height and wavelength of the bed forms are constant, then
the matching elevation at which the velocities from the two regions are
equal can be calculated based on the bed form geometry (Smith and
McLean 1977). Smith and McLean (1977) measured velocity profiles at
several positions on dunes in the Columbia River and showed that the
spatially-averaged (or "zero-order") velocity profile could be
constructed from equation 1-5. The zero-order velocity profile
averages near-bed velocity variations caused by the bed forms and the
resulting total shear stress and grain shear stress are spatially-
averaged values. Expressions for the bottom roughness due to bed forms
have been developed by van Rijn (1984c) for steady flow in alluvial
channels and by Grant and Madsen (1982) for oscillatory flow.
For an oscillatory flow, a simple expression for the maximum
bottom shear stress is (Jonnson 1967)
(1-11)
in which f is a friction factor and
(1-12)
is the maximum bottom orbital velocity from linear wave theory, where a
is the wave amplitude, k is the wave number, w is the angular wave
frequency, and h is the water depth. Shallow-water waves are assumed
Tw -f% IV
_ gak
d u> cosh(kh)

22
to be present for kh < n/10 and deep-water waves are present for kh > n
(Dean and Dalryraple 1984). Equations and diagrams for the friction
factor f as a function of the wave properties and bottom roughness have
been determined empirically (Jonsson 1967, Kamphius 1975). For waves
in the absence of a mean current and for rough turbulent flow, Grant
and Madsen (1979, 1982) determined that the friction factor is given by
f - 0.08 / [Ker2 (2/f) + Kei2(2TO] (1-13)
in which Ker and Kei are Kelvin functions of zero order and
k. u 72
f = ^ 75 (1-U)
30 « u^ yf
in which is the bottom roughness. The friction factor appears on
both sides of equation 1-13, so the equation must be solved
iteratively. Equation 1-13 is valid for rough turbulent flow for which
Ab/kb > 1 where A^=u^/cj is the orbital amplitude just above the
boundary layer. Bottom stress in oscillatory boundary layers (e.g.
Jonsson and Carlsen 1976) has also been computed with turbulent
boundary layer models (Sheng 1984, Sheng and Villaret 1989).
A potentially important resuspension mechanism in estuaries is the
nonlinear interaction of a wave field and a mean current that can
increase the shear stress on the bed to a value greater than the sum of
the wave only and current only shear stresses. Grant and Madsen (1979)
developed a model to estimate the bed shear stress when waves and
current are present. The model is based on the assumption of rough
turbulent flow that is wave dominated. They also developed a model
that includes ripple formation and the effect of ripples on the bed
shear stress (Grant and Madsen 1982). Weaknesses of the Grant and
Madsen models include the introduction of a fictitious reference
velocity at an unknown level, a rather arbitrarily estimated thickness

23
of the wave boundary layer, and the model being valid only for wave
dominant cases (Christoffersen and Jonsson 1985) . The Grant and Madsen
models also assume that 1) the thickness of the logarithmic layer is
constant, which is not correct when waves are present (Sheng 1984), 2)
the wave field can be represented by a single wave period and wave
height, and 3) the eddy viscosity is linear and time invariant.
Cacchione et al. (1987) found that the shear stress and bottom
roughness estimated by the moveable bed model were in good agreement
with estimates from measured velocity profiles, but no bottom
photographs were available to check the estimated bed form geometry.
Drake et al. (1992) took bottom photographs and found that the moveable
bed model overestimated the size of bottom ripples. Larsen et al.
(1981) present a simpler solution for the model formulation by Grant
and Madsen (1979) that is applicable to smooth, transitional, and rough
bottom roughness regimes and the shear stress at the observed threshold
of motion of noncohesive sediments observed in the field was in good
agreement with Shields diagram. The results of the Larsen et al.
(1981) model and the Grant and Madsen (1979) model are virtually
identical for rough bottoms. Simpler wave-current models that compare
well with laboratory data have also been developed by Christoffersen
and Jonsson (1985) for wave and current dominated cases and by Sleath
(1991) for wave-dominated cases and rough beds. All of the above
models consider wave - averaged bottom stresses by invoking some sort of
a priori parameterization of wave-current interaction.
Wave-current interaction in bottom boundary layers has also been
studied without such a priori parameterization. Sheng (1984) used a
Reynolds stress turbulence model to simulate the detailed dynamics of
the boundary layer over the wave cycle by using a small time step

24
(1/100 of the wave cycle) and specifying the mean and orbital currents
at the outer edge of the boundary layer. The results were then
averaged over the wave cycle to produce wave - averaged stresses. Sheng
(1984) found that the model of Grant and Madsen (1979) generally
overestimated the wave - averaged stress and apparent roughness height.
Suspended Load Transport
Suspended sediment is transported by the flow in the water column.
The Reynolds time - averaged equation for three-dimensional sediment
transport, written in tensor notation, is (Vanoni 1975)
3c
3c
3t + Uj 3Xj
3u! c'
i
3x.
J
(1-15)
in which c is the mean suspended-sediment concentration, u is the mean
velocity of the sediment particles, c' is the turbulent fluctuation of
sediment concentration about the mean, u' is the turbulent fluctuating
velocity of sediment particles, t is time, and x is the coordinate
axis. The first term in equation 1-15 represents the time rate of
change of sediment concentration, the second term represents the
advection and settling of particles, and the term on the right hand
side represents the turbulent dispersion of particles. The second
order correlation of velocity fluctuation and concentration fluctuation
is often represented as the product of the mean concentration gradient
and an eddy diffusivity K such that (Vanoni 1975)
ÜÍZ7 = - K Is (1-16)
i v. 3x.
i i
The eddy diffusivity is often assumed to be proportional to the eddy
viscosity A (K =BA ) which is often assumed to be related to mean flow
variables (Fischer et al. 1979) or to have a particular distribution
(Vanoni 1975, Fischer et al. 1979). Eddy diffusivity also can be

25
calculated with an advanced turbulence closure algorithm (Sheng 1986a,
Celik and Rodi 1988, Sheng and Villaret 1989).
An analytic expression for the vertical distribution of suspended
sediment in an open channel can be derived from equations 1-15 and 1-
16. Assuming that lateral and longitudinal variations are small and
that the mean vertical water velocity is small, equation 1-15 reduces
to the vertical conservation of mass equation for sediment
3c 3 . ——
— = — (w c - w' c )
3t 3z s
(1-17)
in which w^ is the terminal settling velocity of sediment particles and
z is the vertical coordinate axis (Vanoni 1975) . The first term within
the parenthesis is the settling flux of sediment and the second term is
the vertical flux of sediment (usually upward) caused by turbulence.
For steady flow and a parabolic distribution of the eddy diffusivity,
equations 1-16 and 1-17 can be used to derive the Rouse equation
/ h-z a .Z
c = c ( -— )
a z h- a
(1-18)
in which z is the elevation above the bed, c^ is the suspended-sediment
concentration at a usually small reference elevation a above the bed,
and the exponent Z is the Rouse number equal to w /(/3/cu^) (Vanoni
1975). Equation 1-18 gives a suspended sediment distribution that is
greatest near the bed, as is expected due to the negative buoyancy of
sediment particles. In addition, the vertical gradient of suspended-
sediment concentration is greatest near the bed. The water velocity is
small near the bed compared to the vertically-averaged velocity, so the
dissimilar distributions of suspended sediment and velocity must be
considered when calculating the suspended load in a river (Schoellhamer
1986, McLean 1991).

26
Flocculation and Aggregation
Salt flocculation of clay minerals and formation of large
organically bound aggregates of inorganic particles may occur in the
water column, especially in estuaries. Clay minerals transported to
estuaries by rivers encounter high cation concentrations that reduce
repulsive forces that prevent flocculation in freshwater. Particle
cohesion begins at salinities of 0.6 to 2.4 ppt, depending on the clay
mineralogy, and increases with salinity up to about 10 ppt, although
the rate of increase is small for salinities greater than 3 ppt (Krone
1962, Mehta 1986). Seawater has salinity of about 34 ppt.
Flocculation has been observed for clay concentrations as low as 50
mg/L (Ozturgut and Lavelle 1986). As a floe grows, the density,
settling velocity, and shear strength of the floe decrease (Krone
1986). Turbulence may break up relatively weak floes (Krank 1984).
Meade (1972) states that salt flocculation has been overemphasized in
the literature while biological agglomeration by filter feeding
organisms has not received enough attention.
Suspended material in estuaries and oceans is commonly found in
the form of large aggregates (length scale 0.5 mm or larger), often
called marine snow (Wells and Shanks 1987). In the ocean, large
aggregates are primarily biogenic material (Fowler and Knauer 1986),
but estuarine aggregates are primarily inorganic particles attached to
organic material (Eisma 1986). The primary collision mechanism that
forms large aggregates is differential settling, not Brownian motion or
fluid shear (Hawley 1982, Eisma 1986). Aggregation by organisms may
also be important in estuaries (Meade 1972, Krank 1984, Eisma 1986).
Large aggregates have been observed to remain intact in currents as
much as 50 cm/s in estuaries (Wells 1989), but large aggregates tend to

27
break apart when sampled (Shanks and Trent 1980, Krank 1984, Eisma
1986, Fowler and Knauer 1986). Sampling procedures are limited to in
situ settling columns (Shanks and Trent 1980, Gibbs 1985, Fowler and
Knauer 1986) and photography (Krank 1984, Eisma 1986, Wells and Shanks
1987, Wells 1989). Eisma (1986) and Dyer (1989) state that the size of
the aggregates is limited by the turbulence microscale, which is the
size of the smallest turbulent eddies. The density of large aggregates
decreases with increasing size and the settling velocity and porosity
increases with increasing size (McCave 1975, Hawley 1982, Gibbs 1985).
Settling and Deposition
Particles that are part of the bed or suspended load may settle
through the water column and deposit on the bed. A noncohesive
particle falling in quiescent fluid is affected by the forces of
gravity, buoyancy, and drag. The terminal settling velocity for a
sphere in quiescent fluid is given by Stokes law and Rubey's equation,
which are presented by Vanoni (1975) and Simons and Senturk (1977). A
nonspherical particle, which is common in nature, may have a different
terminal settling velocity. A shape factor defined by Alger and Simons
(1968) can be used to predict settling velocity and settling behavior
of nonspherical particles and shells (Mehta et al. 1980). Terminal
settling velocity equations are for a single particle, but high
concentrations of noncohesive particles, which are most likely to occur
near the bed, may hinder settling and decrease the terminal settling
velocity (Vanoni 1975, Simons and Senturk 1977). The size of suspended
particles tends to decrease with elevation above the bed, so assuming a
single suspended particle size with a single settling velocity may not
be appropriate (McLean 1991) .

28
Deposition of suspended sediments in natural hydrologic systems is
complicated by turbulence. The effective settling velocity of a
particle settling in a vertically oscillating flow will be less than
the terminal settling velocity for the particle in quiescent fluid
because of nonlinear modification of the drag force (Hwang 1990) or
vortex trapping (Nielson 1984). As a particle settles toward the bed,
the turbulence intensity generally increases and, thus, the probability
increases that a turbulent eddy will carry the particle either upward
or downward. The turbulence intensity will decrease very near the bed
and vanish in the viscous sublayer adjacent to the bed. If a particle
passes through the high turbulence zone near the bed, it can then
deposit on the bed. Li and Shen (1975) and Bechteler and Farber (1985)
presented random walk models that stochastically simulate particle
settling. Turbulence, however, is not an independent variable.
Density stratification by suspended sediments can dampen turbulence
(Sheng and Villaret 1989) and reduce the transport capacity of the flow
(McLean 1991).
Because turbulent intensity and the vertical gradient of sediment
concentration are greatest near the bed, near-bed hydrodynamic
processes determine deposition rates. Sheng (1986c) derived a
deposition velocity formula by considering the resistances that
sediment particles experience in various near-bed layers including the
logarithmic layer, vegetation canopy, laminar sublayer, and biochemical
effects. Numerical suspended-sediment transport models that solve
equation 1-15 generally have finer vertical grid resolution closer to
the bed and represent the bottom boundary condition either by setting
the net upward sediment flux equal to an erosion rate minus a
deposition rate (Sheng and Lick 1979, Schoellhamer 1988, Sheng et al.

29
1990a), by estimating a near-bed sediment concentration (van Rijn
1986a, Celik and Rodi 1988, Schoellhamer 1988), or by setting a net
erosion or deposition flux which is dependent on the bottom shear
stress (Thomas and McAnally, 1985).
Estimates of sediment deposition rates in estuaries have been made
with sediment traps and acoustic devices. Interpretation of sediment
trap data is difficult, but sediment traps have been used to estimate
deposition rates (Oviatt and Nixon 1975, Gabrielson and Lukatelich
1985). Bedford et al. (1987) used an acoustic transceiver to measure
near-bed suspended-sediment concentration profiles and calculated
deposition and erosion fluxes over a 3.5 hour period and a tidal cycle
at one site in Long Island Sound.
Large aggregates control settling and are an important mechanism
for transporting material to the bottom of oceans (McCave 1975, Shanks
and Trent 1980, Hawley 1982, Fowler and Knauer 1986) and estuaries
(Wells and Shanks 1987, Dyer 1989). Fowler and Knauer (1986) give a
minimum range of large aggregate settling velocities of 1 to 1000
m/day. Shanks and Trent (1980) measured settling velocities of large
aggregates in Monterey Bay, California, and the northeastern Atlantic
Ocean and found that the range of settling velocities was 43 to 95
m/day.
The settling velocity of depositing cohesive sediments is
dependent upon the sediment concentration. Krone (1962) measured
settling velocities of San Francisco Bay sediment in still water and
determined that the median settling velocity was proportional to the
concentration to the 4/3 power. This is a typical result for settling
column experiments with cohesive sediments (Mehta 1986), probably
because differential settling is the dominant collision mechanism

30
(Farley and Morel 1986). In estuaries, however, collisions caused by
velocity gradients are most important because they form the strongest
aggregates (Krone 1986). Ross (1988, also in Mehta 1989) conducted a
settling column experiment and found that the settling velocity of
Tampa Bay mud increased as the concentration increased up to about 1
g/L, the settling velocity was about constant (about 0.32 mm/s or 27
m/day) for concentrations from about 1 to 10 g/L, and the settling
velocity decreased as the concentration increased above 10 g/L due to
hindered settling.
Deposition of floes of cohesive sediments may be prevented by the
turbulent boundary layer above the bed in which floes may be broken
apart and lifted up into the water column. Krone (1962) conducted
deposition experiments in a recirculating flume from which he
determined that the rate of deposition of cohesive sediment from a
vertically mixed flow is
(1-19)
in which C is the vertically well-mixed suspended-sediment
D = C w (1 - r/r ), r < r
s cr cr
concentration and r is the critical shear stress for deposition that
must be determined by analyzing time series of concentration and shear
stress measured in the laboratory or field. Laboratory experiments
indicate that r is less than r , the critical shear stress for
cr c
erosion. If ; > TCI-’ no deposition occurs, and if r < r , equation 1-
19 will eventually deposit all of the sediment in suspension.
Laboratory experiments by Mehta and Partheniades (1975), however,
showed that a constant fraction of the original suspension will be
maintained in suspension indefinitely for r > r > r . where r . is
y cr mm mm
a minimum shear stress below which all of the suspended sediment will
deposit. Equation 1-19 is an empirical formula for deposition that

31
does not include the near-bed hydrodynamic processes that determine
deposition rates. Equation 1-19 has been used to simulate noncohesive
suspended-sediment transport in the lower Mississippi River
(Schoellhamer and Curwick 1986) in addition to cohesive sediment
transport (Ariathurai and Krone 1976, Thomas and McAnally 1985, Uncles
and Stephens 1989) .
Other Bed and Near-bed Factors
Many bed and near-bed factors may affect hydrodynamics and
sediment transport. These factors include bed forms, bed armoring,
suspended-sediment stratification, fluid-mud, and porous beds. Some of
these factors (bed forms, bed armoring, suspended-sediment
stratification, and fluid-mud) are the result of sediment transport and
affect the hydrodynamics, which, in turn, affect the sediment
transport. Biological activity also affects sediment transport.
One consequence of noncohesive sediment transport can be the
formation of bed forms in riverine (Kennedy 1969, Vanoni 1975, Simons
and Senturk 1977, Yalin 1977) and coastal (Boothroyd 1985)
environments. Bed forms such as ripples and dunes do not occur in
cohesive sediment beds. Bed forms increase the bottom roughness of
open channels compared to flat bed conditions in which the only
roughness elements are the bed sediment particles. Because some of the
total bottom shear stress is caused by the bed forms, the shear stress
applied to the particles will decrease, so the total (grain and form)
critical shear stress for initiation of particle motion will increase
(Vanoni 1975, McLean 1991). On the upstream face of a dune, the grain
shear increases from zero at the reattachment point to a maximum at the
crest (Shen et al. 1990). van Rijn (1984c) used flume and field data
to develop and verify a methodology to predict bed form dimensions and

32
effective hydraulic roughness for steady flow in alluvial channels.
For oscillating flows, Grant and Madsen (1982) present empirical
relations for bed ripple geometry and an expression for the bottom
roughness. Drake et al. (1992), however, found that the Grant and
Madsen empirical relations overestimated ripple height on the Northern
California continental shelf.
An armored or paved bed has finer particles removed from the bed
surface so that only coarser noncohesive particles remain at the
surface thus preventing erosion of finer particles below (Simons and
Senturk 1977, Sutherland 1987). For equilibrium conditions, Jain
(1990) defines an armored bed as having a coarse surface layer that is
inactive (or immobile) and a paved bed as having a coarse surface layer
that is actively eroding and depositing (or mobile). For
nonequilibrium or degrading conditions, the particle - size distribution
of the surficial bottom sediments coarsens and the erosion rate
decreases with time. Therefore, near-bed sediment transport may be
dependent upon the armoring process, especially in alluvial channels.
Dawdy and Vanoni (1986) review several bed armoring and pavement
studies and predictive algorithms. More recently, bed armoring
algorithms have been presented by Karim and Holly (1986) and Park and
Jain (1987).
Near-bed suspended-sediment stratification will affect the
hydrodynamics and, therefore, affect sediment transport processes at
the bed. As previously mentioned, high near-bed sediment
concentrations may hinder settling of particles. Several authors have
found that sediment-laden flows reduced near-bed turbulence intensity
or bottom shear stress in steady and uniform open-channel flows (Vanoni
and Nomicos 1960, Itakura and Kishi 1980, Lau 1983, Julien and Lan

33
1988, Xingkui and Ning 1989). West and Oduyemi (1989) measured
turbulence and near-bed density stratification in an estuary and found
that density stratification damped turbulence. Flume experiments by
Vanoni and Nomicos (1960), however, indicated that the effect of bed
forms on the total bottom shear stress is much greater than the effect
of suspended sediment. Parker and Coleman (1986) found that suspended
sediments may either increase or decrease near-bed turbulence intensity
and bottom shear stress (discussed by Julien and Lan (1988)). Near-bed
stratification in sediment - laden flows may reduce near-bed turbulent
shear stresses and, therefore, reduce erosion rates (Sheng and Villaret
1989) and the sediment-transport capacity of the flow (McLean 1991).
Costa and Mehta (1990) collected hydrodynamic and suspended sediment
data in a high energy coastal environment and found a hysteresis in the
relationship between suspended-sediment concentration and the flow
velocity, with higher concentrations for accelerating flows, due to
near-bed density stratification.
An extreme case of near-bed suspended-sediment stratification is
the formation of an unconsolidated fluid-mud by cohesive sediments
above a consolidated bed in estuarine and near-shore environments. In
this situation, the water column is composed of two layers--a thin
dense non-Newtonian fluid underlying a Newtonian fluid. The fluid-mud
may interact with the overlying fluid. Surface waves cause mud waves
to form in the fluid-mud and the fluid-mud acts to attenuate (dampen)
surface waves (Suhayda 1986, Wells and Kemp 1986, Mehta 1991, Jiang and
Mehta 1992). Suhayda, Mehta, and Jiang and Mehta developed models to
simulate the interaction of the two fluids. Wells and Kemp also point
out that the formation of mud waves can produce significant
reentrainment of the fluid-mud.

34
The bed is commonly assumed to be an impermeable boundary but
water exchange between the bed and water column may advect sediment and
ripples may enhance water exchange at the bed/water column interface.
In an alluvial river water may exchange between the river and pore
space of the alluvium (Bencala et al. 1984) and this water exchange may
transport fine sediments by advection to and from the relatively coarse
alluvium (Jobson and Carey 1989). Thus, advection may be an important
transport process at the bed/water interface for fine, noncohesive
sediments in an alluvial channel. For oscillatory flows over porous
beds in coastal environments, the total water exchange across the
bed/water column interface averaged over the wave period is
significantly greater for rippled beds than for flat beds (Shum 1992).
Benthic biological communities may influence sediment - transport
processes, especially in biologically abundant estuaries. Erosion
rates may be decreased by microbial films and benthic algae that
stabilize sandy sediments (Gabrielson and Lukatelich 1985, Grant et al.
1986, Meadows et al. 1990) and cohesive sediments (Montague 1986).
Tracks made by motile bivalves, however, reduced the critical shear
velocity of fine sandy sediments in a laboratory flume by 20 percent
(Nowell et al. 1981). Fecal mounds from polychaetes and a deposit¬
feeding bivalve in a laboratory flume had a higher critical shear
velocity than ambient cohesionless sediments and were transported as
bed load (Nowell et al. 1981). Sediments that have been bound by
secretions from benthic invertebrates may settle more slowly than
unbound particles when resuspended (Meadows et al. 1990). Seagrasses
reduce bottom orbital velocities of wind-waves and thus reduce erosion
and increase deposition (Ward et al. 1984). Biological effects
frequently are ignored in sediment-transport studies because biological

35
activity is difficult to quantify in the field, difficult to reproduce
in a laboratory, and difficult to incorporate into a numerical model.
Field Studies Related to Estuarine Sediment Transport
Field studies of estuarine sediment transport are often conducted
to determine the mechanisms that control sediment transport processes,
such as resuspension and horizontal transport. Data is collected by in
situ instrumentation, water sample collection and analysis, and/or
bottom sediment sampling and observation. Statistical analysis, time
series analysis, and numerical process models are used to analyze the
data. Field studies provide less control than laboratory studies, but
they are more applicable because of the difficulty recreating natural
conditions in the laboratory. For numerical studies, an initial or
concurrent field study may indicate the processes that must be included
in the numerical model in order to accurately simulate sediment
transport and a field study will provide data for calibration and
validation of the numerical model. Sediment resuspension mechanisms
are often the focus of estuarine field studies because the bottom of
the estuary is an omnipresent potential source of suspended sediment
and many potential sediment resuspension mechanisms are present in the
estuarine environment. The potential sediment resuspension mechanisms
include tidal currents, wind waves, wave/current interactions, seiches,
trawling, and vessel traffic. Many of these potential mechanisms are
also present on the continental shelf and in large lakes, so some
relevant field studies in these environments will also be mentioned in
this section.
The mean current in estuaries and on the continental shelf may
resuspend bottom sediments. Wimbush and Lesht (1979) deployed a tripod
with current meters and a bottom camera at a site with a bottom

36
sediment of medium sands in the deep (710 meters) Florida Straits and
estimated the critical velocity for ripple formation. Lavelle et al.
(1984) deployed a current meter and transmissometer 5 meters above a
fine sediment bottom in 200 meters of water in Puget Sound. They
observed that tidal currents resuspended bottom sediments and that the
erosion rate could be described with the shear stress power law given
by equation 1-4. Both of these studies were conducted in deep water
where wave motion was not observed. Bohlen (1987) deployed an
instrument array that included an electromagnetic current meter and
transmissometers for monitoring suspended-solids concentrations in 12
meters of water in Chesapeake Bay. Spectral analysis of the suspended-
solids concentration showed variation at tidal frequencies, including a
spring/neap variation. Roman and Tenore (1978) collected and analyzed
water samples over several tidal cycles in Buzzards Bay, Massachusetts,
and observed resuspension of organic carbon and chlorophyll-a at a site
with a muddy bottom in 13 meters of water by tidal currents that was
significant enough to potentially affect estuarine productivity. They
did not address resuspension by wind waves, possibly because the data
may contain a fair weather bias due to the manual collection of water
samples and the lack of in situ instrumentation. Costa and Mehta
(1990) observed resuspension by tidal currents in Hangshou Bay, China,
a high energy tidal environment.
Wind waves may resuspend bottom sediments in relatively shallow
water. Anderson (1972) collected water samples in a tidal lagoon with
fine sediments and found that wave heights of only a few centimeters
resuspended bottom sediments in water depths of 40 to 150 cm. Water
samples and sediment traps were used by Ward et al. (1984) to determine
that shallow water sites (less than 2 meters) in Chesapeake Bay with

37
seagrasses attenuate wave motion and reduce resuspension compared to
sites without seagrasses. Gabrielson and Lukatelich (1985) found that
sedimentation rates calculated from sediment traps deployed in the
Peel-Harvey estuarine system were temporally correlated with the
strength and duration of wind events and spatially correlated with wind
direction and fetch. Kenney (1985) deployed sediment traps in Lake
Manitoba at a depth of 4.2 meters and found that resuspension of bottom
sediments during wind events stratified the water column. Lavelle et
al. (1978) deployed a current meter and turbidimeter 1 meter above the
medium sand bed of Long Island Sound at an average depth of 10.5
meters. Wind waves during a storm resuspended bottom sediments and
tidal currents did not cause resuspension. An empirical relationship
between suspended sediment concentration and wave orbital velocity in
Long Island Sound was developed by Lesht et al. (1980). In addition to
resuspension by tidal currents in Chesapeake Bay discussed previously,
root-mean-squared velocity fluctuations and suspended-solids
concentrations increased when the wind was blowing up the longitudinal
axis of Chesapeake Bay (Bohlen 1987). Davies (1985) deployed a
tetrahedra containing electromagnetic current meters and a video camera
in 4 to 10 meters of water in Start Bay, England, and found that the
observed threshold of sediment motion in oscillatory flow was in good
agreement with Shields diagram (fig. 1-1). Sheng et al. (1990b)
collected synoptic suspended sediment data and deployed anemometers,
pressure transducers, electromagnetic current meters, and optical
backscatterance suspended-solids sensors from several platforms and
piles over two one-month periods in Lake Okeechobee, Florida. It was
found that wind waves associated with the diurnal lake breeze
resuspended fine sediments and this field data were used to calibrate

38
and validate three-dimensional and vertical one - dimensional numerical
sediment transport models (Sheng et al. 1990b, Sheng et al. 1992).
Mehta (1991) also collected data and applied a vertical one - dimensional
model to study fluid-mud and sediment resuspension by wind waves in
Lake Okeechobee. Perjup (1986) deployed an instrument tower in about 2
meters of water in the Ho Bugt estuary, Denmark, from which water
velocity, suspended-solids concentration, salinity, depth, wind speed,
and wind direction were measured. Perjup found that the suspended-
solids concentration did not correlate with mean water velocity but was
correlated to parameters containing wind speed and onshore wind
direction and inversely correlated with salinity, which was well-
correlated with water depth. These results indicate that resuspension
was caused by onshore wind waves, especially at low tide when the near¬
bed orbital wave motion can be greatest.
As mentioned previously, the nonlinear interaction of waves and
current can significantly increase the bottom shear stress and thus it
may be an important sediment resuspension mechanism. Drake and
Cacchione (1986) used data from Norton Sound, Alaska, and the northern
California continental shelf to calculate the grain shear stress with a
modified version of the fixed bed wave/current interaction model of
Grant and Madsen (1979). The observed resuspension threshold was in
good agreement with Shield's diagram (fig. 1-1). Cacchione et al.
(1987) and Drake et al. (1992) compared field data collected on the
northern California continental shelf (water depth 85 meters) and
results of the moveable bed wave/current interaction model of Grant and
Madsen (1982) and found good agreement for bottom shear stress but not
bed form geometry. The high bottom stresses caused by wave/current
interaction during winter storms were a major factor controlling the

39
distribution of surficial sediment on the northern California
continental shelf. Measurements were made with a tripod containing
electromagnetic current meters, a pressure transducer, a nephelometer
(for measuring light scattering which can be calibrated to suspended
solids), and a camera (Cacchione and Drake 1979).
Estuaries contain abundant fisheries and they are convenient sites
for ports, so trawling and commercial vessels are potential sediment
resuspension mechanisms. Churchill (1989) reviewed several sets of
hydrodynamic and sediment data from the middle Atlantic Bight and
determined that sediment resuspension by trawling is a significant
source of suspended sediments. Schoellhamer (1991b) found that during
the departure and arrival of a cruise ship at the Port of St.
Petersburg the suspended-solids concentration increased almost an order
of magnitude due to the maneuvering of the vessel. The resuspended
sediments settled within 1 to 2 hours once the cruise ship either
docked or departed.
In partially-mixed and well-mixed estuaries, the maximum
suspended-solids concentration is often present in brackish waters and
is greater than concentrations found elsewhere in the estuary (Uncles
and Stephens 1989). This feature is called a turbidity maximum and
field data collection programs and numerical models have been used to
determine the controlling mechanisms. Uncles and Stephens (1989)
collected water samples and data from an optical suspended-solids
sensor to measure salinity and suspended-solids concentrations during
twice monthly sampling trips that proceeded up the Tamar estuary,
England. These data were used with a longitudinal one-dimensional
model to determine that the location of the turbidity maximum is
associated with the location of the freshwater/saltwater interface and

40
that local resuspension, and perhaps gravitational circulation and
stratification, determined suspended-solids concentrations in the
turbidity maximum. West and Oduyemi (1989) deployed electromagnetic
current meters and suspended-solids sensors on a bed frame in the Tamar
estuary and observed that near-bed stratification by suspended sediment
reduced the turbulence intensity. Hamblin (1989) collected vertical
profiles of velocity, salinity, and suspended-solids concentrations
from a vessel anchored at several stations near the turbidity maximum
in the upper Saint Lawrence estuary. These data showed that local
resuspension by the mean current controlled the suspended-solids
concentrations at the measurement sites and that a landward flux of
sediment near the bed is maintained by ebb-flood asymmetry and a
reduction in vertical mixing during flood tide caused by the salt
wedge. A vertical one-dimensional sediment transport model was
developed with these data. Grabemann and Krause (1989) analyzed time
series of long-term salinity, current meter, and optical transmittance
sensor data collected in the Weser River estuary to determine that
tidally controlled resuspension and deposition is the dominant process
in the turbidity maximum and that gravitational circulation is a long¬
term source and sink of particles. An intensive two-week experiment on
the Weser River estuary included the deployment of instrumentation to
measure velocity, salinity, and suspended-solids concentration at
several locations and similar measurements were taken from vessels
(Lang et al. 1989). These data showed that there was a close
relationship between suspended-sediment concentration and near-bed
velocity gradient and stratification and the data was used to develop a
three-dimensional numerical model.

41
Most of the field studies discussed so far have focused on tidal
transport processes and vertical sediment transport processes, but
field studies have also been conducted to quantify subtidal horizontal
sediment transport. Powell et al. (1989) collected water samples in
South San Francisco Bay and observed that during spring runoff fresh
water and suspended sediment from the Sacramento River entered South
San Francisco Bay. Wells and Kim (1991) used vibracores, surficial
sediment data, and vertical profiles of velocity, salinity, and
suspended sediment concentration collected during monthly sampling
trips from several sites in the Neuse River estuary, North Carolina, to
describe long-term sedimentation patterns. In Puget Sound, Baker
(1984) collected suspended-solids concentration data with a
transmissometer at several sites during several sampling trips to help
determine that gravitational circulation and surface and bottom sources
of particles control the distribution and transport of suspended
solids.
Sample collection for the preceding studies was generally
performed by collecting water samples and/or collecting pressure,
velocity, and suspended solids concentration data from conventional
sensors. Alternative methods of data collection have been utilized to
collect data on estuarine sediment transport processes. Rubin and
McCulloch (1979) used side scan sonar to determine the shape of
bedforms in central San Francisco Bay, which indicate near-bed
circulation patterns and sediment transport directions. Bedford et al.
(1987) used an acoustic transceiver to sample the sediment
concentration in 1 cm bins in the bottom 70 cm of the water column over
a 3.5 hour period and a tidal cycle at a site in Long Island Sound.
This device provides much better resolution of the near bed sediment

42
concentration profile than is available from optical instrumentation,
but calibration is difficult due to sensitivity to the particle size
distribution. Resuspension fluxes were calculated and were found to be
best correlated with the squared velocity fluctuation (horizontal and
vertical) due to wind waves and turbulence about the mean velocity.
Portable flumes that are deployed on the bottom of the estuary have
been used to study the erosion of in situ sediments under controlled
conditions. For example, Young and Southard (1978) deployed a sea
floor flume in Buzzards Bay, Massachusetts, and observed that the in
situ critical shear velocity was one-half the value found in laboratory
experiments due to bioturbation. Laboratory and sea flume values for
the critical shear velocity also differed in Puget Sound (Gust and
Morris 1989) . To estimate the residence time of fine particles
introduced at the water surface in Puget Sound (11-16 days), Lavelle et
al. (1991) used vertical profiles of radioactive isotope activities and
a sorption model.
Due to practical limitations, it is very difficult to collect
synoptic samples throughout a large water body by conventional means,
but remote sensing from aircraft and satellites can be used to
synoptically determine suspended-solids concentrations near the water
surface in large water bodies. The advantage of remote sensing is that
a measurement of an entire estuary can be made instantly but the
disadvantages are that remote measurements must be calibrated with
suspended-solids concentrations, sampling times and locations are
limited by the satellite orbit, clouds and other weather may degrade or
prevent satellite observation, and resolution may be limited. Sheng
and Lick (1979) used remote - sensing data and field data to produce the
near-surface suspended-sediment concentrations in the western basin of

43
Lake Erie, which were then used to provide initial conditions and
validation for a numerical sediment transport model of Lake Erie. Huh
et al. (1991) used remote sensing to help determine that storms 1)
produce landward sediment transport along coastal Louisiana and 2) help
build marshes. In Mobile Bay, remote sensing has shown rapid changes
in sediment concentrations due to high river inflow and wind-induced
sediment resuspension (Stumpf 1991).
Numerical Models Applicable to Estuarine Sediment Transport
Numerical models can be used to simulate or predict estuarine
sediment transport, resuspension events, sedimentation rates, adsorbed
constituent transport, and light availability. Transport processes are
dependent upon hydrodynamics, so sediment transport models require an
accurate hydrodynamic model. Deposition, erosion, and density
stratification caused by suspended sediments may affect the
hydrodynamics, so a coupled hydrodynamic and sediment transport model
may be required. Many numerical models of suspended sediment transport
have been developed for steady riverine flows (for example van Rijn
1986a, Celik and Rodi 1988, Schoellhamer 1988), but they are not
applicable to estuaries because of the unsteady motions of tidal waves,
seiches, and wind waves. Some riverine models are stochastic or random
walk models that use Lagrangian particles to represent suspended
sediment (Alonso 1981, Bechteler and Farber 1985). The random walk
approach may be applicable to estuarine sediment transport. Mehta et
al. (1989b) reviewed estuarine applications of primarily cohesive
sediment transport models, and they discussed simulation of the bed and
zero-, one-, two-, and three-dimensional models. A similar outline
will be followed herein. Some estuarine sediment transport processes
are also present on the continental shelf and in large lakes, so some

44
relevant numerical models for these environments will also be discussed
in this section.
The properties of the sediment bed may vary with time and depth
below the interface with the water column, especially for cohesive
sediments. Bed properties such as density and shear strength may vary
with distance below the top of the sediment bed, the elevation of which
may vary during a tidal cycle. In order for a numerical sediment
transport model to account for these temporal and spatial variations,
the bed could be divided into layers with different properties, and
new layers could be added during deposition and existing layers could
be removed by erosion. Properties such as layer density, thickness,
and shear strength can vary temporally and spatially in the simulated
estuarine bed (Thomas and McAnally 1985, Hayter 1986, Sheng 1991).
If the spatial variation of suspended-sediment concentration can
be ignored, then only the temporal variation of suspended-sediment
concentrations needs to be considered. This type of modeling is
referred to as zero-dimensional and is equivalent to assuming that the
study area is well-mixed. Krone (1985) used a zero-dimensional model
to simulate and predict deposition in a marsh. Amos and Tee (1989)
simulated the Cumberland Basin in the Bay of Fundy as a well-mixed
water body in order to calculate sediment fluxes at the mouth of the
Basin. Because the distribution of sediment sources in an estuary is
likely to be nonuniform and because the settling property of sediment
increases concentrations deeper in the water column, the assumption
that the spatial variation of suspended sediment is negligible is
generally poor.
The longitudinal variation of suspended sediment in an estuary can
be simulated with horizontal one - dimensional models. Cross sectional

variations are averaged transversely and vertically, so if the
suspended-sediment concentration varies significantly in the cross
section, one-dimensional model may not be applicable. Uncles and
Stephens (1989) used a longitudinal one - dimensional model to describe
the magnitude and location of the turbidity maximum in the Tamar
estuary. Equations 1-3 and 1-19 were used to simulate deposition and
erosion and the coefficients in the equations were selected by
calibration with measured suspended-sediment concentrations. Hayter et
al. (1985) predicted shoaling rates in the Hooghly River estuary,
India, with a longitudinal one - dimensional model that was calibrated
with measured channel dredged material volumes.
The vertical profile of suspended sediment at a given location in
an estuary can be simulated with a vertical one - dimensional model.
These models are applicable when horizontal gradients of suspended-
sediment concentration can be neglected. Weisman et al. (1987)
simulated a depositional tidal lagoon with a series of vertical layers
for which vertical dispersion was neglected and the simulated shoaling
rate was reasonable compared to shoaling rates estimated with
radioactive isotopes. Teeter (1986) developed a vertical transport
model that uses a Richardson number dependent parabolic eddy
diffusivity to include the effect of density stratification. Hamblin
(1989) used this model to simulate vertical mixing of suspended
sediment at a site in the upper St. Lawrence estuary were suspended-
sediment concentrations were observed to depend upon local
resuspension. Field data were used to determine the erosion function
and particle settling velocity. Costa and Mehta (1990) also applied a
Richardson number dependent model to simulate vertical sediment
transport in Hangzhou Bay, China. Steady state vertical profiles of

46
near-bed suspended sediment in the Florida Straits were estimated with
a model by Adams and Weatherly (1981) that used three sediment size
classes. Velocity data but no suspended-sediment concentration data
were collected to calibrate the model. Sheng and Villaret (1989) used a
vertical one - dimensional model (0CM1D, which is presented in detail and
utilized later) with a simplified second-order turbulence closure model
to determine vertical profiles of velocity and suspended-sediment
concentration and the erosion rate of bottom sediments for laboratory
experiments. They found that near-bed stratification by high
suspended-sediment concentrations reduces turbulence intensity and
erosion rates. The same basic model was used to determine erosion
rates of sediments from measured suspended-sediment concentrations from
Lake Okeechobee and was successfully applied to simulate the dynamics
of the vertical structure of suspended-sediment concentration over
several 3-day and 1-week periods (Sheng et al. 1990b, Sheng 1991, Sheng
et al. 1992).
Vertical hydrodynamic models have also been developed for
estuarine applications. 0CM1D has been used to simulate storm-induced
currents in Grand Bank (Sheng 1986b) and in the Atlantic Ocean during
the passage of hurricane Josephine (Sheng and Chiu 1986). Davies et
al. (1988) used a one - dimensional vertical hydrodynamic model to
simulate the interaction of waves and a mean current. This model
achieves turbulence closure with a dynamic equation for turbulence
energy and turbulence scaling relations for the mixing length and eddy
viscosity, but results were not compared to data. A vertical
hydrodynamic model with complete second order turbulence closure model
(i.e., Reynolds stress model) was used by Sheng (1984) to simulate the

hi
development and evolution of the logarithmic wave boundary layer for
laboratory and field data.
The horizontal transport of sediment in an estuary has been
simulated with depth-averaged two-dimensional models. Ariathurai and
Krone (1976) developed a two-dimensional finite element model for
simulating cohesive sediment transport in estuaries. Erosion and
deposition were simulated with equations 1-3 and 1-19. This model is
included in the U.S. Army Corps of Engineers TABS-2 modeling system for
estuarine hydrodynamics and sedimentation (Thomas and McAnally 1985)
which has been applied to several estuaries (Heltzel 1985, Granat 1987,
Hauck 1991). Heltzel (1985) and Granat (1987) used physical model
results for the simulated hydrodynamic boundary conditions and the
validation of simulated hydrodynamics and measured shoaling rates
(instead of measured suspended-sediment concentrations) were used to
calibrate sediment simulations. For San Francisco Bay (Hauck 1991),
hydrodynamic simulations were in agreement with measured data but
sediment simulations did not successfully reproduce field data,
possibly because simulated settling velocities for cohesive sediment
were not dependent upon the concentration, poor simulation of wave
action and related shear stress, and only one grain size for cohesive
sediments was simulated.
Depth - averaging may not be appropriate for estuarine hydrodynamic
and sediment transport models. Density stratification and
gravitational circulation are three-dimensional flow features in
estuaries that can not be simulated by a depth-averaged model.
Sediment resuspension may be dependent upon the bottom shear stress but
depth-averaged models do not calculate the vertical velocity profile
and therefore empirical relations must be used to calculate the bottom

48
shear stress instead of equation 1-5. Because of the settling property
of sediment, sediment concentrations are usually much higher near the
bed than up in the water column, so depth - averaging may not be
appropriate. For example, in an open channel, the near-bed region
contains the largest suspended-sediment concentrations but the smallest
velocities, so the depth-averaged longitudinal velocity of suspended
sediment is less than the depth-averaged water velocity (Schoellhamer
1986). Downing et al. (1985) combined an analytic vertical one¬
dimensional sediment model with linear eddy viscosity and diffusivity,
the Grant and Madsen (1979) wave-current model, and a horizontal two-
dimensional sediment transport model and obtained reasonable simulation
results based on a comparison with field data from the Sagavonirktok
River Delta in Alaska.
Three-dimensional models permit vertical discretization for
simulation of vertical suspended sediment profiles and density
stratification in addition to vertically variable horizontal transport
by tidal currents, wind-induced circulation, and gravitational
circulation. Sheng and Lick (1979) used vertical two- and three-
dimensional circulation and sediment transport models and a wave¬
hindcasting model, in addition to remote - sensing data, to simulate
wind-wave sediment resuspension and transport in Lake Erie. Laboratory
experiments were used to determine settling velocity, critical shear
stress, and erosion rates which were a bilinear function of the excess
shear stress. Wang et al. (1987) used a three-dimensional hydrodynamic
and sediment transport model to simulate sediment transport in Kachemak
Bay, Alaska, but field data were not included in the study. A three-
dimensional hydrodynamic and sediment transport model of the turbidity
maximum in the Weser estuary, Germany, by Lang et al. (1989) was able

49
to reproduce some of the features present in measured suspended-
sediment concentrations. Hayter and Pakala (1989) applied a three-
dimensional model of estuarine hydrodynamics, sediment transport, and
contaminant transport to the Sampit River in South Carolina but field
data was not available to validate the model. Sheng (1991) and Sheng
et al. (1992) collected field data and successfully applied a three-
dimensional model of hydrodynamics, fine sediment transport, and
contaminant transport to study phosphorus dynamics in Lake Okeechobee,
Florida. A preliminary simulation of three-dimensional sediment
transport in Tampa Bay was performed by Sheng et al. (1992).
Relation of this Research to Previous Studies
The purpose of this research was to improve the understanding and
numerical modeling of sediment resuspension and the vertical transport
of resuspended sediment in the shallow estuarine environment and this
was accomplished by combining three important elements of previous
studies that have not been previously combined. These three elements
are: 1) resuspension by wind-waves in a shallow estuary, 2) field
measurements of suspended-sediment concentrations, and 3) a vertical
sediment transport model. Estuarine sediments and their transport are
important because they may reduce the amount of light penetrating the
water column, may act as a source for adsorbed constituents, and may be
transported to undesirable locations. Estuaries are also biologically
active, and this activity may affect sediment transport. Wind waves
are an important resuspension mechanism in many estuaries (table 1-1),
and they are shown to be an important resuspension mechanism in Old
Tampa Bay in chapter 3. Field measurements of sediment concentrations
are needed to understand estuarine sediment transport processes and to
develop accurate numerical models. Resuspension from the bed and

50
Table 1-1, Previous studies that are related to this research and
include an estuarine environment, wind waves, field measurements of
suspended-sediment concentrations, or a numerical vertical sediment
transport model.
Estuarine Wind Field Vertical
Environment waves cone. sed, model
Adams and Weatherly (1981) N
Amos and Tee (1989) Y
Anderson (1972) Y
Baker (1984) Y
Bedford et al. (1987) Y
Bohlen (1987) Y
Cacchione et al. (1987) N
Churchill (1989) N
Costa and Mehta (1990) Y'
Davies (1985) Y
Davies et al. (1988) Y
Downing et al. (1985) Y
Drake and Cacchione (1986) N
Drake et al. (1992) N
Gabrielson and Lukatelich (1985) Y
Hamblin (1989) Y
Hauck (1991) Y
Hayter and Pakala (1989) Y
Kenney (1985) N
Lang et al. (1989) Y
Lavelle et al. (1978) Y
Lavelle et al. (1984) Y
Lavelle et al. (1991) Y
Lesht et al. (1980) Y
Mehta (1991) N
Perjup (1986) Y
Powell et al. (1989) Y
Roman and Tenore (1978) Y
Schoellhamer (1991b) Y
Sheng (1991) N
Sheng and Lick (1979) N
Sheng and Villaret (1989) N
Sheng et al. (1990b) N
Sheng et al. (1992) N
Stumpf (1991) Y
Teeter (1986) N
Uncles and Stephens (1989) Y
Wang et al. (1987) Y
Ward et al. (1984) Y
Weisman et al. (1987) Y
Wells and Kim (1991) Y
West and Oduyemi (1989) Y
N N Y
NY N
Y Y N
NY N
NY N
NY N
Y Y N
NY N
NY Y
Y N N
Y N N
Y Y N
Y Y N
Y Y N
Y N N
NY Y
Y Y N
N N Y
Y N N
NY Y
Y Y N
NY N
NY Y
Y Y N
Y Y Y
Y Y N
NY N
NY N
NY N
Y Y Y
Y Y Y
N N Y
Y Y Y
Y Y Y
Y N N
N N Y
NY N
N N Y
Y Y N
N N Y
NY N
NY N

51
settling of suspended sediment exemplify the importance of simulating
the vertical axis in a numerical sediment transport model.
None of the field and numerical model studies described previously
include estuarine wind-wave resuspension, field measurements of
suspended-sediment concentration, and a vertical sediment transport
model (table 1-1). Studies that include almost all of the elements
include those by Hamblin (1989), Costa and Mehta (1990), Sheng et al.
(1990b), Mehta (1991), and Sheng et al. (1992). Hamblin studied
resuspension by tidal currents near a turbidity maximum, Costa and
Mehta studied resuspension by tidal currents in a high tidal energy
environment, and Mehta and Sheng and his colleagues studied sediment
transport in a large shallow lake. This research used field
measurements of suspended-sediment concentration and a vertical
sediment transport model to study sediment resuspension by wind waves
in an estuary. The numerical model was used as a tool to help analyze
the Old Tampa Bay data and to help determine significant sediment
transport processes in Old Tampa Bay.

CHAPTER 2
SEDIMENT RESUSPENSION DATA COLLECTION METHODOLOGY
In 1987, the U.S. Geological Survey began a study to determine the
effect of fine sediment resuspension on light attenuation in Tampa Bay
and to determine the mechanisms that cause resuspension of fine
sediments. Light attenuation in the waters of Tampa Bay may adversely
affect benthic organisms, seagrasses, and fish and other marine
communities that are dependent upon the seagrasses. Resuspension of
sediment on the bottom of the bay may contribute to light attenuation,
and the mechanisms that cause sediment resuspension in Tampa Bay had
not previously been studied. The author was the project chief for the
study and his duties included project administration, project planning,
data collection, data analysis, presentation of project results at
meetings, and report preparation.
During the U.S. Geological Survey study, pressure, water velocity,
and suspended-solids concentration data were collected in Old Tampa
Bay, a subembayment of Tampa Bay, in order to observe sediment
resuspension events and to determine the hydrodynamic mechanisms that
cause sediment resuspension. In this research, sediment resuspension
data collected from Old Tampa Bay were simulated with a numerical model
of vertical one-dimensional hydrodynamics and sediment transport, and
the model results were analyzed.
Study Area
Tampa Bay is located on the west-central coast of Florida as shown
in figure 2-1. The estuary is Y-shaped, areally large (about 1000
52

53
Figure 2-1, Old Tampa Bay study area.
53

54
km2), shallow (average depth 3.6 meters), vertically well-mixed,
microtidal (spring tide range about 1 meter), and warm (temperature
range from about 14 to 31 °C in 1988 and 1989) (Goodwin 1987, Boler
1990). The northwest subembayment is called Old Tampa Bay and the
northeast subembayment is called Hillsborough Bay. These subembayments
are of most concern ecologically because seagrass loss is more common
and water-quality is probably more impacted by point and non-point
nutrient loading and by reduced tidal flushing (Lewis et al. 1985,
Goodwin 1987). The cities of Tampa, St. Petersburg, and Clearwater are
adjacent to the bay. The subtropical weather includes almost daily
thunderstorms during the summer, occasional storms from winter cold
fronts, and the possibility of tropical storms primarily during the
fall. The river inflow is small compared to the volume of the bay, and
the riverine flushing time, the bay volume divided by the combined
river discharge, is about 2 years (Goodwin 1987). Bottom sediments in
Old Tampa Bay are generally silty very fine sands in the deeper water
(4 meters) and fine sands in shallow water (less than 2 meters) near
the shoreline. Goodell and Gorsline (1961) found clay minerals only in
isolated portions of Old Tampa Bay, and the sedimentology has not
changed significantly since their study (Schoellhamer 1991a).
Sediment Resuspension Monitoring Sites
State variables in an estuary, such as water velocity, salinity,
and suspended-solids concentration, vary spatially and temporally.
Unfortunately, it is neither technically or economically feasible to
obtain complete spatial and temporal coverage when measuring these
variables, so a limited data collection network must be designed that
is representative of a large portion of the estuary. Therefore,
representative sites for resuspension monitoring were selected.

55
The most important site selection criterion was that a potential
site be at the center of a large area of homogeneous sediment. A
potential problem with monitoring sediment resuspension at one site is
the possibility that horizontal advection may transport suspended
sediment to the site and the resulting increase in suspended-solids
concentration may be mistaken for local resuspension. Selection of a
site in the center of a large homogeneous area of bed sediments reduces
the possibility that more erodible sediments will be transported to the
site and insures that the site is representative of a large fraction of
the bay bottom. Careful data analysis is required to identify the
source of an increase in suspended-solids concentration, and specific
data are discussed in chapter 3. Other criteria were 1) nearly uniform
residual currents over the homogeneous sediment bed, based upon a
depth-averaged two-dimensional barotropic hydrodynamic model by Goodwin
(1987), 2) site location far from ship channels for safety and
homogeneity of bottom sediments and currents, and 3) a secluded
location to reduce vandalism.
The size classification of the bottom sediments in upper Tampa Bay
(north of a line that extends approximately east from St. Petersburg)
were determined with a fathometer and grab samples in 1987 and 1988
(Schoellhamer 1991a). Finer sediments, which are more easily
suspended, are generally found in the deeper parts of the bay. The
fine inorganic bed sediments are commonly in the form of fecal pellets
and organically bound aggregates (Ross 1975) . Coarser sediments found
closer to shore in shallower water may experience more wave activity,
however, and also are likely to be resuspended. Thus, selection of a
deeper site with finer sediments and a shallow site with coarser
sediments in Old Tampa Bay was desired.

56
In Old Tampa Bay, typical deep- and shallow- water sediment
resuspension monitoring sites were selected. A deep-water site
(average depth about 4 meters) was located in the approximate center of
a large area of silty-fine sand at latitude 27°57'01" N and longitude
82°37'55" W. The particle size distribution at this site is shown in
figure 2-2, and it has changed little from the 1950's to the 1980's
(Goodell and Gorsline 1961, Taylor and Saloman 1969, Schoellhamer
1991a). The mean particle diameter is 127 /¿m, and 16% of the material
is fine material (particle diameter less than 63 urn). The density of
the bottom sediments is 2.68 g/cm3 and 2.7%, by weight, of the bottom
sediments are organic. A shallow-water site (average depth about 2
meters) was selected 3.0 km south-southwest of the deep-water site in
an area of fine sands on the estuarine shoal at latitude 27°55'30" N
and longitude 82°38'33" W. The mean particle diameter is 152 nm, and
the material is 1.5% fine sediment. A submersible instrument package
was used to collect hydrodynamic and sediment resuspension data at the
shallow-water site (Schoellhamer 1990), but only a single point
velocity was measured so the bottom roughness could not be determined.
Therefore, the data collected at the shallow-water site is not well-
suited for numerical modeling and only data collected at the platform
were utilized in this research.
Old Tampa Bay Instrumentation Platform
In June 1988, a platform was constructed at the Old Tampa Bay
deep-water site in order to support sediment resuspension monitoring
instrumentation (fig. 2-3). The platform consists of three vertical
pilings that are the apexes of a 3.7 m equilateral triangle
(Schoellhamer 1990, Levesque and Schoellhamer in press). The pilings
support a triangular galvanized expanded-steel deck approximately 2

57
Figure 2-2, Size distribution of bottom sediment at the Old Tampa Bay
platform.

58
Figure 2-3, Old Tampa Bay platform (Levesque and Schoellhamer,
manuscript in review).

59
meters (average) above the water surface. Water column instrument
sensors were mounted on movable horizontal aluminum arms that were 61-
cm-long and extended perpendicular to a vertical 610-cm-long, 10-cm-
diameter aluminum pipe that was fixed to the center of the steel deck.
The entire pipe structure resembled an inverted tree.
Several types of sensors were deployed from the platform. A
biaxial electromagnetic current meter was mounted at the end of each
horizontal arm, and an optical backscatterance (OBS) suspended-solids
sensor was mounted at the midpoint of each arm. In addition to a
current meter and an OBS sensor, one of the horizontal arms also
supported a pressure transducer for measuring water depth and wave
activity. Wind velocity was measured with a cup anemometer and a wind
vane that were mounted at the top of one platform pile, located about 3
meters above the steel deck. The sensor electronics, data recorder,
and associated power supplies were housed in an aluminum shelter
mounted at one corner of the steel deck. An underwater camera for
taking bottom photographs was not deployed because visibility was
usually insufficient, especially during resuspension events.
Resuspension monitoring instrumentation consisted of Marsh
McBirney Model 512 biaxial electromagnetic current meters, Downing and
Associates Instruments Model OBS-IP backscatterance sensors, and two
types of pressure transducers. The biaxial current meters have a 5.1-
cm-diameter sphere attached very near the end of a 20.3-cm-long metal
rod. The biaxial electromagnetic current meters measure water velocity
using the Faraday principle of electromagnetic induction, where a
conductor (water) moving in a magnetic field (induced by the current
sensor) produces a voltage that is proportional to the water velocity.
The OBS sensors are thumb-size, and they have an optical window at the

60
relative position of the thumbnail (Downing et al. 1981, Downing 1983).
The optical window is used to transmit an infrared pulse of light that
scatters or reflects off particles in the water up to a distance of
about 10 to 20 cm at angles up to 140° in front of the window. Some of
this scattered or reflected light returns to the optical window where a
receiver converts the backscattered light to an output voltage. For
well-sorted suspended material, the output voltage is proportional to
the suspended-solids concentration and turbidity in the water column.
The calibration of the OBS output to suspended-solids concentration
varies depending on the size and optical properties of the suspended
solids, so the OBS sensors must be calibrated either in the field or in
a laboratory with the same suspended material as is found in the field.
A laboratory evaluation by Ludwig and Hanes (1990) concluded that
instrument response to suspended mud was linear up to a concentration
of 3,000 to 4,000 mg/L, and they recommended that OBS sensors not be
used for the measurement of suspended sand in areas that concurrently
experience suspended mud. Originally, a Geokon vibrating-wire pressure
transducer was used at the platform-site and was eventually replaced
with a Druck strain-gage transducer for improved reliability and
increased sensitivity. Data acquisition, data storage, and sensor
timing were controlled by a Campbell Scientific CR10 data logger. A 5-
minute burst sample of the current meter outputs, OBS sensor outputs,
and the pressure transducer output was collected every hour during
deployments at the platform-site. The burst sample consisted of 1-
second data of all sensor outputs for the duration of the 5-minute
sampling interval. The burst sample was temporarily stored in the data
logger and following the end of the burst sample collection the data
was sent to an external data storage module.

61
The instruments were submerged continuously when initially
deployed in August 1988. Data was transmitted from the platform in Old
Tampa Bay to the U.S. Geological Survey office in Tampa by a modem and
a cellular phone. Every night, the platform data logger would turn on
a cellular telephone. At the same time, a shore-based personal
computer would automatically call the cellular phone through a modem,
establish communications with the data logger through a modem on the
platform, and issue commands for the data logger to transmit data that
were then stored by the shore-based personal computer. Approximately 2
hours were required to transmit data from 24 burst samples.
Transmission time and power requirements of the cellular phone required
the connection of a deep-cycle 12 volt battery to the solar panel on
the platform, which was accomplished in mid-October 1988. If the
weather conditions were poor during data transmission, the transmission
would fail and cause a loss of data. Both the platform and shore-based
modems used an error checking protocol to help insure accurate data
transmission.
In October 1988, analyses of the available data indicated that the
OBS sensors had fouled, and when the sensors were cleaned by SCUBA
equipped divers, large amounts of marine growth were observed on all of
the sensors. The output from the OBS sensors began to increase as the
sensors fouled, usually about 24 to 48 hours after cleaning, and the
current meters fouled in about seven days. The OBS sensors were coated
with an antifoulant for optical surfaces (Spinard 1987) that only
prevented barnacle growth on the optical surface. The cause of the
fouling was probably an algal slime that would grow on the face of the
sensors and affect their optical properties. In late 1988, when the
instruments were submerged continuously, cleaning dives were conducted

62
about every two weeks. Therefore, the OBS sensors were fouled most of
the time, and only data collected within 24 to 48 hours of cleaning
were reliable.
The sensor fouling caused by the continuously submerged system
proved to be impractical, and a modification was required, so the
vertical pipe that supported the instruments was attached to an A-frame
and pulley system in December 1988. The vertical pipe was suspended
from an A-frame steel-pipe structure secured to the steel deck that
allowed the vertical pipe to be raised above the water surface for
sensor cleaning and storage. Daily servicing visits to clean the
sensors were usually made when the sensors were deployed, so the
cellular phone and modem were removed from the platform and the data
storage module was exchanged daily during the servicing visits.
Flow around the platform pilings is a potential cause of sediment
resuspension that could affect suspended-solids concentrations at the
platform, so several steps were taken to reduce this possibility and to
determine that any local scour caused by the platform did not
significantly affect concentrations at the platform. Barnacles were
removed from the platform pilings on February 22, 1990, to reduce their
effect on the flow. Scour holes were not observed by divers at the
bases of the pilings, possibly due to bioturbation. The bottom of the
aluminum pipe that supported the instruments was about 20 cm above the
bed to reduce the possibility that it would cause local scour. Four
sets of water samples collected at the platform and 750 and 1500 meters
south-southwest of the platform on November 30, 1989, July 13, 1990,
October 12, 1990, and November 30, 1990, indicate that the average
concentration of suspended-solids at the platform was 6.9 mg/L greater
than the other sites. In March 1990, however, two water samples were

63
collected at the platform at the same time on 8 different occasions,
and the average concentration difference between concurrently collected
sample pairs was 7.1 mg/L. Thus, the higher observed platform
concentration is equivalent to the sample concentration variation.
Although only a few data points are available, these results indicate
that any local scour caused by the platform did not significantly
affect suspended-solids concentrations at the platform.
Calibration and Output of Electromagnetic Current Meters
The relationship between the output voltages of the
electromagnetic current meters and the water velocity must be known.
The electromagnetic current meters have two separate output voltages,
one for each velocity component, that are linearly related to the water
velocity components. Linear calibration equations are used to convert
output voltages from the meters to water velocities. After
construction and following any repairs, the manufacturer calibrated the
meters by adjusting the output voltages to match specifications. About
annually, the current meter calibrations were checked by the U.S.
Geological Survey hydraulics laboratory at the Stennis Space Center in
Mississippi. The calibration check generally agreed within 10% of the
manufacturers stated calibration values. All calibrations were for
steady flows. If a U.S. Geological Survey calibration was available,
then it was used; otherwise, the manufacturer's calibration was used.
A potential limitation of the electromagnetic current meters used
in this study is a reduction in the meter's output response to short
period water waves, such as wind-waves with 2 to 4 second periods
(frequencies 0.25 to 0.5 Hz). The current meter output response to
short period water waves is reduced by an electronic filter network
that is used to suppress a 60 Hertz carrier signal that is inherent in

64
the current meter design. At wind-wave frequencies of interest to this
study, the gain (output voltage) of the meters is reduced by the
electronic filter so that actual velocities are greater than the
recorded values.
The recorded velocities can be corrected for the electronic
filtering (Guza 1988) . The output filter is an active RC
(resistor/capacitor) 2-pole filter, 6dB per octave rolloff, with a time
constant RC = 0.94 seconds for the meters used in this study. The
filter reduces the magnitude of output signal and the reduction
increases as the frequency of the input signal increases. For a
periodic input signal with angular frequency w, the gain of the filter
is
G(w) = [1 + («RC)2]"1* (2-1)
The filter also causes a phase delay of the output signal. The phase
delay, a negative number in radians, is
¿(w) = tan'1 [ 1/(wRC) ] - tt/2 (2-2)
Equations 2-1 and 2-2 can be applied to correct the recorded data
in the frequency domain. The time series is converted to the frequency
domain via the fast Fourier transform (FFT), resulting in the series
N/2+1
a(l) +2 2 a(n) cos[(n-l) Aw t] + b(n) sin[(n-l) Aw t] =
n=2
N/2+1
2 a(n) cos[(n-l) Aw t] + b(n) sin[(n-l) Aw t] +
n=l
N
2 a(n) cos[(n-N-l) Aw t] + b(n) sin[(n-N-l) Aw t] (2-3)
n=N/2+2
for which N is the number of data points, a power of 2, the angular
frequency increment Aw=27r/(NAt), At is the time interval of the data,
and the Fourier series coefficients a(2)=a(N), b(2)=-b(N), a(3)=a(N-l),
b(3)=-b(N-l), . . ., a(n)=a(N-n+2), b(n)=-b(N-n+2), . . .,

65
a(N/2)=a(N/2+2), b(N/2)=-b(N/2+2). The left hand side of the equality
is how the Fourier series is commonly presented and the right hand side
is how the FFT algorithm represents the Fourier series, which is
visually more complicated but computationally more efficient. Each
discrete frequency u> is represented by a sine and cosine term that can
also be written as
a(n) cos(ut) + b(n) sin(cjt) = c(n) cos(u>t+e (n)) (2-4)
in which the magnitude is
c(n) = ( a(n)2 + b(n)2 )h (2-5)
and the phase is
e(n) = tan ^ (b(n)/a(n)) (2-6)
The corrected magnitude at the frequency w is
cc(n) - c(n)/G(«) (2-7)
and the corrected phase is
*c(n) = £(n) + The corrected Fourier series coefficients are
ac(n) = cc(n) cos[€c(n)] (2-9)
bc(n) = cc(n) sin[e (n)] (2-10)
The inverse FFT is then applied to the corrected Fourier coefficients
to determine the corrected velocity time series. Guza and Thornton
(1980) found that the significant wave height from pressure and
velocity sensors agreed within 20%, and similar agreement occurred
between pressure and corrected velocity data from platform sensors at
the same elevation in November 1990. Raw wave spectra from pressure
and corrected velocity data were also in good agreement, so the
corrected velocities seem to be reasonable.

66
Response Threshold and Biological Interference of OBS Sensors
Ambient suspended-solids concentrations were often below the
response threshold of the OBS sensors, and biological interference with
the sensors was a potential problem (Schoellhamer, manuscript to be
published in Marine Geology). The sediment load of the rivers that
flow into Tampa Bay is small and Tampa Bay is microtidal, so the
ambient suspended-solids concentrations are also small, about 10 to 50
mg/L. Due to the response threshold of OBS sensors, accurate
interpretation of OBS data may be difficult except during episodic
events that resuspend bottom sediments. Backscatterance from
phytoplankton may be detected when suspended-solids are at ambient
concentrations. The OBS sensor electronics were factory adjusted in
mid-1989 to improve their sensitivity, which diminished but did not
eliminate these problems. Laboratory calibrations of the OBS sensors
with bottom sediments from the platform site did not agree with the
suspended-solids concentrations of collected water samples, so the
sensors were calibrated with water sample data. The standard error of
an OBS sensor in Old Tampa Bay is 5.8 mg/L, based upon a set of 21 OBS
measurements and water samples collected from an elevation 70.1 cm
above the bed by an automatic water sampler during a storm in March
1990 (fig. 2-4). Shallow depths, high water temperatures, and
eutrophic conditions encouraged biological growth on the OBS sensors
that sometimes increased their output voltages and invalidated the
data, so daily cleanings were desirable.
Fish would sometimes interfere with the OBS sensors. During dives
and instrument cleaning, it was noted that fish would sometimes be
congregated around the instrumentation and occasionally would swim past
the OBS sensors. The infrared light pulse would reflect off the fish

SUSPENDED SOLIDS
CONCENTRATION, IN MG/I.
67
30 35 40 45 SO 55 50 65
MEDIAN OBS OUTPUT, IN MILLIVOLTS
Figure 2-4, Suspended-solids concentration and median OBS sensor output
70 cm above the bed at the Old Tampa Bay platform, March
1990 (Schoellhamer, manuscript to be published in Marine
Geology).

68
and produce a high spike (short-duration increase in output voltage)
during the burst sample collection. Usually no more than a few spikes
would occur during a burst, but they were large enough to significantly
affect the resulting mean value for the burst, so the median value
proved to be a simple and more appropriate measure of the OBS burst
average than the mean value. Regular sensor maintenance and careful
data analyses to identify spikes and fouling were used to minimize
abnormalities in OBS data.
Water Sample Collection
Water samples were collected manually and automatically at the
platform. The water samples were usually analyzed by the methods of
Fishman and Friedman (1989) to determine specific conductance,
turbidity, and concentrations of suspended-solids, volatile suspended-
solids, and dissolved chloride. At the Old Tampa Bay platform, point
water samples used for the calibration of the OBS sensors were
collected each day from each OBS sensor depth using a peristaltic pump
connected to tygon tubing that was attached at the end of a long pole
that was lowered to the desired depth.
A continuous water sample collection technique was required for
accurate suspended solids monitoring during storm events and nighttime.
An automatic water sampler was secured in one corner of the steel deck
of the Old Tampa Bay platform, beginning with deployments in March
1990. A SIGMAMOTOR Model 6601 automatic water sampler, connected to
nylon-reinforced teflon-tubing, collected an OBS calibration point
sample every hour at one OBS depth for the duration of most instrument
deployments. The water sampler was set to sample during the sensor on-
time .

69
Instrument Deployment Strategies
Sediment resuspension monitoring instrumentation was deployed
intermittently in Old Tampa Bay from 1988 to 1990. As mentioned
previously, instrumentation was continuously deployed from the Old
Tampa Bay platform in fall 1988. Analyses of the data indicated that
bottom sediment resuspension did not occur with normal or spring tidal
currents. Waves generated by strong winds were determined to be the
most likely sediment resuspension mechanism in Old Tampa Bay. In
Florida, the typical sources for strong winds are winter storm systems,
tropical storms, and summer thunderstorms. Therefore, in late 1989 and
1990, instrumentation was deployed in Old Tampa Bay before the
anticipated arrival of selected meteorological events. The automatic
water sampler was set up at the platform, the instruments were tested,
and the vertical pipe that supported the instruments was lowered into
the water and secured to the steel deck at the beginning of each
deployment. The submersible instrument package was also deployed at
the shallow-site shortly after the platform instrumentation was
deployed. Weather permitting, daily servicing trips were made to clean
sensors, retrieve data, and collect water samples. The vertical pipe
was secured out of the water, and the submersible instrument package
was recovered several days after being deployed.

CHAPTER 3
SEDIMENT RESUSPENSION DATA AND ANALYSIS
Data collected intermittently from 1988 to 1990 in Old Tampa Bay
shows that sediment resuspension coincided with wind-waves generated by
strong sustained winds associated with storm systems (Schoellhamer
1990, Schoellhamer and Levesque 1991, Schoellhamer manuscript in
review). Tidal currents were too weak to resuspend measurable
quantities of sediment at the Old Tampa Bay platform, but some bottom
sediment motion probably did occur because of the stochastic nature of
the process (Lavelle and Mofjeld 1987a). Suspended-solids
concentrations returned to ambient values within several (4 to 8) hours
as wave activity diminished.
Sediment resuspension data collected at the Old Tampa Bay platform
during storms in March 1990 and November 1990 were suitable for
numerical simulation, and these data and the analysis of these data by
Schoellhamer (manuscript in review) are presented in this chapter.
Instrumentation deployments at the Old Tampa Bay platform are
summarized in table 3-1. Platform data collected in March 1990 and
November 1990 were suitable for simulation because net sediment
resuspension occurred and both hydrodynamic and suspended-solids
concentration data were collected successfully. Several data sets were
collected during which the OBS sensors could not be calibrated,
sediment resuspension was not observed, or instruments malfunctioned.
Data collected during two tropical storms unfortunately were not
suitable for numerical simulation, but these data and the analysis of
70

71
Table 3-1.--Old Tampa Bay platform instrumentation deployments.
Instrumentation
deployment
dates
Hydrodynamic Suspended-solids
data concentration
available data available
Net sediment
resuspension
observed
Fall 1988 Y
Sept 20-21, 1989 Y
Nov 28-30, 1989 Y
March 8-10, 1990 Y
July 11-13, 1990 Y
Oct 9-12, 1990 N
Nov 28 -
Dec 3, 1990 Y
N
N
N
Y
Y
Y
N
N
N
Y
N
Y
Y
Y

72
these data by Schoellhamer (manuscript in review) are presented and
compared to the March and November 1990 data. Hydrodynamic data, but
no suspended-solids concentration data, were collected successfully
during tropical storm Keith November 21-24, 1988. No hydrodynamic data
were collected successfully during tropical storm Marco in October
1990. The limited data collected during tropical storms Keith and
Marco indicate that tropical storms can resuspend more sediment than
winter storms can resuspend.
The bottom roughness at the Old Tampa Bay platform was determined
with equation 1-5 and velocity profiles collected during several
instrumentation deployments. Velocity profiles that were measured
during periods of small wave motion and during relatively strong flood
and ebb tides were used. Velocity data collected 183 cm above the bed
were not used because the values usually were not logarithmic compared
to velocities closer to the bed. Data collected before and immediately
after sediment resuspension events did not indicate that bottom
roughness changed significantly. Bottom photographs taken by divers
were not useful due to poor visibility. Divers observed that the bed
was nearly flat with some undulations, possibly from bioturbation, and
that there were no regular bed forms. Thus, bed load transport at the
platform probably was not significant, except possibly during major
sediment resuspension events. The bottom sediment included 16% fine
material, and it is possible that this was the material that was
observed in suspension and that the sandy material either did not move
or did not create ripples that significantly affected the data. The
analysis of the velocity data produced an optimal bottom roughness
equal to 0.3 cm, and the bottom roughness regime was usually
transitional between the rough and smooth limits. The total bottom

73
roughness is composed of contributions from form drag and grain
roughness, but only the roughness associated with the particles
determines particle motion (Vanoni 1975, McLean 1991). Spatially-
averaged grain shear stress can be calculated by collecting velocity
data within the flow layer adjacent to the bed that is influenced by
grain roughness or by applying empirical relationships based on ripple
geometry (Smith and McLean 1977). For this study, however, velocity
data could not be collected close enough to the bed to recognize
different bottom roughness scales, and no regular ripples were
observed. Therefore, in this chapter, the total shear stress
calculated with the total bottom roughness was used to determine the
sediment resuspension mechanisms at the platform. The spatially-
averaged grain shear stress was estimated by the numerical model that
is presented in chapter 4. For a given particle diameter, a calculated
total shear stress that is greater than a critical shear stress (such
as Shields critical shear stress, fig. 1-1) may not indicate that
motion will occur because not all of the total shear stress is acting
on the grains and biological activity may increase the critical shear
stress.
March 1990 Storm
Data were collected at the Old Tampa Bay platform after a cold
front moved through the Tampa Bay area on March 8, 1990. The high
pressure system behind the front generated 8- to 9-meter-per-second
sustained northeasterly winds from 1100 to 2100 hours on March 8 (fig.
3-1, table 3-2). Wave activity increased as a result of the sustained
northeasterly winds, providing favorable conditions for sediment
resuspension. Operational equipment at the platform consisted of
electromagnetic current meters at elevations of 70 and 183 cm above the

Figure 3-1, Measured and calculated quantities at the Old Tampa
Bay platform, March 1990
MAXIMUM BOTTOM
ORBITAL VELOCITY, IN SIGNIFICANT WAVE
CENTIMETERS PER SECOND AMPLITUDE, IN CENTIMETERS
WIND SPEED.
IN METERS PER SECOND
MEAN CURRENT SPEED, IN
CENTIMETERS PER SECOND
£
>
CD D
o
I
(0
O
O
> o
U3 JO
n
i
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CD CD CD
I 1 1 r
to o o
MAXIMUM BOTTOM SHEAR
STRESS FOR CURRENT
AND WAVES, IN DYNES/CM
MAXIMUM
BOTTOM SHEAR STRESS FOR
WAVES ONLY, IN DYNES/CM2
BOTTOM SHEAR STRESS FOR,
CURRENT ONLY. IN DYNES/CM
ID CD ~Nj o -* W CJ » CD CD
SUSPENDED SOLIDS
CONCENTRATION, IN MG/L
100

75
Table 3-2.--Old Tampa Bay platform data, March 8, 1990.
Hour
Water
depth
(cm)
Mean current
(cm/s) at elev
70 cm 183 cm
Wind
speed
(m/s)
1400
402.4
3.8
4.7
9.2
1500
410.2
1.4
1.3
8.1
1600
409.8
3.4
4.8
8.4
1700
405.7
8.3
9.6
8.6
1800
399.1
8.9
9.5
8.5
1900
395.4
2.6
2.7
8.6
2000
398.1
0.6
4.2
8.1
2100
405.4
8.7
10.0
8.3
2200
413.9
7.8
8.7
6.0
2300
420.3
5.7
7.0
5.8
*
Wave
amp.
(cm)
Wave .
k
period
(sec)
Suspended-solids
cone. (mg/L)
24 cm 70 cm 183 cm
38.2
2.46/2.43
54.0
42.0
44.0
30.8
2.78/2.53
66.0
47.9
44.0
30.0
2.64/2.50
58.0
47.9
49.1
26.4
2.69/2.52
74.0
51.5
47.8
27.7
2.46/2.52
98.0
68.2
59.3
30.8
2.75/2.54
86.0
67.0
63.2
21.6
2.15/2.41
71.9
62.2
52.9
26.2
2.31/2.42
53.9
45.6
44.0
24.8
2.27/2.35
44.0
43.2
40.1
14.0
2.19/2.58
42.0
42.0
36.3
Wave periods are maximum energy of the surface amplitude spectrum/zero
upcrossing period of the squared bottom orbital velocity spectrum.

76
bed and OBS sensors at 24, 70, and 183 cm above the bed. Water samples
were collected from 1500 March 8 to 1100 March 9 at a position 70 cm
above the bed using the automatic water sampler. In addition, discrete
water samples were manually collected during instrument on-time once
each day throughout the instrument deployment (March 8 - 10) at the
elevations of the OBS sensors and analyzed for suspended-solids
concentration. The discrete samples were used to calibrate the output
of the OBS sensors to suspended-solids concentration, and the automatic
samples validated the calibration of the OBS sensor 70 cm above the
bed. The suspended-solids concentrations (fig. 3-1) peaked at 1800
hours March 8, then decreased rapidly. No data was successfully
recorded before 1400 hours on March 8 because of a power supply
problem, but the suspended-solids concentrations for the first platform
measurement at 1400 hours were slightly greater than the upper limit of
the observed ambient concentrations (20 to 40 mg/L), which indicates
that only the initial resuspension was missed.
The temporal variation in the bottom shear stresses calculated
from the measured mean current with equation 1-5 did not correspond to
the temporal variation of the measured suspended-solids concentrations.
The mean current speeds measured 70 and 183 cm and the bottom shear
stresses calculated from the mean current speed 70 cm above the bed are
shown in figure 3-1. A bottom roughness of 0.3 cm was used. A small
ebb tide from 1600 hours to 1900 hours March 8 and a small flood time
from 1900 hours March 8 to 0100 hours March 9 had maximum speeds of
about 9 cm/s and increased the mean current bottom shear stress to
about 0.15 dynes/cm2, but these increases are not correlated with the
observed suspended-solids concentrations. A strong ebb tide at the
platform during a period of relatively little wave activity from 0200

77
to 0900 hours March 9 had maximum speeds of 12 to 16 cm/s and increased
the mean current bottom shear stress to 0.28 dynes/cm2, but apparently
did not resuspend bottom sediments. This total (grain and form) shear
stress is smaller than the Shields critical shear stress for the
platform sediment. The mean current during the morning of March 9 was
relatively large for the platform site, and the lack of a corresponding
increase in suspended-solids concentration indicates that the tidal
currents did not generate enough shear stress to resuspend bottom
sediments at the platform site. The suspended-solids concentrations
did not correlate with mean current bottom shear stress (r=-0.4, table
3-3) .
Horizontal advection is not a likely cause of the observed
increase in suspended-solids concentration because the tidal excursion
was within the large area of homogeneous sediments that surrounded the
platform and sediments further upcurrent were probably not resuspended.
The tidal excursion of the small ebb tide from 1600 to 1900 hours
(about 750 meters) was within the large area of silty very fine sands
that surrounded the platform. The ebb tidal flow was from the
northwest to the southeast at the platform, so the most likely source
of resuspended sediment for transport to the platform during an ebb
tide was resuspension in relatively shallow water 1500 meters northwest
of the platform and within 500 meters of the southern side of the
Courtney Campbell Causeway. The wind was from the northeast, however,
so wind waves were not approaching the southern side of the causeway,
and resuspension was unlikely.
Wave properties were calculated using spectral analysis. Usually,
buoy acceleration or pressure data are used to calculate the energy
spectrum, but the pressure transducer was only partially responding to

78
Table 3-3Correlation coefficients for various wave properties and
bottom shear stresses with suspended-solids concentrations at the Old
Tampa Bay platform, March 1990.
Elevation of measured
suspended-
solids
concentration
24 cm
70 cm
183 cm
Shear stress: mean current only
-0.29
-0.41
-0.52
Shear stress: wave only (Kamphius 1975)
0.74
0.61
0.70
Shear stress: wave only
(Grant and Madsen 1979 and 1982)
0.73
0.59
0.68
Shear stress wave-current
(Grant and Madsen 1979)
0.73
0.59
0.67
Wave amplitude
0.73
0.66
0.78
Bottom orbital velocity
0.74
0.61
0.70
Square of bottom orbital velocity
0.69
0.58
0.66

79
the changes in pressure from wave activity, so the velocity component
pairs measured by the lowest current meter were used to calculate the
energy spectra after correcting the raw data for the electronic output
filter of the electromagnetic current meters as described in chapter 2.
The wave energy was located almost exclusively at wave periods from 2
to 3 seconds, and the maximum energy period of the surface amplitude
spectrum was selected to represent the wave period. The zero-
upcrossing period of the squared bottom orbital velocity spectrum
(square root of the second moment divided by the zero moment), however,
is probably more indicative of wave periods that affect the bottom
shear stress. Table 3-2 indicates that these periods are similar, and
the interpretations that result from this analysis are not affected by
this difference. For narrow banded spectra such as these, the
significant wave amplitude is twice the square root of the area under
the wave spectrum (Ochi 1990). Significant wave amplitudes calculated
with data from the current meter 70 cm above the bed (fig. 3-1)
corresponded with the wind speed and decreased after 2200 hours March
8. The wave amplitude was somewhat correlated with the suspended-
solids concentrations (r-0.7, table 3-3). The waves during the storm
(1400 to 2100 hours) were transitional between the deep-water and
shallow-water limits, but as the wind diminished the waves became deep¬
water waves. The maximum orbital particle velocities calculated from
linear wave theory based upon the significant wave amplitude were close
to measured values, so the calculated wave properties appeared to be
reasonable. The bottom orbital velocity (fig. 3-1) decreased in
conjunction with the wind speed. Note that only a single wave
amplitude and period are considered, whereas realistically, there are
many periods and amplitudes present in the wave field. Thus, the

80
results of the spectral analysis were used to provide approximate wave
data in a consistent manner.
The bottom orbital velocities corresponded with the observed
suspended-solids concentrations. The bottom orbital velocities were
9.8 to 16 cm/s until 1900 hours March 8 and during this time the
suspended-solids concentrations increased from slightly greater than
ambient values to the maximum values measured during the deployment.
After 1900 hours March 8, the waves were deep-water waves, the bottom
orbital velocities were less than 7 cm/s, and the suspended-solids
concentrations decreased to ambient values in the early morning of
March 9. Thus, resuspension seems to have occurred during the period
of greatest wave activity, and the resuspended sediments settled as the
wave action diminished. The bottom orbital velocity and squared bottom
orbital velocity were somewhat correlated with suspended-solids
concentrations (r=0.7, table 3-3).
The calculated bottom orbital velocity and estimated maximum
bottom shear stress were more dependent on the water depth and wave
period than the wave amplitude. The bottom orbital velocity increases
with increasing wave amplitude, increasing wave period, and decreasing
mean water depth. A sensitivity analysis was performed to investigate
the relative importance of wave amplitude, wave period, and mean water
depth on the bottom orbital velocity calculation for this data set.
Typical storm values for this data set are a significant wave amplitude
of 30 cm, a maximum energy period of 2.6 seconds, and a water depth of
400 cm. A 10% increase in wave amplitude, a 10% increase in wave
period, and a 10% decrease in water depth, increase the bottom orbital
velocity 10, 29, and 25%, respectively. The bottom orbital velocity
during resuspension at the Old Tampa Bay platform was more sensitive to

81
wave period and mean water depth than wave amplitude because the waves
are depth transitional. The maximum bottom shear stress is
proportional to the square of the maximum bottom orbital velocity (eqn.
1-11), so an error in the estimated bottom orbital velocity may
severely degrade the estimated bottom shear stress. For example,
assuming that the wave friction factor is unchanged, if a 10%
overestimate of the wave period produces a 29% overestimate of the
maximum bottom orbital velocity, then the maximum bottom shear stress
will be overestimated by 66%.
The maximum bottom shear stresses estimated for wave motion only
are much greater than the bottom shear stresses estimated for the mean
current only and correspond to the suspended-solids concentrations.
Equation 1-11 and friction coefficients determined empirically
(Kamphius 1975) and theoretically (eqn. 1-13, Grant and Madsen 1979,
1982) were used to estimate the maximum bottom shear stress for the
observed bottom roughness (fig. 3-1). The estimated bottom shear
stress considering wave motion only is much greater than the estimated
bottom shear stress considering the mean current only. The greatest
wave shear stress occurred during the period of sediment resuspension
on March 8 and the wave shear stress is somewhat correlated with
suspended-solids concentration (r=0.7, table 3-3).
Poor knowledge of the behavior of the wave friction factor for
regime transitional waves may account for the differences between the
results of the two methods for calculating the wave only bottom shear
stress (fig. 3-1). The waves were transitional between the laminar
(smooth bottom) and fully turbulent (rough bottom) flow regimes.
Kamphius (1975) states that the data used to determine the friction
factors for regime transitional waves are poorly ordered and that the

82
resulting values should be used with caution. Grant and Madsen (1979)
state that their approach is applicable to regime transitional waves
but fully rough turbulent flow has previously been assumed (Drake and
Cacchione 1986, Drake et al. 1992, Cacchione et al. 1987, Grant and
Madsen 1979 and 1982, Signell et al. 1990).
The maximum wave-current bottom shear stresses were estimated with
the Grant and Madsen (1979) model (fig. 3-1). Estimated maximum bottom
shear stresses were greatest from 1400 to 1900 hours during which time
the suspended-solids concentration increased. This qualitative
behavior and the correlation coefficient with suspended-solids
concentration for the wave-current bottom shear stress (r=0.7, table 3-
3) are virtually identical to that for the maximum bottom shear
stresses estimated considering wave motion only.
Compared to the bottom shear stress estimated by the Grant and
Madsen model for wave motion only (eqns. 1-11 and 1-13) and the sum of
this wave shear stress and the mean current shear stress (eqn. 1-5),
consideration of wave-current interaction slightly increases the
estimated bottom shear stress, but this increase is smaller than the
uncertainty associated with the wave friction factor. During the
period of greatest wave activity from 1400 to 1900 hours, the maximum
bottom shear stresses estimated with the wave-current model were 9%
greater than those estimated considering waves only (eqns. 1-11 and 1-
13) and 6% greater than the sum of the mean current (eqn. 1-5) and wave
only shear stresses. The maximum wave bottom shear stress during this
period calculated with the friction factor diagram by Kamphius (1975)
is 44% greater than the shear stress calculated with the friction
factor of equation 1-13. Therefore, for this data set, the estimated
maximum bottom shear stress seems to be more sensitive to the selected

83
estimation procedure than the possible effect of wave-current
interaction.
Because the waves at the platform are depth transitional, the
bottom orbital velocity and estimated wave bottom shear stress are also
sensitive to the wave period and water depth and errors in these
quantities can produce large errors in the wave bottom shear stress, as
discussed previously. A similar sensitivity analysis of the wave-
current model using a water depth of 400 cm, wave period of 2.6
seconds, wave amplitude of 30 cm, an angle between the wave and current
of 150 degrees, a 0.3 cm bottom roughness, and a mean velocity of 10
cm/s at an elevation 70 cm above the bed indicates that a 10% increase
in wave amplitude, a 10% increase in wave period, and a 10% decrease in
water depth, increases the maximum wave-current bottom shear stress 14,
39, and 37%, respectively. The maximum wave-current bottom shear
stress was relatively insensitive to 10% changes in mean velocity (4%),
angle (0.4%), and bottom roughness (4%). Selection of a representative
wave period from a measured wave spectrum is probably the most likely
source of inaccuracy.
The sediment resuspension observed on March 8, 1990, at the Old
Tampa Bay platform was caused by increased wave motion associated with
strong and sustained northeasterly wind. The bottom shear stresses
estimated by considering the mean current only were much less than the
maximum bottom shear stresses estimated by considering wave motion
only. Wave-current interaction may have contributed to the bottom
shear stress, but this difference is not as significant as the
differences associated with the selected wave period and the selected
procedure used to calculate the wave friction factor. The period of
the largest estimated wave and wave-current shear stresses corresponds

84
to the period of sediment resuspension. The mean current shear
stresses did not correspond to the suspended-solids concentrations and
were less than the Shields critical shear stress for the sediments at
the platform.
November 1990 Storm
After passage of a cold front, a high pressure system north of
Florida generated northerly to easterly winds from November 29 to
December 1, 1990, during which time sediment resuspension monitoring
instrumentation was deployed in Old Tampa Bay. Maximum wind speeds of
10 to 12 m/s occurred during the afternoon of November 30 (fig. 3-2 and
table 3-4). Wave activity increased as a result of the sustained
winds, providing favorable conditions for sediment resuspension. The
platform instrumentation was deployed on November 28 in anticipation of
sediment resuspension. Operational equipment at the platform consisted
of electromagnetic current meters at elevations of 24, 70, and 183 cm
above the bed, OBS sensors 70 and 183 cm above the bed, and a pressure
transducer. Water samples were manually collected during instrument
on-time each day during the instrument deployment (November 28 to
December 3) at the elevations of the OBS sensors. The samples were
used to calibrate the output of the OBS sensors to suspended-solids
concentrations. An automatic water sampler at the platform
malfunctioned during the storm. The suspended-solids concentrations
rapidly increased above ambient values late in the morning of November
30 and decreased rapidly late in the evening of November 30 (fig. 3-2).
The bottom shear stress for the mean current only was calculated
with equation 1-5 and the mean current speed 24 cm above the bed, and
the temporal variation of this shear stress is not similar to the
variations of suspended-solids concentrations. The mean current speeds

Figure 3-2, Measured and calculated quantities at the Old Tampa
Bay platform, November 1990
MAXIMUM BOTTOM
ORBITAL VELOCITY, SIGNIFICANT WAVE AMPLITUDE,
IN CENTIMETERS PER SECOND IN CENTIMETERS
WIND SPEED,
IN METERS PER SECOND
MEAN CURRENT SPEED,
IN CENTIMETERS PER SECOND
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SUSPENDED-SOLIDS
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86
Table 3-4.--Old Tampa Bay platform data, November 30 - December 1,
1990.
Hour
Water
depth
(cm)
Mean current speed
(cm/s) at elev.
24 cm 70 cm 183 cm
Wind
speed
(m/s)
Wave
amp.
(cm)
Wave .
k
period
(sec)
Susp.-
cone .
70 cm
solids
(mg/L)
183 cm
0800
317.4
8.7
14.0
11.8
7.1
6.5
2.02/2.71
32.4
49.0
0900
314.0
2.4
4.5
2.4
8.8
15.4
2.10/2.47
40.1
42.3
1000
320.4
9.9
10.2
11.1
10.0
18.7
2.19/2.79
52.8
55.7
1100
331.8
10.3
9.7
9.7
11.6
24.7
2.42/2.55
70.6
65.7
1200
344.2
10.6
10.9
-
9.9
25.8
2.56/2.50
93.3
76.9
1300
356.5
8.5
8.4
8.8
10.9
25.6
2.39/2.57
80.8
79.0
1400
367.1
5.6
4.7
5.1
11.0
25.6
2.67/2.59
90.7
80.2
1500
375.6
5.5
4.4
4.0
12.2
29.7
2.81/2.63
93.3
80.2
1600
381.8
2.9
1.4
2.5
12.5
28.0
2.98/2.64
93.3
88.0
1700
385.1
5.3
1.8
4.1
11.7
30.6
2.46/2.62
106.2
91.4
1800
386.5
4.9
3.7
5.0
7.9
21.2
2.81/2.68
103.6
93.5
1900
385.9
2.2
3.5
1.8
8.0
19.4
2.56/2.39
96.0
77.9
2000
390.3
4.3
5.9
5.3
7.7
12.0
2.21/2.48
62.6
60.1
2100
400.3
9.6
10.7
11.6
6.8
10.5
2.01/2.39
57.7
50.0
2200
413.4
9.1
8.9
9.6
5.5
4.7
2.02/3.08
50.1
45.5
2300
426.6
8.8
6.6
8.6
4.2
3.0
2.31/4.25
42.5
34.4
0000
437.1
6.5
7.6
7.7
4.2
1.7
2.15/3.69
27.1
35.5
0100
443.7
4.2
3.2
4.0
4.8
1.8
2.06/3.80
24.6
32.1
k
Wave periods are
upcrossing period
maximum
of the
energy of the
squared bottom
surface amplitude
orbital velocity
spectrum/zero
spectrum.

87
24, 70, and 183 cm above the bed and the calculated bottom shear stress
are shown in figure 3-2. The complete measured velocity profile was
sometimes either nonaligned or not logarithmic, especially near slack
tide, so only the mean current speed 24 cm above the bottom was used to
calculate the bottom shear stress. Maximum mean current speeds 24 cm
above the bed during morning ebb tides were about 12 cm/s, and the
corresponding shear stress calculated with equation 1-5 was 0.36
dynes/cm2. These shear stresses do not correspond to the elevated
suspended-solids concentrations during the late morning and afternoon
of November 30 (r=-0.3, table 3-5). The mean current is usually less
than 5 cm/s during the period of increased suspended-solids
concentrations so horizontal advection is probably not significant, as
was found for the March 1990 data set.
Bottom shear stress considering wave motion only was calculated
with the methods of Kamphius (1975) and Grant and Madsen (1979, 1982),
and these shear stresses and other wave properties correspond to the
observed suspended-solids concentrations. Spectral analysis of the
pressure data was used to calculate the significant wave height and
maximum bottom orbital velocity (fig. 3-2). The wind was from the
north during the evening of November 29 and wave formation at the
platform may have been hindered by the Courtney Campbell Causeway 1.85
km north of the platform. The wind direction slowly shifted to be
north-easterly during the morning of November 30 and almost easterly by
the end of November 30. The greater fetch and greater wind speeds on
November 30 increased wave activity at the platform. The waves were
depth transitional from 0600 to 1900 hours on November 30 and otherwise
the waves were deep-water waves. The maximum bottom orbital velocity
(u^) was slightly better correlated with suspended-solids

88
Table 3-5Correlation coefficients for various wave properties and
bottom shear stresses with suspended-solids concentrations at the Old
Tampa Bay platform, November 1990.
Elevation of measured
suspended-solids concentration
70 cm 183 cm
Shear stress: mean current only
-0.31
-0.30
Shear stress: wave only (Kamphius 1975)
0.90
0.91
Shear stress: wave only
(Grant and Madsen 1979 and 1982)
0.85
0.86
Shear stress wave-current
(Grant and Madsen 1979)
0.86
0.87
Wave amplitude
0.84
0.82
Bottom orbital velocity
0.89
0.90
Square of bottom orbital velocity
0.81
0.82

89
concentrations (r=0.9, table 3-5) than the wave amplitude (r=0.83).
The correlation between suspended-solids concentration and u£ (r=0.82)
is not as good as that with u^. The critical maximum orbital velocity
is about 8 cm/s. The shear stress considering wave motion only that is
calculated with the method of Kamphius (1975) is usually greater than
that calculated with the method of Grant and Madsen (1979, 1982). The
wave-induced shear stresses are much greater than the shear stress
calculated from the mean current and correlate well with suspended-
solids concentration (r=0.9, table 3-5).
Bottom shear stresses calculated with the wave-current model also
correlate well with suspended-solids concentrations (r=0.87, table 3-5)
because the wave-current shear stresses are only slightly greater than
those calculated considering wave motion only. During the period of
greatest wave activity from 0900 to 1900 November 30, the bottom shear
stresses estimated with the wave-current model were 14% greater than
those estimated by considering wave motion only and 9% greater than the
sum of the mean current (eqn. 1-5) and wave only (eqns. 1-11 and 1-13)
shear stresses. The friction factor from Kamphius (1975) gives wave-
only shear stresses that average 66% greater than those from equation
1-14. Therefore, as was the case for the March 1990 platform data, the
mean current and wave-current interaction made small contributions to
the bottom shear stress, and the error created by neglecting these may
be less than the error associated with the calculation of the wave-only
bottom shear stress.
The observed sediment resuspension on November 30, 1990, at the
Old Tampa Bay platform was caused by wind-waves, similar to the
sediment resuspension observed on March 8, 1990. Wave properties and
shear stresses that consider wave motion only are in good agreement

90
with observed suspended-solids concentrations. The mean current in the
absence of waves did not resuspend sediments, and wave-current
interaction was probably not significant.
Tropical Storm Keith
Tropical storm Keith made landfall approximately 50 km south of
the Old Tampa Bay platform early in the morning of November 23, 1988,
and platform instrumentation measured wind and wave properties during
the storm. Horizontal velocity components were measured 94 and 295 cm
above the bed at a 1 Hz frequency for 5 minutes every hour. Mean
values of water depth, wind speed, and wind direction were collected at
the same time. The pressure transducer was vented to the atmosphere to
prevent measurement of changes in atmospheric pressure. Wind direction
was in agreement with wind directions recorded at Tampa International
Airport (approximately 10 km to the east northeast) until early in the
morning of November 23, when the wind vane was damaged by 23 m/s winds.
The OBS sensors were fouled and the automatic pumping sampler could not
be deployed before the storm arrived, so suspended-solids
concentrations during the storm are unknown.
Wave activity was much greater during tropical storm Keith than
during the observed winter storm systems discussed previously, and
therefore sediment resuspension was likely. Wind speed increased
during November 21 and 22 as the storm approached Tampa Bay, a maximum
wind speed of 23 m/s was measured at 0100 hours on November 23 at the
platform, and the wind speed decreased during November 23 and 24 (fig.
3-3). The wind was from the east and northeast during November 22 and
from the north on November 23 (at Tampa International Airport).
Spectral analysis of the velocity data collected 94 cm above the bed
and linear wave theory were used to calculate the maximum bottom

91
1800 0600 1800 0600 1800 0600
NOVEMBER
Figure 3-3, Mean water depth, mean current speed, and maximum bottom
orbital velocity at the Old Tampa Bay platform during tropical storm
Keith, November 1988

92
orbital velocities (fig. 3-3). The bottom orbital velocity increased
during November 22 as the east and northeasterly winds increased, and
the critical bottom orbital velocity for sediment resuspension of about
8 cm/s observed in November 1990 was consistently exceeded after 1400
hours on November 22. The greatest bottom orbital velocity was 53 cm/s
at 0200 hours on November 23, which is about 2.7 times larger than the
greatest values calculated for the winter storm systems in March and
November 1990. If the friction coefficient in equation 1-11 is assumed
to be constant, the maximum bottom shear stress considering wave motion
only was about 7 times greater during tropical storm Keith than during
the observed winter storm systems which resuspended bottom sediments.
Therefore, sediment resuspension was likely during tropical storm
Keith. After 0200 hours on November 23, the wind speed decreased
slowly but the bottom orbital velocity decreased rapidly because the
wind shifted from northeast to north and the Courtney Campbell Causeway
north of the platform reduced the fetch.
Decreasing atmospheric pressure associated with the storm may have
caused high water levels and subsequent large ebb water velocities
during the morning of November 23. At 0100 hours on November 23, a
relatively large maximum water depth of 456 cm was measured at the
platform (fig. 3-3). At approximately this time, a high tide was
predicted and the atmospheric pressure measured at Tampa International
Airport was near the minimum value measured during the storm. The
measured water level was about 40 cm greater than predicted, possibly
because additional water entered Old Tampa Bay in conjunction with a
long wave forced by the moving system of low atmospheric pressure (Dean
and Dalrymple 1984) . Wind could not account for the increased water
level in Old Tampa Bay because the wind was from the northeast to

93
north. The ebb water velocity measured at 0200 hours 94 cm above the
bed was 20 cm/s, which is a very large mean velocity at the platform,
and large ebb water velocities continued until 0600 hours on November
23 (fig. 3-3). The combination of ebb tide and the ebbing of the long
wave forced by the moving atmospheric pressure disturbance may account
for the relatively large ebb water velocities.
Despite the large ebb water velocities, the most likely bottom
sediment resuspension mechanism during tropical storm Keith was the
oscillatory wave motion because the estimated bottom shear stress for
wave motion only is greater than the estimated bottom shear stress for
the mean current only and almost as large as the bottom shear stress
estimated by the wave/current model. Because the bottom orbital
velocities during tropical storm Keith were the largest measured at the
platform, bed forms may have increased the bottom roughness during the
tropical storm. A sufficient number of near-bed velocity measurements
are not available to determine the bottom roughness in November 1988,
however, so the previously determined bottom roughness of 0.3 cm will
be used. At 0200 hours on November 23, the mean water velocity and the
bottom orbital velocity were each maximum values and the estimated
bottom shear stress considering the mean current only was 0.74
dynes/cm2, the estimated bottom shear stress considering wave motion
only (eqn. 1-11 and 1-13) was 29.3 dynes/cm2, and the estimated bottom
shear stress with the Grant and Madsen (1979) wave/current model was
32.7 dynes/cm2. The difference between the wave/current and the sum of
the wave and current shear stresses is about 2.7 dynes/cm2, which
represents the contribution of the nonlinear interaction of the waves
and mean current. Most of the total bottom shear stress was caused by
oscillatory wave motion with smaller contributions from wave/current

94
interaction and the mean current. Analysis of other data sets
collected during the tropical storm indicates that the bottom shear
stress considering waves only was much greater than the shear stress
considering the mean current only and almost as large as the shear
stress estimated by the wave/current model during the period of likely
sediment resuspension.
Tropical Storm Marco
Tropical storm Marco moved northward along the coast of west-
central Florida on October 11, 1990, generating strong winds and rough
seas. The wind was from the east at about 5 m/s during the afternoon
of October 10, and the wind speed increased to 15 m/s and the wind
direction shifted from easterly (270° azimuth) to southerly (0°
azimuth) during the morning of October 11 (fig. 3-4). The speed of the
southerly winds decreased during the afternoon of October 11.
Suspended-solids concentrations at the Old Tampa Bay platform
increased from 50 mg/1 to 200 to 300 mg/1 at the peak of the storm
(fig. 3-4). The suspended-solids concentrations in fig. 3-4 are from
an OBS sensor 183 cm above the bed and from an automatic water sampler
that collected hourly samples 24 cm above the bed. The sample storage
capacity of the automatic sampler was reached at 1200 hours on October
11, but it could not be serviced due to rough seas. The suspended-
solids concentration increased during the morning of October 11 as the
wind speed increased and the wind shifted from easterly to southerly.
The maximum measured suspended-solids concentrations correspond to the
maximum southerly wind and are the largest concentrations ever measured
at the platform. The suspended-solids concentration decreased to
ambient levels as the wind speed decreased during the afternoon and
evening of October 11. The rapid increase and decrease in suspended-

95
OCTOBER
10
1990
Figure 3-4, Wind speed, wind vector azimuth, and suspended-solids
concentration at the Old Tampa Bay platform during tropical storm
Marco, October 1990

96
solids concentration associated with wind speed and wind direction was
similar to observations during smaller storms in March and November
1990. Velocity and pressure were not successfully measured at the
platform during the storm.
Implications for Numerical Modeling
A vertical one-dimensional numerical model can be used to simulate
sediment resuspension in Old Tampa Bay because horizontal advection is
not a likely cause of the observed increases in suspended-solids
concentration. The tidal excursion was within the large area of
homogeneous sediments that surrounded the platform and sediments
further upcurrent were probably not resuspended. If horizontal
transport of resuspended sediments were to be studied, however, a
three-dimensional model would be required.
Sediment resuspension in Old Tampa Bay is caused by wind-waves, so
oscillatory motion at wind-wave frequencies must be included in a
numerical model of sediment resuspension. Although a single wave
amplitude and wave period were selected for the preceding analysis,
there are actually many amplitudes and frequencies in the wave field,
so a numerical model should include more than a single wave frequency.
Wind-waves in Old Tampa Bay are depth transitional, so the vertical
attenuation of wave motion with increasing distance below the water
surface should be simulated by a numerical model.
A numerical sediment resuspension model should erode bottom
sediments as a function of the grain shear stress. Not surprisingly,
the erosion of bottom sediment in Old Tampa Bay seems to depend upon
the bottom shear stress, so a model should include an accurate shear
stress algorithm. The preceding analysis calculated the total bottom
shear stress, but erosion is actually determined by the grain shear

97
stress. The spatially-averaged grain shear stress is expected to vary
with the spatially-averaged total shear stress and to be less than the
total shear stress. The shear stress algorithm should also account for
regime transitional flow at the bed.
The numerical simulation results should be compared to the hourly
suspended-solids concentration data. Spectral analysis of the burst
OBS data indicated that wave frequencies were not dominant and that the
spectrum was broad-banded. The lack of a dominant wind-wave signal in
the OBS data is probably caused by local advection and patchiness of
suspended solids and inability of the OBS sensors to detect small
concentration changes caused by vertical advection. Therefore, the OBS
data collected during each burst sample can not be simulated by a
vertical one-dimensional model. Local advection and patchiness
probably has little effect on the mean concentrations collected during
the 5 minute burst sample, so simulation results should be compared to
hourly mean concentrations.
A model should be able to successfully simulate all of the phases
of the observed episodic resuspension events. These phases are net
erosion during the storm, net deposition as the storm diminishes, and
ambient conditions before and after the storm. Starting a simulation
with ambient conditions before the storm also provides the best initial
condition. The lack of data for 55 minute periods each hour, however,
will require interpolation or extrapolation of measured data. Because
the duration of the simulation will be on the order of many hours and
the time scale of wave-induced grain shear stress is on the order of a
second, the simulation must contain thousands of time steps and may
require significant computational resources.

CHAPTER 4
NUMERICAL MODEL
Additional analysis and interpretation of the Old Tampa Bay data
can be achieved by using a numerical model, that is based on physical
laws, to simulate suspended-solids concentrations and comparing
simulation results with measured data. If the model reasonably
represents the important physical processes, such as settling and
turbulent transport, then the simulation results should compare
favorably with measured data, and the calibration coefficients used by
the model should be reasonable and physically relevant. For example, a
a polynomial could be fitted to a data set, but the coefficients of the
polynomial would have no physical significance. A model that is
constrained by equations that represent physical laws, such as
conservation of momentum and conservation of mass, and that can produce
results that are in reasonable agreement with measured data, must
include a reasonable numerical representation of the relevant physical
processes. Physically-based calibration coefficients (such as settling
velocity or erosion rate coefficients) that are determined by applying
such a model should be reasonable compared to known properties of the
system being modeled (such as particle size) and coefficient values
found by other studies. If the results of a physically-based model are
poor, then relevant processes are either neglected or not properly
represented. Consideration of additional physical processes or
improved representation of processes already included in the model
should improve simulation results. In this manner, a physically-based
98

99
numerical model can be used as a tool to help analyze measured data and
to determine significant physical processes that affect the data.
Simulations of sediment transport in Old Tampa Bay were conducted using
this philosophy.
A one - dimensional vertical hydrodynamic and sediment transport
model that includes an advanced turbulence closure model would be well-
suited for simulating the Old Tampa Bay data. As discussed in chapter
3, horizontal advection of suspended solids was not significant during
sediment resuspension events at the Old Tampa Bay platform, and
therefore a vertical one-dimensional model would be appropriate. Wind-
wave motions are important and the bottom roughness regime may be
transitional between the rough and smooth limits, so advanced
turbulence closure is desired. Vertical one - dimensional sediment
transport models without advanced turbulence closure include those by
Weisman et al. (1987), which neglected vertical dispersion, and by
Hamblin (1989), which used a parabolic eddy diffusivity. A model by
Adams and Weatherly (1981) assumed that turbulence was in local
equilibrium. A vertical one-dimensional sediment transport model by
Sheng and Villaret (1989) includes simplified second order turbulence
closure. This model is called 0CM1D (Ocean Current Model: One-
Dimens ional) and was used in this study because it includes advanced
turbulence closure and has been successfully applied to several water
bodies (Sheng 1986b, Sheng and Chiu 1986, Sheng et al. 1990b).
The numerical model 0CM1D was developed by Sheng (1986a) to
simulate hydrodynamics and vertical transport in the water
column. The spatial domain to be simulated is divided into vertically-
stacked computational layers and the simulation procedes forward in
time. The model solves the unsteady one-dimensional (vertical) flow

100
and transport equations and uses a simplified second order closure of
turbulent transport, which was modified from the original turbulence
model developed by Donaldson (1973) and Lewellen (1977) for atmospheric
flows. In the original turbulence model, density was dependent on
temperature only. Sheng (1986a) added the influence of salinity on
density, and Sheng and Villaret (1989) added the influence of
suspended-sediment concentration on density to the turbulence model.
0CM1D has been used to simulate storm-induced currents in Grand Bank
(Sheng 1986b) and in the Atlantic Ocean during the passage of hurricane
Josephine (Sheng and Chiu 1986). 0CM1D has also been used to simulate
the wave-induced erosion and vertical mixing of fine sediment in a
shallow lake (Sheng et al. 1990b) and to simulate the effect of
sediment stratification on bottom exchange processes (Sheng and
Villaret 1989). For completeness, the governing equations for
momentum, transport, and turbulence closure are presented in this
chapter.
This research began with the 1986 version of 0CM1D (Sheng 1986a)
and modifications were made by the author to 0CM1D for this study.
These modifications are presented in detail in this chapter and are
summarized in table 4-1. The 1986 version included equilibrium closure
for turbulent transport and the turbulent macroscale was determined
with integral constraints. A dynamic equation for the turbulent
velocity was added to 0CM1D by Sheng and Villaret (1989) after 1986 and
independently added by the author to the version of 0CM1D used in this
research. Use of this dynamic equation is called turbulent kinetic
energy (TKE) closure of turbulent transport. Viscous terms that were
part of the original turbulence model (Lewellen 1977) and a dynamic
equation for the turbulence macroscale were added by the author to

101
Table 4-1-Modifications made to the 1986 version of 0CM1D (Sheng
1986a) for this research.
1986
This research
Closure of
turbulent
transport
Viscous
effects
Equilibrium closure with
integral constraints on
the turbulent macroscale
None
Equilibrium closure with
integral constraints on
the turbulent macroscale
or TKE closure with
integral constraints or
dynamic equation for the
turbulent macroscale
Included
Steady state Given wind and water
calculation surface slope
Given wind and up to 3
velocities
Waves
Single frequency
Multiple frequencies
Total bottom Fully turbulent flow and
shear stress a rough bottom
Laminar, transitional, or
rough flow, and smooth,
transitional, or rough
bottom
Grain shear None Estimated
stress
Suspended- None Included
sediment
stratification

102
OCM1D because the simulated hydrodynamics were not always fully
turbulent. The author added an option to the model that allowed
specification of up to three velocity component pairs to permit
determination of steady state conditions for a set of velocity
measurements. A wave-induced pressure gradient submodel that allows
multiple wave frequencies was added by the author to 0CM1D. The 1986
version of 0CM1D calculated the bottom shear stress with relationships
for fully turbulent flow and a rough bottom. The author modified the
calculation of the total bottom shear stress to account for laminar and
transitional flows near the bed and to account for smooth and
transitional bottom roughness. A submodel that estimates the
spatially-averaged grain shear stress was added by the author to 0CM1D
to improve simulation of suspended sediment. A relationship for
sediment density stratification was added to 0CM1D by Sheng and
Villaret (1989) and independently added by the author to the version of
0CM1D used in this research. Sheng and Villaret (1989) also
independently added a wave-induced pressure gradient and smooth and
transitional bottom roughness to the model.
Momentum and Transport Equations
The time - averaged Reynolds equations for three dimensional flow
and transport in tensor notation are
du.
i
dx.
0
(4-1)
u.
J
duu'.
k_J.
dx.
J
1 dp
dx.
l
u.
J
dc
dx
d2u.
2eiik°iuk + "
J J j
(4-2)
dx.
J
+ e
(4-3)

103
in which u are the mean velocity components, pis a reference fluid
density, p is pressure, € is the alternating tensor, Q is the angular
velocity of the Earth, c is the mean suspended-sediment concentration,
temperature, or salinity, and 0 is a source/sink term with units of
concentration per unit time (Donaldson 1973, Sheng 1986a, Sheng and
Villaret 1989). Equation 4-1 is the continuity, or conservation of
fluid mass equation, equation 4-2 is the conservation of momentum
equation (actually 3 equations, one for each principal axis), and
equation 4-3 is the transport or conservation of constituent mass
equation. The fluid density can be determined from the sediment
concentration, salinity, and/or temperature by an equation of state.
The vertical form of these equations is obtained by neglecting the
horizontal gradients of velocity and constituent concentration. As
discussed previously, horizontal transport is not significant at the
Old Tampa Bay platform and therefore horizontal gradients can be
neglected. The continuity equation then gives zero vertical velocity
in the water column for a nonporous bed. The origin of the coordinate
axes is located at the mean water surface, the x and y axes are
horizontal, and the vertical z axis is positive upwards. For the x
axis, the momentum equation becomes
du 3u'w' 1 3d 32u ,, ,.
77 = - — a + fv + v t 2 (4-4)
at az p dx az2
o
in which velocity components (u,v,w) correspond to the coordinate axes
(x,y,z) and f is the Coriolis coefficient.
The pressure term can be split into hydrostatic and non¬
hydrostatic components. Assume that the hydrostatic pressure
distribution is valid so that
az
= -p g
(4-5)

104
P = - J| PS dz +
in which density p varies along the vertical (z) axis. Integration
from the water surface to a depth z gives
(4-6)
where £ is the surface displacement from the mean water depth that
varies along the x and y axes and p^ is the pressure at the water
surface (atmospheric or for small amplitude waves). Differentiation
and the Leibnitz rule (Abromowitz and Stegan 1965) give the pressure
gradient
a ap,
dx dx
rz d_ . . , d£
U dx <'*> dz + po^dx
(4-7)
Substitution of equation 4-7 into equation 4-4 produces the
momentum equation along the x axis
dp
3u
at
au'w' i i rz a , . . af r a2u ..
T aT + T áü (PS) dz ’ sáx + fv + " ^ (4‘8)
o o
dz p dx p dx °dx dz"
o o
The term on the left hand side is the unsteady (temporal) term. The
terms on the right hand side are the vertical gradient of the second
order correlation of fluctuating velocities, horizontal pressure
gradient, horizontal density gradient, surface slope, Coriolis force,
and viscous terms. The derivation of the momentum equation along the y
axis is similar, and the result is
a2v
dv
at
aPc
dv'w' 1 l£ L fz á— / N .
â–  po ay po h ay (PS) dz
dz
- fu + v . 2
bd y dz2
(4-9)
dc dc 3 w’c
— = W — - — + 0
at s dz dz
The vertical one-dimensional transport equation is
(4-10)
The term on the left hand side of equation 4-10 is the unsteady term
and the right hand side terms are settling, vertical turbulent flux of
suspended sediments, and source/sink terms. Equation 4-10 is similar
to equation 1-17.

105
The second order correlation terms in equations 4-8 to 4-10 can be
written in terms of the vertical gradient of time-averaged variables.
The vertical eddy viscosity is defined as
du
and
-u'w' = A 1~
v dz
——r a
v'w' = A ~
v 9z
The vertical eddy diffusivity K^is defined as
dc
(4-11)
(4-12)
-w'c' = K
v dz
(4-13)
The eddy diffusivity can also be defined by replacing c in equation 4-
13 with density p. Equation 4-13 is the same as equation 1-16. The
vertical eddy viscosity and diffusivity vary vertically and temporally
and are determined from a turbulence closure model to be described
later.
Boundary conditions are needed at the top and bottom of the
vertical model domain. If the upper model boundary is at the free
surface, the upper boundary conditions are
(4-14)
(4-15)
(4-16)
ar stress components at the free
surface. If the upper model boundary is below the free surface, the
upper boundary conditions are specified velocities and concentration.
If the upper model boundary is below the free surface and within the
constant stress layer, the upper boundary conditions are
= 0 (4-17)
= 0 (4-18)
c = c (4-19)
-p u'w1
= p
A
du
= T
ro
yo
V
dz
WX
-p v'w1
= p
A
dv
= r
o
o
V
dz
wy
-w'c' =
K ^
_
0
which r
v dz
and t
are
wind
wx
wy
d -1—7
_ d_
A
du
dz
dz
V
dz
a -i—r
d_
A
dv
dz
dz
V
dz

106
- D
u'w'
1 + p
du
v - =
p
(A + v)
du _
T
O
0
dz
0
V
dz
X
- D
v'w’
' + p
v — =
p
(A +i/)
<3v _
T
O
0
dz
O
V
dz
y
- w' c ' =
K ÍT
v dz
= E
where is a specified concentration at the upper boundary. The
kinematic viscosity terms in the momentum equations are assumed to
equal zero at the upper boundary. The bottom boundary conditions are
(4-20)
(4-21)
(4-22)
in which r and r are the total bottom shear stress components,
x y r
Turbulence Closure
In order to solve the momentum and transport equations, the eddy
viscosity and eddy diffusivity defined in equations 4-11 to 4-13 must
be determined. 0CM1D allows specification of either constant values or
values that are dependent upon the Richardson number (Sheng 1986a).
Constant eddy coefficients are useful for comparing model solutions
with analytic solutions, but they are not realistic. Both the constant
eddy coefficient and the Richardson number dependent eddy viscosity are
not realistic because they fail to represent the vertical and temporal
variability of turbulence. The Richardson number dependent eddy
coefficients are not applicable if stratification is unstable.
Therefore, a simplified second order closure submodel of turbulent
transport was included within 0CM1D for the purpose of providing a more
realistic algorithm for calculating the eddy coefficients.
The dynamic equation for the second order velocity correlations is
(Lewellen 1977, Sheng 1982)
du'.u'.
—J-J.
a t
<3u'u!
k
5u.
‘i^ d
du.
i
u'. p'
x,_ • ¿r+ Si -j- +
u' p '
1
- 2eikiVíuj - 2€jikQiukui
a au'.u'.
+ V° ^k ( }
q , —:—r , a2. r 2ba3
- 7 ( u.u! - 6..—r~) - 6.. —77-
A 1 j ij 3 ij 3A

107
+ i/
a2u:u:
dx, 2
k
2au u!u'.
i J.
(4-23)
in which the total root mean squared turbulent fluctuating velocity q =
(u^u^) , A is a length scale of turbulent eddies also called the
turbulence macroscale, p' is the turbulent density fluctuation about
the mean density, &. . is the Kronecker delta, and a, b, and v are
invariant constants that were determined to be 3, 0.125, and 0.3,
respectively (Lewellen 1977). The terms on the left hand side are
temporal and advective evolution terms. The first two terms on the
right hand side are shear production terms and they are followed by two
buoyancy terms, two rotation terms, a turbulent diffusion term, a
tendency toward isotropy term, a turbulent dissipation term, a viscous
diffusion term, and a viscous dissipation term. The turbulent
diffusion term, tendency toward isotropy term, turbulent dissipation
term, and viscous dissipation term are modeled terms which are
simplified expressions of the original terms which contain third order
correlations and pressure fluctuations and would otherwise prevent
closure.
A dynamic equation for mean squared turbulent fluctuating velocity
can be derived from equation 4-23 by summing the equations for i=j=l,
i=j=2, and i=j=3. The resulting dynamic q2 equation is
dq2
t 9 du.
+ u
dt i dx. * ~
i k
- 2u:u7 —~ + 2g. —
IK dx, p
d
fli
+ v ~— ( qA j3- ) - 2b
c dx^ dx^ A
+ i/
d2a2
dx. 2
k
2at^q:
(4-24)
The vertical one-dimensional dynamic equation for the mean squared
turbulent velocity fluctuation is

108
Üül
at
r,——r 3u 7—- 3v 2e ——r
2u w — - 2v w' — - w' p'
dz dz p
o
+ V — ( qA )
c dz dz
2b ai + „ Üai .
a + " az2 a2
(4-25)
The dynamic equation for the second order velocity and density
correlations is
3u'.p' du'.p'
1 1
+ u.
- 3u. , ,
u:u'. - u'. p' ~1 ~ + g. P P
i i ax. i ax. °i p
J J o
at
j 3x.
J
3 3u!p'
2eijknjUkP' + Vc ÍZ ( }
J J
. 32u!p' aku!p'
, u! p + k — + —75—
A 1 3x.2 A2
J
(4-26)
in which A is an invariant constant equal to 0.75 and k is the
molecular diffusion coefficient. The terms on the left hand side are
evolution terms and the right side contains two production terms
followed by buoyancy, rotation, diffusion, dissipation, and molecular
diffusion terms. The diffusion and dissipation terms are modeled
terms.
The dynamic equation for the second order density correlation is
do'o' do' o’ _ ——- 3p 3 . ,do' o' .
+ u.~t- = - 2 u'.p' -T~ + v -— ( qA—t—1— )
3t n 3x. i 3x. c 3x. n 3x.
J J J J J
)2„-
, d.ls.'.Ml. ?bs.q
K ax.2 " a
J
. I . Í
p p
(4-27)
in which s is an invariant constant equal to 1.8. The terms on the
left hand side are evolution terms and the terms on the right-hand side
are production, diffusion, and dissipation terms. The diffusion and
dissipation terms are modeled terms.
The turbulence macroscale must be determined in order to have a
closed set of equations. A dynamic equation for the turbulence
macroscale is
^ ir- A —;
3A 3A_
3t + Ui 3x.
1
3u. „ .
— u: u! —- + 0.6 7-5 A + 0.3 “— (qA ~—)
l2 1 l 3x. A2 3x. ^ 3x.
j 11
0.35

109
(4-28)
in which A is the Taylor microscale
A = A (a + bqA/u)
(4-29)
For large turbulent Reynolds numbers (qA/i/) , the second term on the
right hand side of the dynamic turbulence macroscale equation reduces
to 0.075q. All of the terms on the right hand side are modeled terms
and therefore equation 4-28 is less precise than the second order
correlation equations (Lewellen et al. 1976, Lewellen 1977, Sheng and
Villaret 1989). The vertical one-dimensional dynamic equation for the
turbulence macroscale is
(4-30)
for which the advective terms are assumed to be negligible.
Because all of the non-evolution terms in the dynamic turbulence
macroscale equation (4-30) are modeled terms, integral constraints can
be used to define the turbulence macroscale instead of the dynamic
equation without much additional loss of accuracy for high Reynolds
numbers (Lewellen 1977, Sheng and Chiu 1986, Sheng and Villaret 1989).
The turbulence macroscale will increase linearly away from fixed walls
(the bed) and the free surface, and the slope of this increase is 0.65
for fully turbulent flows (Lewellen 1977). If the Reynolds number is
low, this value may not be appropriate and turbulence may be far out of
equilibrium, so the dynamic turbulence macroscale equation may be more
appropriate than the integral constraints (Lewellen 1977) . The value
of A is limited by q/N (Sheng and Chiu 1986) where N is the Brunt-
Vaisala frequency
(4-31)

110
The value of A is also limited by the spread of turbulence such that
A < C 5 (4-32)
q q
in which S is the distance from the maximum value of q to where q is
q
one-half its maximum value and the coefficient C is selected based
q
upon the flow situation. Lewellen (1977) used computer optimization to
determine that this coefficient is 0.2 for axisymmetric jets, 0.3 for a
two-dimensional boundary layer, and 0.6 for a two dimensional shear
layer. A value of 0.2 was used by Sheng (1984) to simulate a turbulent
wave boundary layer and by Sheng and Chiu (1986) to simulate vertical
mixing in the Atlantic Ocean during the passage of hurricane Josephine.
The assumption that turbulence is in local equilibrium (called
superequilibrium by Lewellen (1977)) can be used to solve the second
order correlation equations for a vertical one-dimensional model. When
the time scale of mean flow evolution is much greater than the time
scale of turbulence (A/q), the evolution and diffusion terms in
equations 4-23, 4-26, and 4-27 are much smaller than the other terms
and can be neglected (Donaldson 1973, Sheng and Villaret 1989). This
is equivalent to assuming that turbulence in local equilibrium such
that the second order correlations, q2, and A have no knowledge of the
immediately preceding state of turbulence and no knowledge of the state
of turbulence in the surrounding fluid. The viscous dissipation term
is also neglected because the evolution and diffusive terms are
negligible only in high Reynolds number flows. Equilibrium closure has
been found to be valid for many situations (Donaldson 1973, Lewellen
1977, Sheng and Chiu 1986, Sheng and Villaret 1989). A benefit of
making this assumption is that the second order correlation equations
can be solved algebraically. The equations also can be simplified for
a vertical one-dimensional model for which horizontal gradients are

Ill
neglected, rotation is negligible so that the horizontal axes can be
rotated to make v = 0, and vertical velocity w = 0. The second order
correlation equations that are solved by the equilibrium closure
algorithm are
- 2 u'u' - * (u'u' - ^ ) - *=^r!- = 0
rrrrr 5u _ a
dz A
2bq 3
3A
(v'v' - ^ )
2ba3
—r áü
W W dz
^ w' p'
po
du
dz
3
£_
3A
= 0
u'w' = 0
(w'w'
ai ) . _ o
3 ' 3A
u'w' - A ^ u'p' =0
dz A
- w w
77T 3a
dz
b p p - A , w'p' = 0
p A
o
- 2 WJT ^ - 2bsq p'p' = 0
dz
(4-33)
(4-34)
(4-35)
(4-36)
(4-37)
(4-38)
(4-39)
in addition to the definition of q. These equations are written by
dropping the evolution and dispersion terms and setting (i,j)=(l,l),
(i,j)=(2,2), (i,j)=(3,l) and (i,j)=(3,3) in equation 4-23, i=l and i=3
in equation 4-26, and simplifying equation 4-27. Once the second order
correlations are known, the eddy viscosity and eddy diffusivity
coefficients can be determined from their definitions (eqns. 4-11 and
4-13). The procedure for solving the equilibrium closure equations has
been presented by Sheng et al. (1990a) and is given in appendix A.
The dynamics of turbulence and viscous effects can be partially
preserved by solving the dynamic q2 equation with the evolution,
diffusion, and viscous terms and using simplified second order
correlation equations to determine the eddy coefficients. Use of the
dynamic q2 equation combined with neglecting the evolution and
diffusion terms of the individual second order correlation equations is
called quasiequilibrium by Lewellen (1977) and turbulent kinetic energy
(TKE) closure by Sheng and Villaret (1989). The turbulence macroscale

112
can be determined either with the dynamic equation (eqn. 4-30) or the
integral constraints. The eddy viscosity and eddy diffusivity can be
determined from some of the equilibrium closure correlation equations.
Viscous dissipation terms are added to equations 4-35 and 4-36 because
viscosity is included in the dynamic q2 equation (eqn. 4-25) so that
w'w' u'p'
3z po
2at/
u'w' =0
^ w'p' - ^ (w'w' - )
a£
A2
2bq3 2at/
w'w' = 0
(4-40)
(4-41)
3A ' A2
The eddy coefficient definitions (eqns. 4-11 and 4-13) are substituted
into equations 4-37 to 4-41 and these five equations can be solved
algebraically to determine the eddy coefficients (Sheng et al. 1990a,
see appendix A).
In summary, turbulent transport closure can be achieved by 0CM1D
with either equilibrium closure or TKE closure, and the two methods are
compared in table 4-2. Equilibrium closure assumes that turbulence is
in local equilibrium, determines the turbulence macroscale with the
integral constraints, and algebraically solves second order correlation
equations for turbulent velocity q and the eddy coefficients. TKE
closure uses the dynamic q2 equation to preserve some of the dynamics
of turbulence, determines the turbulence macroscale with either the
integral constraints or the dynamic turbulence macroscale equation,
includes viscous effects, and algebraically solves second order
correlation equations for the eddy coefficients. Steady velocity
profiles calculated with the two methods will be compared in chapter 6.
Nondimensional Equations
The dynamic equations can be written in nondimensional form. The
finite differenced form of the nondimensional equations are solved by
0CM1D (appendix A). Nondimensional variables can be defined as

113
Table 4-2-Comparison of the equilibrium closure and TKE closure
methods for turbulent transport.
Equilibrium closure
TKE closure
turbulent velocity:
assumption
solution
equations
turbulence macroscale
eddy coefficients
assumption
solution
equations
viscous effects
local equilibrium
algebraic
4-33 to 4-39
integral constraints
local equilibrium
algebraic
4-33 to 4-39
neglected
dynamic
finite difference
4-25
integral constraints
or dynamic (eqn. 4-30)
local equilibrium
algebraic
4-37 to 4-41
included

114
*
u =
*
£ =
*
p =
*
c =
u
*
V
u ’
r
v =
u
r
, u'
X
X ’
r
y =
y_
X
r
'A'
, o
*
f u
r
X ’
r
“
P-P0
po
, p'
*
'o
1 M
o| a
*
w =
s
w
s
u
r
X
r
z ’
r
V
v ’
r
-U
A" =
V
A
V
A ’
r
*
K
V
u_
u
v'
v'
u
w’
W_
u
r
7 ^
= 7:, H = z H , t = tf
H r
g z
o b r
p u f z
or r
c f
r
*
, E =
c z f
r r
K
v * q . *
K ’ q u ’ A z
r r r
(4-42)
in which subscript r indicates a reference value, nondimensional
variables are indicated with an asterisk (*), and H is the elevation of
the model domain. In addition, dimensionless horizontal Rossby,
vertical Rossby, Reynolds, Ekman, Froude, and Prandtl numbers are
defined as
u u u z
R = t-5-, R = R “
x fx z fz e u
E = ——~
z f z2
u2 A
F2 = —E- P =
g zr’ K_
(4-43)
r ^ r r
Substitute equations 4-42 and 4-43 into equation 4-8 and simplify to
derive the nondimensional u-momentum equation
H j°
o E o 3 R dp.
¿u = _z L ( ¿Uv _x ^f
3t H2 3a C v 3ct; F2 ( 3x +
a 3x
da )
91
3x
+ v +
v R a2
z 3 2u
H2 R 3a2
e
(4-44)
in which the asterisk notation for the nondimensional variables has
been dropped. Similarly, the nondimensional v-momentum equation is
— = (a
3t H2 da ^ v 3a;
1 L 3v
* R
R 3p,
§ ( y— + H J° da ) -
2 3y Ja 3y 3y
u +
32v
H2 R 3a2
e
(4-45)
The nondimensional vertical transport equation is

115
a R a E a a
3c x 3c z 3 ... 3c,
W — + TTT ~ (K —) + 0
(4-46)
3t H "s do P H2 do Vi'v do'
The boundary conditions can also be written in nondimensional
form. Substitution of equations 4-42 and 4-43 into equations 4-24 to
4-26 gives the nondimensional boundary conditions at the free surface
(4-47)
3u _ H_
v da E Twx
z
. 3v H
A 7 = TT- t
v da Ez wy
K f = 0
v da
(4-48)
(4-49)
If the upper model boundary is below the free surface, the upper
boundary conditions are specified velocities and concentration. If the
upper model boundary is below the free surface and within the constant
stress layer, the upper boundary conditions are
0 (4-50)
0 (4-51)
(4-52)
The kinematic viscosity terms in the momentum equations are assumed to
equal zero at the upper boundary. The nondimensional bottom boundary
conditions are
d_
(A
V
du
da
do
d_
(A
V
dv
da
do
c =
c
u
R a
(A E + r^)
v z R do
e
= H T
P-
v z R do
K E
v da E
= H r
(4-53)
(4-54)
(4-55)
z
Substituting the eddy coefficient definitions (eqns. 4-11 and 4-
13), the nondimensional variables (eqn. 4-42), and the dimensionless
numbers (eqn. 4-43), the nondimensional dynamic equation for the mean
squared velocity fluctuations is
or 2E
da2 _ z . 3u 3u 3v 3v , z d¿
dt “ H2 v [ da da do da 1 P F2 H v da

116
+ v
z 3
c H2
u R
3a ( >
- 2bR
da‘
2ai/R q2
z n
H2 R A2
(4-56)
e e
The shear production term is written with the product of instantaneous
and time-averaged velocity gradients in order to prevent the generation
of turbulence by waves. If the production term were written with a
squared instantaneous velocity gradient, then transitional and deep
water waves would produce turbulence.
The nondimensional dynamic equation for the turbulence macroscale
is
3A n T- z A . . 3u 3u 3v 3v . „^r , 0.6at/ z
— = -0.35 7T7~A — + — — + 0.075R q + - —
3t H2 q2 v da do da do z A R
e
' do
, n o Rz 3 , . 3A, 0.375 Rz ,3qA,0
+ 0.3 h2 aa (qA 3a) - q h2 (^)2
0.8A ^z j. 3_£
+ q2 P F2 H v do
(4-57)
Eddy viscosity and diffusivity have been substituted for second order
correlations in equation 4-57. The shear production term is written
with the product of instantaneous and time-averaged velocity gradients
as was done for the dynamic q2 equation.
Steady State Conditions
The author added an option to the model that allows specification
of up to three velocity component pairs for steady simulations. This
option was added to determine steady state conditions for a set of
velocity measurements. The specified velocities are replaced by
pressure gradients as unknowns in the momentum equations. The pressure
gradient is assumed to vary linearly between the elevations of the
specified velocities. The pressure gradient at the elevation of the
lowest specified velocity is assumed to extend down to the bed and the

117
pressure gradient at the elevation of the highest specified velocity is
assumed to extend up to the water surface.
Wave-induced Pressure Gradients
Wind-waves are an important sediment resuspension mechanism in Old
Tampa Bay and therefore they need to be included in this modeling
effort. Surface gravity waves can be simulated by 0CM1D by providing
time-varying values for the pressure gradient components in the flow
equations. As discussed in chapter 3, wind-waves at the Old Tampa Bay
platform were transitional between the deep-water and shallow-water
limits, so the vertical attenuation of wave-induced pressure gradients
must be considered. The following submodel was added to 0CM1D to
permit the calculation of unsteady pressure gradient components
associated with surface waves.
The dynamic pressure gradients in both horizontal directions can
be calculated from velocity data by making the boundary layer
approximation
3d 3u
3x p 3t
(4-58)
A similar equation applies along the y axis. Equation 4-58 neglects
vertical motions and friction which are induced by wave motion, so the
velocity data used to calculate the pressure gradient should be close
to the bed where vertical motions are minimal but not within the wave
boundary layer where friction is significant (Grant and Madsen 1979,
Sheng 1982). Velocity data from the current meter closest to the bed
was used for simulations of sediment resuspension in Old Tampa Bay.
The simulation time step will probably differ from the data
collection interval and the wave motion may be extrapolated beyond the
duration of the 5 minute burst sample, so the pressure gradient is
estimated by applying the fast Fourier transform (FFT) to velocity data

118
to determine the coefficients of the Fourier series for the data
(equation 2-3). The pressure gradient at an elevation with a current
meter can be determined for each discrete frequency in the Fourier
series by dividing the change in velocity during the simulation time
step by the time step and applying equation 4-58,
|^(t,w,zv) = - ^ { a(u>) [cos(wt) - cos (ui( t - At)) ]
+ b(w) [sin(wt) - sin(w(t-At))] ) (4-59)
in which z is the vertical coordinate of the current meter that is
v
used to force the simulation (the meter closest to the bed for the Old
Tampa Bay simulations), a and b are Fourier series coefficients, and At
is the simulation time step. The Fourier series coefficients are
provided to the model to determine the pressure gradient at the
elevation where the data was collected for each frequency. Using a
Reynolds stress model, Sheng (1984) simulated the wave boundary layer
measured by Jonsson and Carlsen (1976) by decomposing the velocity at
the top boundary into 13 Fourier components. Pressure data, a single
wave frequency and amplitude, or an assumed or simulated wave spectrum
can be used to determine the Fourier series coefficients if appropriate
velocity data is not available.
The dynamic pressure gradient is distributed vertically with
linear wave theory. If the waves are shallow water waves, then the
dynamic pressure gradient is a constant value throughout the water
column. In Old Tampa Bay, however, the waves are transitional between
the deep and shallow water approximations. Thus, the wave-induced
dynamic pressure gradient and resulting wave action increases with
elevation above the bed. According to linear wave theory, the dynamic
pressure gradient (and the velocity fluctuations) will be proportional
with the pressure transfer function (Dean and Dalrymple 1984)

119
„ , , . , cosh [ k (u), h) (h+z) 1 ..
K (k(w,h),z) = Trw un ui (4-60)
p cosh[k(w,h) h]
in which k(cj,h) is the wave number that can be determined from the
dispersion relation for an angular frequency u> and mean water depth h
and h+z is the elevation above the bed. If measurements from a
subsurface gage are used to calculate energy spectra and the gage is
exposed to less than 9% of the water surface motion (K (k(w,h),z) <
P
0.09 Kp(k(t¿>,h) ,h) , the deep-water wave limit), then is set equal to
0.09 Kp(k(w,h),h) to reduce high frequency noise in the energy spectra
(J. Kirby, written communication, 1988). The pressure transfer
function is dependent upon the wave frequency and therefore the wave
motions must be transformed to the frequency domain in order to
distribute the dynamic pressure gradient vertically. Given the dynamic
pressure gradient for a particular frequency at a known elevation, the
dynamic pressure gradient at other elevations for the frequency is
(4-61)
¿2 = cosh [ k (cl> , h) (h+z)] dp
3x ’ ’ cosh[k(u,h) (h+z^)] 3x ’ ’ v
The contribution to the dynamic pressure gradient at any elevation
above the bed by each frequency that is represented by a pair of
Fourier coefficients can be calculated with equation 4-61. These
contributions can be summed to determine the total dynamic pressure
gradient.
Bottom Shear Stress and Erosion
The spatially-averaged total bottom shear stress is the bottom
boundary condition for the momentum equations (eqns. 4-44 and 4-45) and
is determined by solving a velocity distribution equation given the
computed velocity in the bottom computational layer. The logarithmic
velocity distribution (eqn. 1-8) can be used if the flow in the bottom
layer is fully rough turbulent flow and the Reichardt velocity

120
distribution (eqn. 1-10) should be used if the flow is not always fully
turbulent. The Reichardt equation is used in this study because the
flow near the bed is transitional between fully turbulent and laminar
conditions. The bottom roughness parameter zq in equation 1-10 is a
function of the size of the roughness elements (k^) and roughness
Reynolds number u^k^/i/ (eqn. 1-9 and fig. 1-2). The spatially-averaged
total bottom shear stress is determined by 1) assuming that the bottom
roughness regime during the preceding time step (either smooth, lower
transitional, upper transitional, or rough) is valid, 2) solving
equation 1-10 for the shear velocity with a Newton-Raphson iterative
procedure given the bottom layer velocity and elevation, and 3)
checking that the assumed bottom roughness regime and solution are
compatible. If the assumed bottom roughness regime is not valid, then
the another regime is assumed to be valid, the shear velocity is
calculated, and the validity of the regime assumption is checked until
a valid solution is found.
The grain component of the spatially-averaged total shear stress
can be estimated with the Reichardt velocity distribution (eqn. 1-10).
The bottom roughness element that controls the resistance in the region
of the water column adjacent to the bed is the grain roughness and
above this region the roughness is controlled by larger roughness
elements such as ripples, dunes, or bioturbation (Smith and McLean
1977). At some matching elevation, the velocity profiles for the two
regions must be equal. If 0CM1D is used to simulate the velocity in
the upper region and the Reichardt velocity profile is assumed to be
valid in the lower region, then the bottom shear stress that determines
the velocity profile in the lower region (due to grain roughness) can
be estimated. Smith and McLean (1977) calculated the matching

121
elevation based upon bed form geometry. As discussed in chapter 3,
however, regular ripples were probably absent from the Old Tampa Bay
platform site and the bed surface contained irregularities such as
small mounds and valleys that were probably caused by bioturbation.
Therefore, instead of matching the two profiles based upon ripple
geometry, the magnitude and slope of the assumed lower region velocity
distribution can be matched to the simulated velocity distribution.
Beginning at the lowest computational layer, the lower region shear
velocity is calculated from the simulated velocity, grain roughness,
and equation 1-10. The slope of the lower region velocity profile is
calculated by differentiating the velocity distribution equation (1-10)
and comparing it to the simulated slopes above and below. If the slope
of the lower region velocity profile is between the simulated slopes
above and below, then velocity profiles are assumed to match at that
layer and the grain shear stress is calculated from the lower region
shear velocity. If the slope of the lower region velocity profile is
not between the simulated slope above and below, the procedure is
repeated for the layer above. If the procedure has not determined a
grain shear stress when the elevation at which the wave motion is
specified is reached, the grain shear stress is assumed to be equal to
the total shear stress. The estimated grain shear stress can not be
greater than the total shear stress, and the total shear stress was
found to be as much as 80% greater than the grain shear stress at the
Old Tampa Bay platform (chapter 6).
The erosion rate can be calculated as a constant rate, power law
function (eqn. 1-4), or as a function of critical shear stress (eqn. 1-
3). The calculated erosion rate is a function of the spatially-

122
averaged grain shear stress, if estimated, otherwise erosion is a
function of the total bottom shear stress.
Suspended-Sediment Stratification
The effect of suspended sediment on fluid density has been added
to this version of the model, as was done by Sheng and Villaret (1989).
The fluid density as a function of the total suspended-sediment mass
concentration c is
m
p = c + p (1-c/p)
m w m s
(4-62)
in which is the water density and p^ is the sediment density. The
nondimensional fluid density used in the model in terms of dimensional
concentration and densities is
p = c ( - )
m P„ P„
(4-63)

CHAPTER 5
NUMERICAL SIMULATIONS OF THE MARINE SURFACE LAYER
AND CRITICAL SHEAR STRESSES ON CONTINENTAL SHELVES
Erosion is dependent on the grain shear stress and vertical mixing
is dependent on turbulence, so a physically-based numerical model must
accurately simulate grain shear stress and turbulence in order to
accurately simulate suspended-sediment transport in a natural water
body, such as Old Tampa Bay. This chapter presents modified 0CM1D
model simulations of turbulence in the marine surface layer and
critical shear stresses on continental shelves and compares simulation
results to field data collected by other researchers. The purpose of
these simulations was to demonstrate that the model modifications
related to turbulence and bottom shear stress made by the author
produce reasonable results that are an improvement over the original
model results. These simulations also demonstrated that the model can
be applied to environments other than Old Tampa Bay.
Simulation of Turbulence in the Marine Surface Laver
Turbulent dissipation rates simulated by the modified 0CM1D model
were compared to turbulent dissipation rates measured in the surface
layer of the Atlantic Ocean by Soloviev et al. (1988). Soloviev et al.
(1988) present several vertical profiles of nondimensional turbulent
dissipation (e«(h-z)/u.?.) as a function of nondimensional depth (g(h-
z)/u£) measured by them and other researchers in oceans and other large
and deep water bodies (fig. 5-1). The measurements are scattered
around and slightly greater than e/c(h-z)/u5. = 1, the expected value for
123

NONDIMENSIONAL DISTANCE BELOW WATER SURFACE (g(h-z)/u*2)10
124
NONDIMENSIONAL TURBULENT DISSIPATION eic(h-z)/u.3
0.001 0.01 0.1 1 10
in
0.01
0.1 -
10 :
ioo L
Figure 5-1, Measured, simulated, and theoretical turbulent dissipation
in the marine surface layer, measurements reported by Soloviev et. al
(1988) .

125
an unstratified fluid near a rigid wall. Thus, e decreases rapidly as
the distance from the free surface (h-z) increases.
Observed wind and wave conditions on July 13-14, 1982, were
simulated and the unstratified dissipation rate was calculated. The
energy dissipation rate expressed for the variables used in the 0CM1D
model is (Lewellen 1977)
<=b_ai + ^_al (5.1)
in which a and b are invariant constants equal to 3.0 and 0.125, and
the turbulent velocity q and turbulence macroscale A are dimensional.
The second term of equation was much less than the first term, and it
was neglected. The wind speed was 6.0 m/s 10 m above the water
surface, wind waves were 0.5 m high with a period of 4 seconds, and the
swell was 1 m high with a period of 7 seconds. The wind and waves were
assumed to be codirectional, both equilibrium and TKE closure of
turbulent transport were used, and the simulation domain was the top 45
m of the marine surface layer, which is greater than the Ekman depth
and the depth at which the wave motion is negligible. Results using
equilibrium closure (averaged over 28 seconds) were poor because
equilibrium closure neglects diffusion of turbulence into the water
column from the water surface. The simulated results are virtually
identical to the theoretical value £/c(h-z)/u£ = 1 (fig. 5-1) when TKE
closure was used, so the modified model with TKE closure can
successfully simulate turbulence when wind shear and surface waves are
present. The simulation results in figure 5-1 are for aim uniform
grid and a denser grid that gradually expanded with distance below the
water surface and had a 0.02 m surface layer. A fine grid near the
surface was not necessary to reasonably recreate the turbulence with
TKE closure. Vertical motion is neglected and the sediment gradient is

126
small near the surface, so a relatively large surface layer is
acceptable for the sediment simulations.
Critical Shear Stresses Observed on Continental Shelves
Larsen et al. (1981) and Drake and Cacchione (1986) have observed
the initiation of sediment motion at several continental shelf sites
and their calculated shear stresses will be compared to shear stresses
from simulations by the modified 0CM1D model. Accurate calculation of
the shear stress acting on the bed sediment grains is needed to
accurately simulate erosion. Both investigations used submersible
instrument tripods to collect velocity, pressure, and transmissometer
data and bottom photographs. The transmissometer data were used to
identify the onset of sediment resuspension and the concurrent velocity
and pressure data were analyzed to determine the critical mean current
and wave properties. Larsen et al. (1981) and Drake and Cacchione
(1986) each modified the Grant and Madsen (1979) wave-current model to
calculate the maximum bottom grain shear stresses, which, for data
collected at the onset of particle motion during storms or strong
tides, are estimates of the critical bottom shear stresses for sediment
motion. The calculated critical shear stresses were generally in good
agreement with the extended Shields diagram presented by Miller et al.
(1977). The 0CM1D model should be able to produce critical bottom
grain shear stresses that are consistent with the previous results and
with the extended Shields diagram. Grain shear stress can not be
measured directly, so confirmation of the simulated grain shear
stresses must be by indirect means such as this.
Drake and Cacchione (1986) collected 8 data sets at the onset of
sediment motion (critical conditions) in Norton Sound, Alaska, and 10
critical data sets on the northern California continental shelf (table

127
5-1). The data includes mean current speed 100 cm above the bed
(Uioq)> the maximum wave orbital velocity 20 cm above the bed (U ), and
the wave period (T). The mean grain size and water depth were 0.007 cm
and 20 m in Norton Sound and 0.0018 cm and 84 m on the northern
California continental shelf. The bed sediment was better sorted at
the Norton Sound site than at the northern California continental shelf
site. Initiation of sediment motion was caused by the mean current,
wave motion, and by combinations of current and waves. The Grant and
Madsen wave-current model (1979) was modified to estimate the grain
shear stress (r ) for the observed ripple geometry. Fully rough
turbulent flow was assumed and at both sites the total bottom roughness
was 2 cm and the bottom roughness due to grains was 0.01 cm. The
results generally are contained in or near the envelope of critical
shear stresses by Miller et al. (1977), as shown in figure 5-2.
The modified 0CM1D model was applied to the critical shear stress
data sets presented by Drake and Cacchione (1986) . The measured mean
velocity 100 cm above the bed and the total bottom roughness were used
to develop a steady state velocity profile that was the initial
condition for the wave simulation. The wave period and orbital
velocity 20 cm above the bed were used to drive the wave motion for the
simulation. The waves and mean current were assumed to be
codirectional. The typical wave period in Norton Sound was 6 seconds
and a 0.25 second time step, 20 second linear ramp time from steady
state, and a simulation duration of 256 seconds resulted in a dynamic
steady state (or repeating) solution at the end of the simulation that
was spatially and temporally convergent. The typical wave period on
the northern California shelf was 16 seconds and a 0.5 second time
step, 40 second linear ramp time from steady state, and a simulation

128
Table 5-1.--Mean current speed, maximum wave orbital velocity, wave
period, and critical shear stresses from a wave-current model (Drake
and Cacchione 1986) and the 0CM1D model.
Norton Sound:
W-c model 0CM1D
U100 (cm/s)
U (cm/s)
w
T (s)
(d/cm2)
ts (d/cm2)
Tb (d/cm2)
5.9
10.3
6.0
0.68
0.53
3.8
5.0
12.4
6.7
0.78
0.56
4.3
6.1
9.7
6.1
0.64
0.57
4.4
17.9
7.8
6.0
0.72
0.52
3.6
29.7
3.8
6.8
1.21
0.57
4.4
30.2
5.2
5.6
1.43
0.64
5.5
30.5
5.3
7.1
1.35
0.65
5.7
36.9
4.5
6.5
1.46
0.70
6.7
Northern California Shelf:
U100 (cm/s) Uw (cm/s)
T (s)
W-c model
rg (d/cm2)
0CM1D
(d/cm2) (d/cm2)
3
.1
18
.0
13
.2
1
.19
0
.66
5.
.8
15
.0
9
.2
13
.6
0
.8
0
.48
3
.1
18
.2
10
.1
14
.8
1
.13
0
.54
3,
.8
10
.4
9
.1
14
.7
0
.67
0
.41
2.
.2
8,
.8
11
.7
14
. 1
0
.78
0
.48
3,
,1
6.
.5
8
.4
13.
.0
0
.52
0
.35
1.
,6
10.
.1
10
.3
14.
.9
0
.77
0
.44
2.
.6
10.
.3
9
.1
16.
.0
0
.63
0
.41
2.
.2
19.
.1
12
. 1
14,
.7
1
.34
0
.60
4.
9
12.
.1
11
.4
17,
.4
0
.74
0
.49
3.
.3
Note:
T
is the s]
patially
-ave
raged j
grain
shear :
stress,
and
ri
total bottom shear stress.

129
duration of 512 seconds was used to obtain a dynamic steady state and
convergent solution. The total and grain bottom roughnesses used by
Drake and Cacchione (1986) were used for the 0CM1D simulations. The
TKE closure submodel and the integral constraints on the turbulence
macroscale were used and the kinematic viscosity was set to 0.013
cm2/sec.
The height of the layers that discretized the model domain
increased with elevation above the bed and the layer heights were
determined with a constant neighboring layer height ratio. For
example, a ratio of 1.15 means that every layer will be 15% taller than
the layer below. The height of the bottom layer that is required for a
given number of layers (N) to fit within a given spatial domain height
(H) is
N-l .
Az - H / 2 F1 (5-2)
i-0
in which F is the neighboring layer height ratio. For simulation of
critical conditions in Norton Sound and on the northern California
continental shelf, the bottom 123 cm of the water column was simulated
with 28 layers and a neighboring layer height ratio of 1.15.
The critical grain shear stresses from the 0CM1D model simulations
were smaller and more constant than those determined by Drake and
Cacchione (1986). For the Norton Sound data, the critical grain shear
stresses calculated by the modified wave-current model ranged from 0.64
to 1.46 dynes/cm2 and the maximum grain shear stresses simulated by
0CM1D ranged from 0.52 to 0.70 dynes/cm2 (table 5-1). When plotted on
the extended Shields diagram (fig. 5-2), the wave-current model results
are in two groups. One group is at the upper boundary of the critical
envelope (current dominated cases) and the other group is slightly

130
10
-i—i—i—r~r r
1 -
0.1
0,01
I I I I I I I
I I I I I I I I
l â–¡
o
h X
+
El
NORTON SOUND (OCM1D: xb)
CALIFORNIA (OCM1D:xb)
NORTON SOUND (OCM1D:x8) ffi
CALIFORNIA (OCM1D:xs) ffl
WASHINGTON 1978 (OCM1D: x8) a
WASHINGTON 1979 (OCM1D: x8) V
AUSTRALIA 1979 (OCM1D: x8) O
NORTON SOUND (WC: xs)
CALIFORNIA (WC:x8)
WASHINGTON 1978 (WC: xs)
WASHINGTON 1979 (WC: xs)
AUSTRALIA 1979 (WC: x9)
_i i i i i i i I i
I ' I L_L
0.01
0.1
R.
10
Figure 5-2, Extended Shields diagram for continental shelf data, total
bottom and grain shear stresses from wave-current models (WC) and
0CM1D.

131
below the lower boundary of the critical envelope (wave-dominated
cases). All of the 0CM1D results based on the grain shear stress are
slightly below the lower boundary of the critical envelope. For the
northern California shelf data, the critical grain shear stresses
calculated by the modified wave-current model ranged from 0.52 to 1.34
dynes/cm2 and the maximum grain shear stresses simulated by 0CM1D
ranged from 0.35 to 0.66 dynes/cm2. The wave-current model results are
scattered along a line from inside the critical envelope to a point
above the critical envelope and the 0CM1D results are shifted down this
line, mostly within the critical envelope and a little more compact.
The northern California shelf data set may be more scattered because
the sediments are not as well sorted as in Norton Sound, so use of a
single grain size to determine critical conditions is less appropriate.
Some tests with wave motion perpendicular to the mean current decreased
the maximum grain shear stress 10 to 15%, so the assumption of
codirectional current and waves may account for some scatter in the
simulation results shown in figure 5-2.
The critical shear stresses from the wave-current model and 0CM1D
differ probably because 0CM1D is applicable to both wave and current
dominated conditions and viscous effects are considered, neither of
which is true for the wave-current model. The wave-current model is
applicable only to wave - dominated environments (Christoffersen and
Jonnson 1985, Grant and Madsen 1979) which may not be correct for the 4
Norton Sound threshold events for which the mean current velocity was
about 30 cm/sec and the maximum wave orbital velocity was about 5 cm/s.
The 0CM1D model includes viscous terms in the flow equations and TKE
closure submodel whereas the modified wave-current model used by Drake
and Cacchione (1986) assumed fully rough turbulent flow and neglected

132
viscous effects. The roughness Reynolds numbers (R = u^k /i/) for the
grain roughness and grain shear stresses from the modified wave-current
model are less than 5 (about 1), so the grains provide a hydraulically
smooth surface and the viscous boundary layer extends above them
(Schlichting 1969). Therefore, the assumptions and results of the
modified wave-current model are not consistent.
The maximum total shear stress calculated with 0CM1D (r, in table
b
5-1) was several times larger than the maximum grain shear stress. The
total shear stresses, which were calculated for critical conditions,
plot far above the critical envelope on the extended Shields diagram
(solid symbols in fig. 5-2). Therefore, the grain shear stress is a
better indicator of critical conditions than the total shear stress for
this data set, and the 0CM1D model simulation results were improved
with the addition of the grain shear stress estimation procedure.
Larsen et al. (1981) collected 8 critical data sets from 2 sites
on the Washington continental shelf in December 1978 and March 1979 and
3 critical data sets from King Bight on the Australian continental
shelf in December 1979 (table 5-2). The data includes mean current
speed 100 cm above the bed (U-^qq) , the mean of the highest 1/10 maximum
bottom wave orbital velocities (U-jy^) , the wave period (T) , and the
angle between the mean current and wave direction (<¿>) . The mean grain
size and water depth were 0.0035 cm and 90 m for the December 1978
Washington continental shelf site, 0.0042 cm and 92 m for the March
1979 Washington continental shelf site, and 0.017 cm and 75 m for the
Australian site. Initiation of sediment motion was caused by a
combination of current and waves. The wave-current model used by
Larsen et al. (1981) was similar to the Grant and Madsen (1979) wave-
current model except that a different solution algorithm was used and

133
Table 5-2.--Mean current speed, maximum wave orbital velocity, wave
period, angle between the mean current and waves, and critical shear
stresses from a wave-current model (Larsen et al. 1981) and the 0CM1D
model.
Washington continental shelf, December 1978:
U100 (cm/s)
ui/io (cm/s)
T (s)
4>
(deg)
W-c model
rg (d/cm2)
0CM1D
t£ (d/cm2)
13.0
10.0
13.5
20
1.15
1.1
9.7
10.7
12.8
40
0.99
0.98
15.0
10.2
13.1
30
1.27
1.2
10.0
10.4
13.6
20
1.03
0.97
Washington
continental
shelf, March
1979:
W-c model
0CM1D
uioo (cm/s)
Ul/10 (cm/s)
T (s)
4>
(deg)
(d/cm2)
(d/cm2)
15.8
9.7
10.8
30
1.26
1.2
13.0
10.2
13.5
30
1.15
1.1
10.0
9.6
13.5
60
0.82
0.83
8.9
10.1
13.0
40
0.90
0.90
King Bight,
Australia,
December 1979
W-c model
OCM1D
uioo (cm/s)
ui/io (cm/s)
T (s)
4>
(deg)
(d/cm2)
(d/cm2)
7.8
23.1
14.9
0
2.55
2.3
9.8
19.4
12.2
20
2.00
2.0
7.0
19.8
12.9
40
2.00
1.9

134
smooth, transitional, and rough bottom roughness regimes were
considered. The wave-current model calculated the total bottom shear
stress which is equal to the grain shear stress for these data because
the bottom roughness was set equal to the mean grain diameter, which is
equivalent to assuming a flat bed. If any bed forms or other roughness
elements were present, they were not accounted for in the analysis. On
the extended Shields diagram (fig. 5-2), the results are either within
the upper half of the critical envelope or are slightly above the upper
bound of the critical envelope.
The 0CM1D model was applied to the critical shear stress data sets
presented by Larsen et al. (1981). The measured mean velocity 100 cm
above the bed and the bottom roughness (equal to the mean grain
diameter) were used to develop a steady state velocity profile that was
the initial condition for the wave simulation. The wave period, bottom
orbital velocity, and the angle between the mean current and waves were
used to drive the wave motion for the simulation. The bottom 123 cm of
the water column were simulated with 28 layers and a neighboring layer
height ratio of 1.15, which is the same grid as used to simulate the
Alaska and California data. The typical wave period for the Washington
and Australian data is slightly less than the wave period on the
northern California shelf, so the same time step (0.5 seconds), ramp
time (40 seconds), and simulation duration (512 seconds) was used to
obtain a dynamic steady state solution as used to simulate the
California data. Spatial convergence of the 28 layer grid was
confirmed by applying a 32 layer grid to the first December 1978 data
set. The total bottom roughness was set equal to the mean grain
diameter. A separate grain roughness was not specified and the grain
shear stress submodel was not used. The Reichardt velocity

135
distribution (eqn. 1-10) was used to calculate the total bottom shear
stress, which is equal to the grain shear stress for these simulations.
The TKE closure submodel and the integral constraints on the turbulence
macroscale were used and the kinematic viscosity was set to 0.013
cm2/sec.
The critical shear stresses calculated with 0CM1D were virtually
identical to those determined by Larsen et al. (1981). The differences
between the critical shear stresses listed in table 5-2 are mostly due
to rounding. The roughness Reynolds numbers are 2 or less which
indicates that the bottom boundary was hydraulically smooth. When
plotted on the extended Shields diagram (fig. 5-2), the wave-current
model results and the 0CM1D simulation results are virtually identical
and are either in or near the upper half of the critical shear stress
envelope.
The critical shear stresses calculated by the wave-current model
and 0CM1D for these data are virtually identical, probably because both
methods account for the smooth bottom boundary and the data were for
wave - dominated conditions. All of the data were for wave - dominated
conditions for which the Grant and Madsen (1979) formulation used by
the wave-current model is applicable. If a rough boundary had been
assumed, then the calculated critical shear stresses would differ but
the roughness Reynolds numbers would probably still indicate that the
bottom boundary was not rough, similar to the Alaska and California
data. The assumption that the grains were the only roughness element
at the Washington and Australian sites seems to be somewhat unlikely
due to the possibility of bioturbation and undulations in the natural
bed. If a larger total bottom roughness and the same grain roughness
were used for the 0CM1D simulations, the simulated near-bed velocities

136
would be smaller and the grain shear stresses would be less than those
presented in table 5-2. Thus, the results on figure 5-2 would be
shifted down toward the lower limit of the critical envelope, which is
reasonable.
The 0CM1D simulations of data collected on continental shelves at
critical conditions for particle motion show that viscous effects
should be considered when calculating the grain shear stress. For the
data presented by Drake and Cacchione (1986) and Larsen et al. (1981),
the beds were hydraulically smooth with respect to the grain roughness.
The maximum (critical) shear stresses for the 0CM1D model simulations
were virtually identical to the results of Larsen et al. (1981) because
both approaches considered viscous effects. The estimated critical
grain shear stresses were also reasonable compared to the extended
Shields diagram (fig. 5-2) . Drake and Cacchione (1986) assumed that
the bed was hydraulically rough with respect to the grain roughness,
which is not consistent with the roughness Reynolds numbers. Viscosity
is also important for transitional hydraulic roughnesses between the
smooth and rough limits.
These results also show that the 0CM1D model and the procedures
used for simulating viscous effects, wave motion, total shear stress,
and grain shear stress are valid for a wide variety of hydrodynamic and
sedimentary environments. For the data presented by Drake and
Cacchione (1986) and Larsen et al. (1981), the mean current speed 100
cm above the bed ranged from 3.1 to 36.9 cm/s, water depths ranged from
20 to 92 meters, the maximum wave orbital velocity ranged from 3.8 to
23.1 cm/s, the wave period ranged from 5.6 to 17.4 seconds, and the
mean grain diameter ranged from 0.0018 cm to 0.017 cm. The simulated
maximum grain shear stresses for these data, which were collected at

137
the onset of sediment motion, are in good agreement with the extended
Shields diagram (fig. 5-2) for sediment resuspension caused by strong
currents, wave motion in the absence of a strong current, and combined
waves and current. The shear stresses from the 0CM1D model simulations
(fig. 5-2) were calculated with the total shear stress submodel for the
data presented by Larsen et al. (1981) because the grain roughness and
total roughness were equal and with the grain shear stress submodel for
the data presented by Drake and Cacchione (1986) . Both shear stress
submodels produce reasonable results. When the total bottom roughness
is greater than the grain roughness, the total and grain shear stresses
can differ significantly (table 5-1), and the grain shear stress is
more appropriate for determining whether critical conditions exist
(fig. 5-2).

CHAPTER 6
OLD TAMPA BAY NUMERICAL SIMULATION RESULTS
The modified OCM1D model was used to simulate suspended-sediment
transport in Old Tampa Bay, and the simulation results were compared to
measured data to help determine significant sediment transport
processes in Old Tampa Bay. Calibration, validation, improved, and
sensitivity simulations of suspended-solids concentrations during
storms in March and November 1990 are presented and discussed.
Hydrodynamic simulation results of steady flow, wave motion, and bottom
shear stresses in Old Tampa Bay are also presented in this chapter.
The purpose of these hydrodynamic simulations was to demonstrate the
ability of the modified model to simulate the hydrodynamic conditions
in Old Tampa Bay, to determine a numerical grid that produces spatially
convergent shear stresses, and to compare spatially-averaged grain
shear stresses with critical conditions for particle motion.
Steady Flow Simulation
The ability of the model to simulate velocity profiles and total
bottom shear stress in steady regime transitional flows was tested by
comparing simulation results with the Reichardt velocity profile (eqn.
1-10) which includes laminar, transitional, and turbulent regimes. A
steady velocity profile was simulated by specifying the mean current
speed measured at 1800 hours March 8, 1990, 70 cm above the bed (8.9
cm/sec) at the Old Tampa Bay platform. This is a typical strength of
flood or strength of ebb velocity at this elevation at the platform.
For the simulation, the following features were used: 45 layers, a
138

139
neighboring layer height ratio of 1.15, a water depth of 399 cm, a
bottom roughness of 0.30 cm, TKE closure with dynamic turbulence
macroscale, zero wind shear stress, and specification of the measured
steady state velocity 70 cm above the bed. The computational grid is
shown in figure 6-1. Variable bottom roughness regimes were used for
both the Reichardt equation and the simulation.
The simulated velocity profile is in excellent agreement with the
Reichardt equation (fig. 6-2). The standard error is 0.070 cm/s and
the simulated total bottom shear stress of 0.132 dynes/cm2 is close to
the bottom shear stress of 0.148 dynes/cm2 from the Reichardt equation.
The simulation results include the logarithmic region far from the bed
and the transitional and laminar regions near the bed where viscosity
is important.
If equilibrium closure is used for the model simulation, the
simulated velocity profile is poor (fig. 6-2, standard error 0.256
cm/s) and the total bottom shear stress is also poor (0.205 dynes/cm2)
because equilibrium closure neglects the effect of viscosity and the
dynamics of turbulence. Near the bed, however, viscosity and the
viscous terms that have been added to the model are important because
the flow is not fully turbulent. Turbulence dynamics are important
because turbulence is transported into the transitional region from the
fully turbulent (logarithmic) region.
If the viscosity terms in the second order correlation equations
are added to the equilibrium closure submodel (eqns. 4-40 and 4-41) and
the dynamic q2 equation is not used, then the transition from turbulent
to laminar flow is very sudden and there is no transitional region in
the simulated velocity profile. Therefore, a realistic simulation must
allow transport of turbulence into the transitional region where the

VERTICAL AXIS, IN CM
140
Figure 6-1, Computational grid for 45 layers, 1.15 neighboring layer
height ratio, and a 399 cm domain height.

ELEVATION, IN CM
141
VELOCITY, IN CM/S
Figure 6-2, Comparison of Reichardt and simulated velocity profiles

142
equilibrium closure assumptions are invalid. Donaldson (1973) and
Lewellen (1977) stated that the equilibrium closure assumptions are
only applicable to high Reynolds number flows, which is not the case
for this example. On the other hand, use of the dynamic q2 equation
produced much better simulation of the turbulence dynamics (fig. 6-2).
If the dynamic turbulence macroscale (A) equation is replaced with
the integral constraints on A for the TKE closure submodel, then A and
the simulated steady flow velocity profile are slightly altered. The
simulation with the integral constraints has a slightly higher standard
error (0.082 vs. 0.070 cm/s) and a slightly lower bottom shear stress
(0.129 vs. 0.132 dynes/cm2) than the simulation with the dynamic
turbulence macroscale equation. The dynamic turbulence macroscale is
slightly less than that given by the integral constraints except near
the bed (fig 6-3). The larger dynamic turbulence macroscale near the
bed may be more realistic because the flow is nearly laminar and the
integral constraints only strictly applicable to fully turbulent flows.
Therefore, the dynamic turbulence macroscale equation is used for the
Old Tampa Bay suspended-sediment simulations because the near-bed
turbulence macroscale may be an important factor affecting the upward
transport of newly eroded sediment.
Reproduction of Energy Spectra of Observed Currents
The model should be able to reproduce measured energy spectra
produced from the 1-Hz current data collected at the Old Tampa Bay
platform. This was tested with the platform data collected at 1500
hours on November 30, 1990. The simulation used a 45 layer grid with
a neighboring layer height ratio of 1.15, TKE closure of turbulent
transport, and a time step of 0.36 seconds. Spectral analysis was used

ELEVATION, IN CM
143
TURBULENCE MACROSCALE, IN CM
Figure 6-3, Comparison of turbulence macroscale from the dynamic
equation and the integral constraints.

144
to convert the simulated velocity time series 24 and 70 cm above the
bed to the frequency domain.
The measured wave spectra and the wave spectra determined from the
simulated velocities are in good agreement. The significant wave
height computed from the current meter data 24 cm above the bed is 75
cm and the significant wave heights computed from the simulated
velocities 24 and 70 cm above the bed are 72 and 74 cm. The raw energy
spectra are in good agreement (fig. 6-4). Some of the discrepancy is
caused by the difference in the simulation (0.36 seconds) and data (1.0
seconds) time steps. The velocity data collected 24 cm above the bed
was used to force the simulation, so good agreement is expected at that
elevation. The good agreement between the measured spectrum 24 cm
above the bed and the model spectrum 70 cm above the bed shows that the
model properly distributes the wave-induced pressure gradient in the
water column. The energy spectra computed from the simulation results
has no energy at frequencies greater than the data Nyquist limit of 0.5
Hz. Therefore, the model can reproduce energy spectra of the 1-Hz
current data collected at the Old Tampa Bay platform.
Simulated Shear Stresses
Simulated results should converge to a solution as the number of
computational cells increases and as the size of the time step
decreases. Convergence tests with the Old Tampa Bay simulations showed
that temporal convergence of velocity and bottom shear stresses was
good for time steps less than 0.5 seconds and that spatial convergence
of velocity at measurement elevations was good. Convergence of the
grain shear stress is important because erosion is a function of the
grain shear stress.

145
Figure 6-4, Raw energy spectra computed from measured and
simulated velocities, 1500 hours November 30, 1990.

146
The simulated total bottom shear stress is spatially convergent,
the grain shear stress is reasonable but converging toward the total
shear stress, and the height of the bottom layer determines spatial
convergence of the shear stresses. The 1800 hour March 8, 1990, data
set was simulated with the elevation of the center of the bottom layer
set to 0.013, 0.027, 0.055, 0.111, and 0.226 cm and a neighboring layer
height ratio of 1.15. Simulated shear stresses were virtually
unchanged when the height of the bottom layer was held constant and the
neighboring layer height ratio was varied, so spatial convergence of
the grain shear stress is determined by the height of the bottom layer.
The average total and grain shear stresses as a function of the
elevation of the center of the bottom layer is shown in figure 6-5.
The total shear stress has virtually converged for the finer grids.
The grain shear stress, however, is converging toward the total shear
stress. As the size of the bottom layer decreases, it eventually will
be located completely within the viscous sublayer. The simulated total
and grain shear stresses will be equal because shear stress in this
region is independent of the height of the bottom roughness elements.
This condition, however, is not consistent with the concept that the
model simulates the region above the bed which experiences a shear
stress dependent on form drag and that grain roughness controls the
bottom shear stress in the near-bed region. Thus, the grid can be too
fine and invalidate the principle used to determine the grain shear
stress.
An optimum grid for the calculation of grain shear stress can be
estimated with the results of lab experiments conducted by Engelund
(see Vanoni 1975, p. 135). Engelund conducted lab experiments to
determine the relation between total bottom shear stress and grain

MEAN SHEAR STRESS, IN DYNES/CM
147
C\J
1.0
0.8
0.6
0.4
â–¡
â–¡
0
0
â–¡
0
â–¡ TOTAL SHEAR STRESS
0 GRAIN SHEAR STRESS
â–¡
0
0
0.00 0.05 0.10 0.15 0.20
ELEVATION OF CENTER OF BOTTOM LAYER, IN CM
0.25
Figure 6-5, Spatial convergence of total and grain shear stress.

148
shear stress for a large range of grain sizes, bed forms, and steady
flows. The lower shear stresses used in the experiments overlap with
the maximum shear stresses calculated with the model for Old Tampa Bay.
The results of the experiments will be assumed to be applicable to the
maximum shear stresses calculated by the model even though the
simulations are of unsteady flows and the grain size in Old Tampa Bay
is smaller than those used by Engelund. The maximum grain shear stress
calculated by the model and from Engelund's results (calculated from
the simulated maximum total shear stress) are in agreement when the
center of the bottom layer is 0.055 cm above the bed (fig. 6-6). If
the bottom layer is larger, then the model underestimates the maximum
grain shear stress. If the bottom layer is smaller, then the model
overestimates the maximum grain shear stress. The velocity and total
bottom shear stress have converged and the simulated maximum grain
shear stress is in agreement with experimental results when the center
of the bottom layer is 0.055 cm above the bed. Thus, this appears to
be the best grid for convergence and accuracy for the Old Tampa Bay
simulations.
The grain shear stress is nearly equal to the total bottom shear
stress when viscous forces are dominant but the grain shear stress is
less than the total shear stress for transitional and turbulent cases.
A typical relationship between the two shear stresses during a storm is
shown in figure 6-7 for the 1800 hour March 8 platform data set. The
line of perfect agreement is also shown in figure 6-7. The average
total shear stress is 40% larger than the average grain shear stress
and the maximum total shear stress is 80% greater than the (concurrent)
maximum grain shear stress. Smaller grain shear stresses are nearly
equal to the total bottom shear stress because viscous forces are

MAXIMUM GRAIN SHEAR STRESS, IN DYNES/CM2
149
2.4
1.6
â–¡
â–¡ OCM1D
0 ENGELUND
2.2 -
â–¡
2.0 -
1.8 -
0
0
â–¡
0
â–¡
0
o.oo
0.05
0 10
0.15
0.20
0.25
ELEVATION OF CENTER OF BOTTOM LAYER, IN CM
Figure 6-6, Maximum grain shear stress calculated by OCM1D and from
Engelund's experimental results.

150
TOTAL SHEAR STRESS, IN DYNES/CM2
Figure 6-7, Simulated total and grain shear stresses, 1800 hours
March 8, 1990.

151
dominant and the shear stresses are independent of the height of the
roughness elements. Larger grain shear stresses are less than the
total shear stress for transitional and turbulent cases because the
shear stresses are larger and depend on the height of the roughness
elements. The grain shear stress was found to be insensitive to the
selected grain roughness because the flow over the grains was usually
laminar.
The simulated grain shear stresses seem to be reasonable compared
with the Shields critical shear for initiation of motion of the
platform sediments. A typical time series of grain shear stress during
a storm is shown in figure 6-8 for the 1800 hour March 8 platform data
set. Wave motion was ramped for the first 16 seconds of the simulation
results shown in figure 6-8. The distribution of estimated total and
grain shear stresses relative to the critical shear stress for 63 fxm,
d^Q=127 /¿m, and dgg=200 ¿urn diameter sediments at the platform is shown
on table 6-1. The data used to determine the critical shear stress for
flat, abiotic, and noncohesive sediment beds forms an envelope of
values, so the average and range of critical shear stress (Miller et
al. 1977) are also given on table 6-1. The number of time steps in
which the simulated grain shear stress was greater than the average
critical shear stress for d^^ was about one-third the number of times
the total shear stress exceeded the average critical shear stress for
d^Q. Most of the time the grain shear stress is less than that needed
to resuspend 63 ¿im diameter sediments. The critical shear stresses are
not regularly exceeded in a periodic manner at the wave frequencies.
The maximum grain shear stress during the 2-3 second wave period will
exceed the critical shear stresses for periods from one wave cycle (d^
at 80 seconds) to 30 seconds (63 ¿¿m from 170-210 seconds). The grain

GRAIN SHEAR STRESS, IN DYNES/CM
152
Figure 6-8, Simulated grain shear stress, 1800 hours March 8, 1990.

153
Table 6-1.--Total and grain shear stress distribution and critical
stresses, 1800 hours March 8, 1990.
Particle
diameter
(um)
Average and range of
critical shear stress
(dvnes/cm2)
Time critical
Total
(percent)
shear stress exceeded
Grain
(percent)
dgo=200 /¿m
2.3 (1.6 - 2.9)
7.3
0.1
d50=127 Mm
1.6 (1.2 - 2.1)
15.6
4.6
63 /xm
1.2 (0.8 - 1.5)
23.7
13.8

154
shear stress is not large enough to resuspend 63 /im diameter sediment
for up to 30 seconds (40-70 seconds). Similar periods of increased
wave activity are (not surprisingly) present in the velocity data.
Thus, the grain shear stress is not large enough to move all of the
bottom sediment particles, and the larger particles that are moving may
be moving as bed load instead of suspended load. The temporal
distribution of excess shear stress shown in figure 6-8 differs from
the periodic result that would be found if a single wave height and
wave period were assumed.
The simulated maximum total bottom bottom shear stresses are
greater than the maximum bottom shear stress calculated with the wave
current model (Grant and Madsen 1979) in chapter 3. The maximum total
bottom shear stresses from 0CM1D and the wave current model for the
November 1990 storm are shown in figure 6-9. The 0CM1D results are
greater because the entire wave spectrum is simulated and constructive
interference of several frequencies can occur whereas only a single
frequency and wave height are considered by the wave current model.
Representation of the wave field with a single frequency may produce
smaller shear stresses and smaller erosion rates than if the entire
wave spectrum is simulated.
Old Tampa Bay Suspended-Sediment Simulation Procedure
The Old Tampa Bay suspended-sediment simulations proceed forward
in time as a series of hour-long segments. This approach is used
because the suspended-solids concentrations collected during each burst
sample contain noise, as discussed in chapter 3, but the hourly mean
burst concentrations are reliable and can be compared to simulation
output. The simulation also can include periods of net resuspension
and net deposition and ambient conditions before and after the storm

MAXIMUM TOTAL SHEAR STRESS, IN DYNES/CM
155
Figure 6-9, Maximum total bottom shear stress from the 0CM1D model and
the Grant and Madsen (1979) wave-current model, November 1990.

156
with this approach. Hourly wind and hydrodynamic data, including water
depth, mean velocities and wave properties, were used to force
simulated hydrodynamics from 30 minutes before the hour until 30
minutes after the hour. The hydrodynamic forcing measured every hour
was extrapolated in time, so if a short-term event, such as slack tide,
a few unusually large waves, or lack of large waves, occurred during a
measurement, then the effect of the event would be magnified by the
simulation. For each segment, the initial velocity profile was the
steady state mean velocity profile, the initial turbulent velocity was
the turbulent velocity at the end of the previous segment, the initial
turbulent macroscale was determined with the integral constraints, and
the initial suspended-solids concentration was the concentration at the
end of the previous simulation. The depth-varying pressure gradients
that force the simulated mean current were those calculated for steady
state conditions. For the first segment of each simulation, the
initial turbulent velocity was the steady state turbulent velocity and
a suspended-solids concentration distribution was assumed. Steady
state conditions for the mean current, considering wind but not waves,
were determined for the measured mean currents as described in chapter
4. Wave motion was simulated by determining the wave-induced pressure
gradients with the Fourier series coefficients determined from the
hourly burst data, as discussed in chapter 4.
Several types of suspended-sediment simulations were performed and
compared to the Old Tampa Bay data. The names of these simulations,
data sets simulated, and calibration coefficients are summarized in
table 6-2. A constant settling velocity (wg) and the power law erosion
rate (eqn. 1-4) with constant coefficients (a and tj) were used for all

157
Table 6-2.--Old Tampa Bay suspended-sediment simulations
Simulation
Data set Calibration coefficients
Calibration
November 1990 a, rt, and w
Validation
March 1990 none
Improved
March 1990 a, ri, and w
' s
Sensitivity
November 1990 either a, r¡, or changed ±20%

158
of the simulations. The rationale for these simulations is described
in the following paragraphs.
The model was calibrated by simulating the resuspension and
deposition of suspended solids observed on November 30, 1990, at the
Old Tampa Bay platform. The calibration coefficients (wg, a, and r),
table 6-2) were selected to minimize the standard (or root mean
squared) error of the simulated and measured concentrations.
Hydrodynamic simulation does not involve any calibration, so these
three coefficients are the only calibration coefficients for the model.
The November data set was used to select the coefficients because it
includes ambient conditions before sediment resuspension and the
initiation of net resuspension whereas the initial observations for the
March data set were made shortly after net resuspension began. Thus,
the November data set includes all of the phases of storm-generated
sediment resuspension, so it was used to select the calibration
coefficients and the March data set was used to attempt to validate the
selected coefficients. Simulations of the November data were also less
sensitive to the assumed initial suspended-solids concentration than
for the March data because ambient concentrations could be used to
initialize the November simulation whereas a concentration profile that
considered ongoing net resuspension had to be assumed for the March
data set.
The March data set was used to attempt to validate the calibrated
coefficients. Ideally, the November calibration would have produced
acceptable results for the March data set, therefore validating the
model. The simulated suspended-solids concentrations for the
validation simulation, however, were less than the measured
concentrations.

159
Thus, the March validation data set was simulated with separately
calibrated coefficients in order to provide an 'improved' simulation of
the March data. Calibration coefficients that successfully simulated
both data sets could not be determined. Probable reasons for the
differences between the two sets of calibration coefficients are
discussed later in this chapter.
The relative significance of each calibration coefficient was
determined by performing sensitivity simulations for the November data
set. Each sensitivity simulation increased or decreased the value of a
calibration coefficient 20% and the remaining coefficients were set
equal to the calibration values. There are 3 calibration coefficients
(a, r), and wg) . so a total of six sensitivity simulations were
performed.
Extending the model domain to the mean water surface was found to
be better than locating the top of the model domain at the elevation of
the OBS sensor furthest above the bed for the Old Tampa Bay suspended-
sediment simulations. A potential disadvantage of simulating the
entire water column is that the upper portion of the water column where
vertical velocities may be significant is included in the model domain
and the model neglects vertical velocity. Experimental simulations
which included a Lagrangian formulation of vertical velocity, however,
were in good agreement with simulations that neglected vertical
velocity. Two advantages of simulating the entire water column are
that all of the measured concentration data can be used to calibrate
the model and the effect of the upper water column on concentrations in
the lower part of the water column is accurately simulated. Both of
these advantages occur because, if the model domain does not extend to
the water surface, the uppermost suspended-solids concentration data

160
must be used as the top boundary condition, so a calibration point is
lost and any error in the uppermost measured concentration will
adversely affect the simulation. Another advantage of simulating the
entire water column is that wind stress can be directly simulated.
All of the hour-long segments used to simulate Old Tampa Bay
platform data used the same discretization and hydrodynamic
coefficients and submodels. The water column was simulated with 45
layers and a neighboring layer height ratio of 1.15. This grid
produced reasonable grain shear stresses that were previously
presented. The computational grid for a 399 cm domain height is shown
in figure 6-1. The initial velocity profile for each segment was the
steady state velocity profile determined by specifying the wind shear
stress and all reliable measured mean velocities. The height of the
top layer was about 52 cm which was about twice the maximum significant
wave amplitude. Small wave amplitude was assumed and the size and
position of the computational layers was not varied. A time step of
0.18 seconds was used for the wave simulations because it was stable
and temporally converged. Waves were ramped for the first 88 time
steps, or 15.84 seconds, of the initial segment. Wave ramping was not
used for the other simulations because net settling occurred during the
ramping period when bottom shear stresses were small. Velocity data
from the current meter closest to the bed were used to determine the
Fourier series coefficients for wave motion. Wind shear stress at the
water surface was calculated from the measured wind speed and
direction, logarithmic profile equation, and the drag coefficient
formula presented by Garratt (1977). Bottom shear stresses were
calculated with a total bottom roughness of 0.30 cm, a grain roughness
equal to d^ (200 urn), and variable bottom roughness regime. The TKE

161
closure submodel was used with the dynamic q2 and A equations. The
minimum turbulence macroscale was set to the integral constraint value
for the bottom layer, 0.65Az^. Measured water temperatures in March
and November were about 20°C and so a kinematic viscosity of 0.01 cm2/s
was used. The density of the suspended sediment was assumed to be 2.35
g/cm3, based upon the observation that 20% by mass of the suspended
material was organic during storms, an assumed inorganic suspended
solids density equal to the measured bed sediment density of 2.68
g/cm3, and an assumed organic suspended solids density of 1.02 g/cm3.
Old Tampa Bay November 1990 Suspended-Sediment Calibration Simulation
The November calibration simulations contained eighteen hour-long
segments from 0730 hours on November 30 to 0130 hours on December 1
that include erosion during the storm, deposition after the storm, and
ambient conditions before and after the storm. The initial suspended-
solids concentration profile for the first segment was determined by
fitting the Rouse equation (eqn. 1-18) to the 0800 hour suspended-
solids concentration data. Suspended-solids concentration data is
available from OBS sensors 70 and 183 cm above the bed during the storm
and from some water samples used to calibrate the OBS sensors.
The calibration coefficients were determined by minimizing the
standard error of the simulated and measured concentrations 70 and 183
cm above the bed. The simulation results were constrained by the
physical laws and relationships included in the model, so the
calibrated coefficients were physically relevant. There were three
calibration coefficients and 36 measured concentrations for the entire
simulation. The calibration coefficient values are reasonable compared
to values presented in previous studies and they produce reasonable
results (figs. 6-10 and 6-11). The standard errors (or root mean

162
(3
2
O
DC
111
O
2
O
o
U)
o
_i
o
C/0
l
Q
LU
O
2
LU
0.
C0
0800 1100 1400 1700 2000 2300
HOUR
Figure 6-10, Simulated and measured suspended-solids concentrations
70 cm above the bed, November 1990 calibration simulation.

SUSPENDED-SOLIDS CONCENTRATION, IN MG/L
163
HOUR
Figure 6-11, Simulated and measured suspended-solids concentrations
183 cm above the bed, November 1990 calibration simulation.

164
squared errors) for the entire simulation were 9.7 mg/L 70 cm above the
bed and 9.2 mg/L 183 cm above the bed.
The calibrated erosion rate coefficient a was equal to 4.08x10 ^
g/cm2/s (for t in dynes/cm2). The sensitivity of the simulation
results to a increased as r¡ was decreased. The calibrated a value is
slightly greater than the greatest value reported by Lavelle et al.
(1984), but it is comparatively reasonable. An explanation for the
relatively large value of a is that the values reported by Lavelle et
al. (1984) appear to have been determined for the total bottom shear
stress instead of the grain shear stress that was used in this study.
If the total bottom shear stress were used in this study to determine
the erosion rate, then the calibrated value of a would be smaller.
Another possible explanation is that the values of a reported by
Lavelle et al. (1984) are for various fine-grained sediments, but the
sediment at the Old Tampa Bay platform is a silty very fine sand.
The calibrated erosion rate exponent r? (1.6) is within the range
of values summarized by Lavelle et al. (1984). Simulation results with
only slightly greater error than the calibration results in figures 6-
10 and 6-11 could be found for ri = 1.0 to 2.0 when w and a were
s
adjusted to minimize the error. Larger rj values tended to cause a
relative increase in concentration from 1100 to 1400 hours and a
relative concentration decrease after 1400 hours.
The settling velocity (0.021 cm/sec or 18.4 m/day) is equal to the
settling velocity of a 24 pm particle with a specific weight of 2.65
g/cm3 from Stokes law. 12% of the bottom material at the Old Tampa Bay
platform is finer than 24 pm, and the median particle size at the
platform is 130 pm, so the calibrated settling velocity and equivalent
particle diameter indicates that sand-size particles were not

165
appreciably suspended at the platform during the storms in March and
November. This is consistent with the Shields critical shear stress
(fig. 6-8 and table 6-1) that shows that the critical shear stress for
sand-sized particles is rarely exceeded during a storm. Sand-size
particles are probably irregularly transported as bed load and only
finer sediments are suspended. The settling velocity was the most
important calibration coefficient for determining the simulated rate of
concentration decrease during the depositional period after 1800 hours.
Simulated and observed suspended-solids concentrations 70 and 183
cm above the bed for the November 1990 storm are in good agreement
(figs. 6-10 and 6-11). The simulated concentrations in figures 6-10
and 6-11 are presented at 15-minute intervals. The increase in
suspended-solids concentration from 0900 to 1300 hours, and the period
of high and fairly constant suspended-solids concentrations from 1300
to 1500 hours were accurately simulated by the model. The suspended-
solids concentration data at 1200 and 1300 hours 70 cm above the bed is
a little scattered but the scatter is only slightly greater than the
standard error of the OBS sensors (5.8 mg/L). The simulation results
70 cm above the bed vary more than the simulated concentrations 183 cm
above the bed due to erosion from the bed.
The hourly data collection interval, a small measured mean
velocity, and the segmented simulation procedure may account for the
simulated suspended-solids concentrations being smaller than the
measured concentrations from 1600 to 1900 hours. The measured mean
velocities at 1600 hours were relatively small (less than 3.0 cm/sec),
and these small mean velocities were used to determine the initial
velocity profile and the mean pressure gradients for the 1600 hour
segment. The effect of these small velocities were simulated for a one

166
hour period, so if the small velocities actually were present for a
shorter amount of time, then the simulation overemphasizes the effect
of these small velocities. Smaller mean velocities decrease vertical
mixing in the water column and permit a greater settling flux, thus
decreasing the suspended-solids concentrations in the water column.
Thus, the hourly interval for collection of burst data, the small
measured mean velocity at 1600 hours, and the segmentation used to
perform this simulation may account for the low simulated
concentrations from 1600 to 1900 hours. Another possible explanation
for the low simulated concentrations is that the model does not account
for bulk erosion, the rapid failure and suspension of part of the bed
(Krone 1986). The larger observed concentrations may be caused if bulk
erosion occurred between 1600 and 1700 hours.
The simulated concentrations were nearly equal to the measured
concentrations during the conclusion of net deposition after 2000
hours. The 2100 hour simulation had relatively large mean velocities
(greater than 8.9 cm/sec) which caused net upward transport. At 0000
and 0100 hours on December 1, the OBS sensors indicate that the
suspended-solids concentration is greater 183 cm above the bed than 70
cm above the bed. The backscatterance from the suspended solids was
probably insufficient to exceed the response threshold of the OBS
sensors at these times, which was common for ambient conditions in Old
Tampa Bay.
Old Tampa Bay March 1990 Suspended-Sediment Validation Simulation
The March validation simulations contained ten segments from 1400
hours to 2300 hours on March 8 that include erosion during the storm,
deposition after the storm, and ambient conditions after the storm.
The initial suspended-solids concentration profile for the first

167
segment was assumed to equal the calibration simulation profile at 0900
hours November 30 when the calibration simulation suspended-solids
concentrations were nearly identical to the measured concentrations at
1400 hours March 8. Suspended-solids concentration data are available
from OBS sensors 24, 70, and 183 cm above the bed during the storm and
from some water samples used to calibrate the OBS sensors. The
calibration coefficient values determined with the calibration
simulation were used.
Validation simulation results at 15-minute intervals (figs. 6-12
to 6-14) are in poor agreement with the measured data because the
coefficients were not fit to the March data. Simulated concentrations
were lower than measured concentrations and decreased during most of
the simulation. The poorest agreement is at an elevation 24 cm above
the bed (standard error 40.3 mg/L). The standard errors 70 and 183 cm
above the bed are 28.7 mg/L and 26.2 mg/L.
The lack of data prior to 1400 hours reduces the accuracy of the
simulation. Unfortunately, data is not available before 1400 hours so
the wave properties and suspended-solids concentration profiles can not
be increased from ambient conditions as was done for the November
calibration data.
The simulated suspended-solids concentrations did not increase up
to the initial values during the net erosional period of the storm from
1600 to 1800 hours. Thus, application of the calibrated erosion
coefficients for the November simulation to the March simulation does
not produce sufficient erosion, or the calibrated settling velocity is
too large and does not produce reasonable validation results.
Many alternative sedimentation submodels and segmentation schemes
were tested but failed to improve the calibration and validation

168
(3
2
z
<
oc
UJ
O
z
o
o
CO
Q
_l
O
co
Q
LU
O
z
OI
a.
co
co
HOUR
Figure 6-12, Simulated and measured suspended-solids concentrations
24 cm above the bed, March 1990 validation and improved
simulations.

169
c3
<
oc
z
111
o
o
o
to
o
-i
o
to
I
a
ni
a
z
tu
CL
to
3
to
80
60
40
20
MEASURED
(AND ERROR)
VALIDATION
SIMULATION
IMPROVED
SIMULATION
0 I i I 1
1400 1600 1800 2000 2200
HOUR
2400
Figure 6-13, Simulated and measured suspended-solids concentrations
70 cm above the bed, March 1990 validation and improved
simulations.

170
c3
z
o
£
tr
i-
z
LU
o
z
o
o
co
o
O
co
i
Q
LU
Q
Z
LU
Q.
CO
3
CO
HOUR
Figure 6-14, Simulated and measured suspended-solids concentrations
183 cm above the bed, March 1990 validation and improved
simulations.

171
simulation results. A bed mass submodel that considered all sediments
deposited on the bed during the simulation to be more erodible than
older sediments below did not improve simulation results. Most of the
alternative sedimentation submodels included a representation of
aggregation. A single suspended particle size class was simulated
with the settling velocity proportional to the Taylor microscale (eqn.
4-29, assumed aggregate diameter, Eisma 1986, Hawley 1982), settling
velocity proportional to the local concentration to the 1.3 power
(Mehta 1986), and settling velocity proportional to the mean
concentration to the 1.3 power. None of these single size class
settling velocity formulations improved the simulation results.
Simulations that included two particle size classes and aggregation as
a second-order process (Camp 1945, Fiedler and Fitch 1959, Hunt 1982,
Farley and Morel 1986) did not improve simulation results. Including
aggregate breakup (Thomas 1964, Parker et al. 1972) did not improve the
simulations which considered aggregation. Various validation
simulation segmentation schemes did not improve the simulation results.
These segmentation schemes included a different initial starting time,
adjusted segment durations, and use of dynamic steady state conditions
at 1400 hours as the initial condition at 1400 hours. Therefore, the
simulation results that are presented in figures 6-10 to 6-14 are the
best calibration and validation results that could be achieved.
Old Tampa Bay March 1990 Suspended-Sediment Improved Simulation
Suspended-sediment transport during the March 1990 storm in Old
Tampa Bay was simulated with revised calibration coefficients (wg, a,
and r¡) to compare coefficient values with the November calibration
simulation values and to identify processes that may account for the
difference. There were three calibration coefficients and 30 measured

172
concentrations. The settling velocity wg , erosion rate coefficient a,
and the erosion rate exponent rj were found to be 0.012 cm/s, 5.5x10 ^
g/cm2/sec, and 8 (table 6-3), respectively, by minimizing the standard
error of the simulation results. The settling velocity is equal to the
settling velocity of a 18 /¿m particle with a specific weight of 2.65
g/cm3 from Stokes law. The largest value of a reported by Lavelle et
al. (1984) is 3.7x10 ^ g/cm2/sec for cohesive sediments in Lake Erie
(Fukuda and Lick 1980), so a for the improved March Old Tampa Bay
simulation is relatively large but reasonable. As discussed
previously, coarser sediments and use of the estimated grain shear
stress in this study may account for the relatively large value of a.
The erosion exponent r¡ is greater than for the November calibration
simulation but within the range of values reported by Lavelle et al.
(1984). The standard errors for the improved simulation results (figs.
6-12 to 6-14) are 12.6, 5.7, and 6.7 mg/L at elevations 24, 70, and 183
cm above the bed. For this settling velocity and 77 = 5 to 9, an a
could be found that produced similar results. The improved simulation
results are in much better agreement with the measured data than the
validation simulation results.
Some of the discrepancy between simulated and measured results is
due to the hourly simulation segmentation. A slack tide was measured
at 1500 hours (velocities less than 1.3 cm/sec) and was used for the
simulation segment from 1430 to 1530 hours, which resulted in decreased
simulated suspended-solids concentrations. The combination of no data
before 1400 hours and a slack tide at 1500 hours may create a poor
start for the simulation. A strong flood tide and a slight increase in
wave activity measured at 2100 hours was used for the simulation

173
Table 6-3.--Values of the calibration coefficients determined by other
studies and determined for the November 1990 calibration simulation and
the March 1990 improved simulation.
Source
Erosion rate
coefficient a
Erosion rate
exponent n
Settling
velocity w
Calibration
simulation
4.08x10 ^ g/cm2/s,
r in dynes/cm2
1.6
s
0.021 cm/s
Improved
simulation
5.5x10 ^ g/cm2/s,
t in dynes/cm2
8
0.012 cm/s
Others
1.9x10'9 to
3.7x10 g/cm2/s,
t in dynes/cm2
(Lavelie
et al. 1984)
0.23 to 10
(Lavelle
et al. 1984)
Particle size:
Calibration: 24 ¿¿m
Improved: 18 ¿¿m
(Stokes law)

174
segment from 2030 to 2130 hours and increased the simulated
concentrations at all three elevations.
Smaller suspended particle size or decreased biological binding of
fine bottom sediments may account for the smaller settling velocity in
March. Wave activity and shear stresses were less in March than
November (figs. 3-1 and 3-2), so the mean resuspended sediment size may
have been smaller in March than in November.e mean suspended
sediment particle sizes from the calibrated settling velocities are 18
/im in March and 24 fj.m in November. Another explanation for the smaller
settling velocity in March is that the fraction of suspended material
that was in the form of fecal pellets, with a relatively large settling
velocity compared to individual fine sediment particles, was less in
March than November. Surficial bottom sediments in Old Tampa Bay are
sands, fecal pellets, and organically bound aggregations of fine
inorganic material (Ross 1975). The production of fecal pellets and
the secretions of benthic organisms are expected to be greatest during
the summer and fall when water temperatures are greatest. Therefore,
the portion of fine sediments in the form of fecal pellets was probably
smaller in March than in November, and the resulting calibrated
settling velocity was smaller in March than in November.
The calibrated erosion rate coefficients indicate that the bottom
sediments were more erodible in March than in November, and this may
have been due to biological activity or preceding storm history. The
erosion rate coefficient was 35% greater in March than in November.
Fecal pellets are more difficult to erode than the primary particles
bound within pellets (Nowell et al. 1981), and therefore the
erodibility of the bottom sediments increases as pelletization
decreases in summer and fall in Old Tampa Bay. Another possible reason

175
that the bottom sediments were more erodible in March was that
preceding winter storms had occurred more recently in March than in
November. Meteorological data from Tampa International Airport
indicates that winds likely to resuspend bottom sediments had
previously occurred 2 weeks before the March storm and 3 weeks before
the November storm.
Old Tampa Bay November 1990 Sensitivity Simulations
The relative significance of the calibration coefficients was
determined by varying coefficient values ±20% as described previously.
For each sensitivity simulation, the change in suspended-solids
concentrations 70 and 183 cm above the bed compared to the calibration
simulation results is presented in table 6-4. For example, the mean
concentration 70 cm above the bed decreased 23% when the settling
velocity w^ was increased from 0.021 to 0.025 cm/s and increased 33%
when w^ was decreased from 0.021 to 0.017 cm/s. The standard errors
(compared to measured concentrations) for all of the sensitivity
simulations were greater than for the calibration simulation, as
expected.
Simulation results were least sensitive to the erosion rate
exponent r¡ (table 6-4 and fig. 6-15). The estimated grain shear
stresses were on the order of 1 dyne/cm2 when net resuspension was
occurring, so the simulation results are relatively insensitive to rj.
Simulation results were more sensitive to the erosion rate
coefficient a (table 6-4 and fig. 6-16). The simulated concentrations
closer to the bed were more sensitive to the erosion coefficients a and
r¡ than the concentrations farther from the bed (table 6-4).
Simulation results were most sensitive to the settling velocity
w . The simulation results 183 cm above the bed were more sensitive to
s

176
Table 6-4.--Mean percent differences of simulated suspended-solids
concentrations 70 and 183 cm above the bed caused by 20% changes in the
calibration coefficients, November 1990 sensitivity simulations.
Altered Simulated concentration difference
coefficient
70 cm
183 cm
a=4.90x10 ^ g/(cm2 s)
+ 14%
+ 13%
q=3.26x10 ^ g/(cm2 s)
-15%
-14%
*7=1.92
+8.9%
+8.6%
*7=1.28
-5.8%
-5.7%
w =0.017 cm/s
s
+33%
+35%
w =0.025 cm/s
s
-23%
-24%
Note: The calibration values of the coefficients are:
Erosion rate coefficient a = 4.08x10 ^ g/cm2/s, r in dynes/cm2
Erosion rate exponent *7 = 1.6
Settling velocity W£ = 0.021 cm/sec

SUSPENDED-SOLIDS CONCENTRATION, IN MG/L SUSPENDED-SOLIDS CONCENTRATION, IN MG/L
177
HOUR
Figure 6-15, Sensitivity of November 1990 calibration simulation
results to erosion rate exponent T|.

SUSPENDED-SOLIDS CONCENTRATION, IN MG/L
(D H-
(A (Q
c c
ft (D
W
O'»
rr i
O m
or
(D -
ri
o (n
W (D
H- 3
0 w
P H-
rr
M H-
ÍD <
rr H-
(D rr
K
O
0 0
(D rt>
m
r-h ^
H- O
O <
H- (D
ri
P
vo
VO
o
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H-
cr
0»
rr
H-
o
p
w
H-
I
h-*
Í1»
rr
H*
0
P
150
HOUR
SUSPENDED-SOLIDS CONCENTRATION, IN MG/L
178

179
changes in the settling velocity than the simulation results 70 cm
above the bed (table 6-4 and fig. 6-17). Changes of 20% in settling
velocity changed the average simulated concentrations 23 to 35%

SUSPENDED-SOLIDS CONCENTRATION, IN MG/L SUSPENDED-SOLIDS CONCENTRATION, IN MG/L
180
120
1
183 CM ABOVE BED
CALIBRATION, w=0.021 CM/S
w=0.0025 CM/S
0800
1100
1400
HOUR
1700
2000
2300
150
100
0800
1100
1400
HOUR
1700
2000
2300
1
70 CM ABOVE BED
CALIBRATION, w=0.021 CM/S
w=0.025 CM/S
Figure 6-17, Sensitivity of November 1990 calibration simulation
results to settling velocity wg.

CHAPTER 7
SUMMARY AND CONCLUSIONS
Resuspension and transport of estuarine sediments are important
factors affecting the health of estuaries because estuarine sediments
may limit light availability for photosynthesis, supply nutrients to
the water column, and help determine the fate of contaminants. These
adverse impacts of estuarine sediments are important in Old Tampa Bay,
a shallow estuary in west-central Florida that is representative of
many shallow estuaries in the southeastern United States. Hydrodynamic
and suspended-solids concentration data were collected in Old Tampa
Bay, Florida, and analyzed to determine the significant sediment
resuspension mechanisms and sedimentation processes. A vertical one¬
dimensional hydrodynamic and sediment transport model (0CM1D, Sheng
1986a) was modified and used to help interpret the Old Tampa Bay
sediment resuspension data.
Bottom sediments in Old Tampa Bay are resuspended by wind-waves
generated by strong and sustained winds associated with winter and
tropical storm systems. Vertical profiles of suspended-solids
concentrations and velocity were collected from a platform in Old Tampa
Bay during selected potential resuspension events such as winter
storms, tropical storms, spring tides, and thunderstorms. Sediment
resuspension by depth-transitional wind-waves associated with winter
storm systems in March 1990 and November 1990 was observed. Observed
variations in suspended-solids concentrations were similar to
variations in wave properties such as bottom orbital velocity and
181

182
bottom shear stress. Sediment resuspension during a tropical storm in
October 1990 was also observed. Net sediment resuspension by tidal
currents and thunderstorms was not observed at the Old Tampa Bay
platform because Old Tampa Bay is a microtidal environment and winds
associated with thunderstorms do not have the duration or fetch needed
to generate waves capable of resuspending sediment at the platform.
Resuspended sediments settled rapidly as the storm intensity
diminished. Frontal storm systems that move as far south as Tampa Bay
occur infrequently (intervals on the order of weeks) and only during
winter, tropical storms are rare and generally occur during fall, and
fetch may limit wave formation, so significant sediment resuspension is
not a common occurrence in Old Tampa Bay.
The bottom roughness regime for Old Tampa Bay is transitional
between the rough and smooth limits, so the numerical model was
modified to account for transitional roughness regimes, and simulated
velocity profiles were in good agreement with the Reichardt velocity
distribution. The bottom roughness elements are small irregular
undulations, probably caused by bioturbation, and sediment particles.
A variable bottom roughness regime submodel, the dynamic equation for
the turbulence macroscale, and viscous terms from the original
formulation of the turbulence submodel were added to the model. The
additional terms were successfully tested by comparing simulated
results with the Reichardt velocity distribution, which includes
laminar flow near the bed, a transition region, and fully turbulent
flow far from the bed. The model also successfully simulated turbulent
dissipation in the marine surface layer.
Wave motion resuspends bottom sediments in Old Tampa Bay, so a
submodel that virtually reproduces measured energy spectra produced

183
from 1-Hz current data was added to the model. Oscillatory motion at
many frequencies is present in Old Tampa Bay, and a single wave height
and wave period may not be able to adequately represent the wave field.
The Fourier series coefficients for the velocity data were determined
and the coefficients were used by the model to determine the depth-
dependent wave-induced pressure gradient at every grid point. Energy
spectra calculated from the simulated velocities were in excellent
agreement with spectra calculated from the measured velocities.
A submodel that estimates the spatially-averaged grain component
of the total bottom shear stress was added to the model. The total bed
shear stress contains a component that acts on the bed forms and a
component that acts on the particles on top of the sediment bed.
Initiation of sediment motion and sediment resuspension is caused by
the grain component of the total shear stress. The submodel fits the
Reichardt velocity distribution to the grain roughness and the
simulated near-bed velocity distribution (based upon the total bottom
roughness) in order to estimate the spatially-averaged grain shear
stress. The convergence of simulated shear stresses is dependent upon
the height of the bottom layer and simulated shear stresses were in
good agreement with laboratory measurements of the relation between
total and grain shear stress for steady flow. Spatially-averaged grain
shear stresses in Old Tampa Bay do not have a single frequency
periodicity and rarely are large enough to move sand-sized sediments.
Therefore, only the finer sediments are probably suspended and the
sand-sized sediments are probably irregularly transported as bed load.
Results of the grain shear stress submodel were in good agreement
with published data on critical conditions observed at several
continental shelf sites for which waves, mean current, and combined

184
waves and mean current were present. Total shear stress can be a poor
indicator of critical conditions because it can be much greater than
the grain shear stress. Viscous effects, including variable bottom
roughness regimes, are an important factor affecting the spatially-
averaged grain shear stress because of the small grain roughness. This
application also demonstrated that the model can simulate waves,
currents, and wave-current interaction in settings other than Old Tampa
Bay. The estimated spatially-averaged grain shear stress was used to
determine the erosion rate of the bottom sediments for the Old Tampa
Bay suspended-sediment simulations.
Significant sedimentation processes and factors that may affect
sediment transport processes were identified by comparing simulation
results with data measured in Old Tampa Bay. A series of hour-long
segments, during which the mean current and wave spectrum were
constant, were used to simulate suspended-solids concentrations
measured in March 1990 and November 1990. A settling velocity was
specified, and erosion was simulated with a power function of the
estimated spatially-averaged grain shear stress. The spatially-
averaged grain shear stress and the erosion rate were greatest during
the periods of the greatest wave activity. The November 1990
simulation results were used to calibrate three settling and erosion
coefficients, and the March 1990 data set was used to attempt to
validate the model. The validation simulation results were poor, so an
improved simulation with more appropriate calibration coefficients for
March 1990 was conducted. The calibrated coefficients for both March
and November were reasonable compared to values found by other studies
and the bottom sediment size distribution at the Old Tampa Bay

185
platform. Sensitivity simulations of suspended-solids concentrations
in November 1990 were also performed.
Physical and biological processes explain the differences between
the calibration coefficients for the November calibration
simulation and the improved March simulation. Smaller suspended
particle size or decreased biological binding of fine bottom sediments
probably account for a smaller calibrated settling velocity in March.
Wave activity and shear stresses were less in March than November
(figs. 3-1 and 3-2), so the mean resuspended sediment size may have
been smaller in March than in November. Another explanation for the
smaller settling velocity in March is that the fraction of suspended
material that was in the form of fecal pellets, with a relatively large
settling velocity compared to individual fine sediment particles, was
less in March than November. Surficial bottom sediments in Old Tampa
Bay are sands, fecal pellets, and organically bound aggregations of
fine inorganic material (Ross 1975). The production of fecal pellets
and the secretions of benthic organisms are expected to be greatest
during the summer and fall when water temperatures are greatest.
Therefore, the portion of fine sediments in the form of fecal pellets
was probably smaller in March than in November, and the resulting
calibrated settling velocity was smaller in March than in November.
The Old Tampa Bay simulations indicate that the bottom sediments
were more erodible in March 1990 than in November 1990, and this is
probably due to biological binding of the bed sediments or previous
storm history. Fecal pellets are more difficult to erode than the
primary particles bound within pellets (Nowell et al. 1981), and
therefore the erodibility of the bottom sediments increases as
pelletization decreases in summer and fall in Old Tampa Bay. Another

186
possible reason that the bottom sediments were more erodible in March
was that preceding winter storms had occured more recently in March
than in November. Meteorological data from Tampa International Airport
indicates that winds likely to resuspend bottom sediments had
previously occurred 2 weeks before the March storm and 3 weeks before
the November storm.
Several results of this study may apply to other estuarine
studies. Wind waves associated with storms are an important sediment
resuspension mechanism in Old Tampa Bay, and this is probably true in
other shallow estuaries. Data collection is more difficult when seas
are rough, but sampling during storm-events may be important because
suspended-solids concentrations and associated water - quality parameters
can reach extreme values and change rapidly. Numerical sediment
transport models for shallow estuaries should also account for wind
waves and associated sediment resuspension. Seasonal biological
activity may be a factor affecting the erodibility of bottom sediments
and their settling properties. If resuspended sediments are all fine
sediments, as is the case in Old Tampa Bay, then sediment resuspension
is more likely to have a significant effect on nutrient and contaminant
transport because of the ability of fine sediments to adsorb chemical
constituents. Finally, a vertical one-dimensional model has been shown
to be a valuable tool for interpreting hydrodynamic and suspended-
solids concentration data. Use of the model before and during a
sediment resuspension data collection program could also indicate
improvements to a data collection program.
Additional studies that are needed to follow-up this study involve
data collection, numerical modeling, and the impacts of fine sediment
resuspension. Accurate measurements of near-bed velocity profiles and

187
suspended-solids concentrations are necessary because sediment
resuspension and transport is dependent on near-bed processes.
Acoustic instrumentation should be further developed because it has the
capability of providing near-bed vertical profiles of velocities and
suspended-solids concentrations with fine resolution and minimal effect
on the flow. Field data that characterize the suspended material for
ambient and storm conditions would aid in the understanding of sediment
dynamics in Old Tampa Bay and in the development and refinement of
numerical sediment transport models. Numerical suspended-sediment
transport models need relatively fine vertical resolution near the bed
because of settling and erosion. The near-bed resolution of three-
dimensional hydrodynamic and transport models, however, is generally
limited by computational resources, so simulation of suspended
sediments in a large water body by linking a vertical one-dimensional
sediment transport model with a fine near-bed grid with a three-
dimensional model with a coarser vertical grid should be beneficial.
Sediment transport is an important factor affecting nutrient and
contaminant transport in estuaries, so transport of adsorbed
constituents should be added to the vertical one-dimensional model and
model results should be compared with field data. The effect of
resuspended fine sediments on nutrient and contaminant transport in
estuaries with predominately sandy bottom sediments should be
determined. Finally, multi-disciplinary studies that are directed
toward determining the relationship between sediment transport,
adsorbed constituent transport, and biological communities are needed
because fine sediment resuspension may expose harmful adsorbed
constituents to estuarine biota.

APPENDIX A
0CM1D FINITE-DIFFERENCED EQUATIONS AND TURBULENCE CLOSURE ALGORITHMS
The nondimensional differential equations for momentum (eqns. 4-44
and 4-45), suspended-sediment transport (eqn. 4-46), turbulent velocity
(eqn. 4-56), and turbulent macroscale (eqn. 4-57) are solved by writing
the equations in finite - differenced form. The finite-differenced
equations are linearized, semi - implicit, forward in time, and either
centered or upwinded in space. The grid used to write the finite-
differenced form of the equations is shown in figure A-l. The vertical
domain is divided into a stack of equally or unequally spaced layers.
The grid is staggered with velocity and constituent concentrations
located at the center of each layer and eddy coefficients, q, and A
located at the top of each layer. A computational point is also
defined at the bed. For layer k, the nondimensional layer elevation is
and the nondimensional distances from the center of layer k to the
center of the layers above (layer k+1) and below (layer k-1) are Aa+^
and Aa , .
-k
Finite-Differenced Equations for Momentum and Suspended Sediment
The momentum and suspended-sediment equations are written with
rotation, pressure, density, surface slope, and settling terms that are
determined with known values at time step n and viscosity and vertical
mixing terms that are evaluated at the unknown time step n+1. The
equations are solved to determine velocity and suspended-sediment
concentration. The finite-differenced form of the nondimensional u-
momentum equation is
188

189
k+1
Aak
k-1
z=h’ °='1
Figure A-l, Coordinate axes definition and grid structure for
program 0CM1D.

190
n+1 n
"k
At
n+1 n+1
n+1 n+1
— — f A n
H A% vt
. !* (
F2
1/ R
dx
1_
H2 R Act,
e k
l “k+r^
A n
^ -Vi
Act ,
• A
v.
Act ,
+k
k-1
-k
+ h ;°
dcr ) -
d€ n
— + V
JCT dX
dx
(
n+1 n+1
“k+1 ~ “k
A o .
n+1 n+1
^ - uk-i
A a
)
(A-l)
+k ““-k
in which superscripts n and n+1 indicate time steps, At is the
nondimensional time step, and subscripts k-1, k, and k+1 indicate layer
numbers with layer 1 adjacent to the bed. The nondimensional finite-
differenced v-momentum equation is
E
n+1 n
v, -v
k k
At
n+1 n+1
— — Í A n VK±-1--V-k,.. . A n
H2 Acr. v Act . v
k k +k k-1
R 3p.n n . n
- ( -Z- * H J° to )
dy ^ o, dy
n+1 n+1
vk ~Vk-l
F2
i/ R
A a
3fn
dy
)
H2 R Act,
e k
n+1 n+1
V - v
1_ ( k+1 k
A a .
n+1 n+1
v, - v, i
k k-1
A a
)
(A-2)
+k -k
The nondimensional finite-differenced suspended-sediment transport
equation is
n+1 n
c, -c,
At
D n n
Rx . ck+l"ck .
r ws ( >
k
„ n+1 n+1
E , c, . -c,
± 3 1 . v n k+1 k
2 A „ (
P H2 A ct, ' *'v, Act
k k +k
K
n+1 n+1
Ck Ck-1
Act
)
(A- 3)
k-1 -k
The production term has been dropped from equation A-3. The settling
term is solved with an upwind finite difference scheme for which each
layer is assumed to be well-mixed. The nondimensional time step for
which the settling term will always be stable is
H Act,
At <
R w
x s
(A-4)
The Old Tampa Bay simulations used a time step of 0.18 sec which is
less than the maximum value from equation A-4 (5.1 sec for the bottom

191
layer and w=0.021 cm/s). If a central difference scheme were used for
the settling term, then the model is more likely to be unstable and a
near-bed concentration at the bottom of the bottom layer would have to
be estimated or extrapolated. The dispersion terms are fully-implicit
and therefore are unconditionally stable.
The finite-differenced equations can be rearranged in the form of
a tridiagonal matrix which can be solved efficiently. The tridiagonal
form of the finite-differenced equation for u-momentum is
n+1
“k
E At
1 + TTo :— (
V.
H2 Acr^ v Acr+k
A a
n
/, t if R At
2—
-k
H2 R Act,
e k
Act
+k
Act
) ]
n+1
+ Vi
n+1
+ “k+l
R At
x
E At A
z v.
k-1
v R At
z
H2 Act^Act
E At A n
_f Zk-
n2 AakAa+k
H2 R Act, Act
-k
v R At
z
H2 R Act, Act
(
3p
+k
^- + H J° dCT ) - At ( -
ak 5x
n . n
a^T + v > + uk
(A- 5)
F2 v dx
The tridiagonal form of the finite-differenced equation for v-momentum
is
n+1
. n . n
A A
E At v. v. i/ R At
. z , k k-1 „ z
1 + 7^— ( TZ + ) +
+ v.
n+1
k-1
+ v.
n+1
k+1
H2 Act
, Act ,
k +k
n
Act
-k
H2 R Act,
e k
Act
E At A
_f Ik.
H2 Act^Act+^
E At A n
_! Ik.
H2 Act, Act ,
k +k
v R At
z
H2 R Act, Act
v R At
z
H2 R Act, Act
-k
-k
+k
Act
)]
R At
x
F2
(
♦ H /° ¡¡£ d. ) ■ At ( f-
dy au dy dy
n
n v n
u ) + vk
(A-6)
The tridiagonal form of the finite-differenced equation for suspended-
sediment transport is

192
LT ^ 1/ ^
E At v, v. ,
n+1 r , , _z . k k-1 . ,
Ck PH2 Acr^ Aa+k k
n
E At K
n+1 , __f Vk-1 . n+1
+ Ck-1 1 ' P H2 AakAa k J Ck+1
O n n
R c. . - c.
x . k+1 k n
- — w At ( ~ ) + c,
H s A a. k
k
E At K
_! It
P H2 A a, A a
k +k
(A-7)
The left hand sides of equations A-5 to A-7 contain the implicit terms
and the unknowns and the right hand sides contain the explicit terms.
The boundary conditions are given by equations 4-47 to 4-55.
Turbulence Closure Algorithms
For the equilibrium closure algorithm, the algebraic solution of
equations 4-33 to 4-39 is streamlined to maximize computational
efficiency. The turbulence macroscale A is defined by the integral
constraints and equations 4-33 to 4-39 and the definition of q2 are
solved algebraically (Sheng et al. 1990a) to determine the
nondimensional quantity
Q2 =
(A- 8 )
A2 [(du/da)7 + (dv/da)2]
in which the variables on the right hand side are nondimensional and v
may be nonzero. After Q2 is determined, q, w'w', A^, and are
determined algebraically. The procedure has been presented by Sheng et
al. (1990a) and is given later. Calculation of Q2 and the correlation
w'w' are convenient intermediate steps. The other correlations are not
needed for estimating the eddy coefficients and therefore are not
determined.
If the TKE closure algorithm is used to determine the eddy
coefficients, q2 is determined with an implicit linearized dynamic
equation and equations 4-37 to 4-41 are used to determine the eddy

193
coefficients algebraically (Sheng and Villaret 1989) . The linearized
nondimensional finite-differenced equation for q2 is
>n n n
n n+ 1 9 1
k ^ k
At
2E
H2
z . n .Vt-l'V .Vu'V vk+l'vk. vk+l'vk.
" V [ ( Aa >( "¿o' '> + (-—---H--- ' ) ]
k +k +k +k +k
2E
n n
P ‘ P1,
P F2 H
K
Vk
' Aa+k
+ Vc H2
4A o
1
+ qk)
(Ak+l
+ Ak)
(q
A o, .
k+l
1
A o.
k
(qk +
qk-l>
(Ak +
Ak-l)
(q
+k
0n+l
,n+l
>2r‘>
- q‘
¡n+l
k-1
) ]
„ 2b n 9n+l
RZ r qk q k
k
i/ R
H2 R Aa .
e +k
2n+l 2n+^'
(q k+l - q k ^k+l
,n+l
>n+l,
2ai/R
>n+l
H2 R A2 q"k
e
k 1
(A-9)
Equation A-9 is written for every grid and solved implicitly with a
tridiagonal matrix solver. The top boundary conditions are that the
second derivative of q2 equals zero (linear q2) and equations 4-47 and
4-48 are substituted into the shear production term. The bottom
boundary condition is that q equals a specified minimum value. Once q2
is determined, equations 4-37 to 4-41 are used to algebraically
determine w'w', A , and K in a similar manner to that used for
v v
equilibrium closure except that viscous terms are included. The
equation for w'w' is
a 2(1 - 2b)/3
1 - 2
-R./AQ2
(A-10)
2ai;
(-R./AQ2)/bs + 1 + qA Re
in which Q is defined by equation A-8 and the Richardson number
H_ d& 1
R. =
l
F2 do (du/do)2 + (d\r/do)2
(A-11)
The eddy viscosity

194
A R
A z
(-R./AQ2)/A
(-R./AQ2)/bs - 1
Av W'W' q E 1 + 2ai//(qAR ) - R./AQ2
and the eddy diffusivity
A R p
A z
Kv W’W> q E A 1 - (-R./AQ2)/bs
(A-12)
(A-13)
z 1
The equilibrium closure algorithm used equations A-10 to A-13 with i/ =
0 to determine the vertical eddy coefficients given an algebraically
determined q2.
The turbulence macroscale A for the TKE closure algorithm can be
defined by the integral constraints or by the dynamic A equation (eqn.
4-57). The integral constraints were discussed in chapter 4. If the
Reynolds number is low, turbulence may far out of equilibrium and the
dynamic turbulence macroscale equation may be more appropriate than the
integral constraints (Lewellen 1977). The Old Tampa Bay simulations
presented in chapter 6 had low Reynolds numbers near the bed, so the
dynamic turbulence macroscale equation was used for these simulations.
The linearized finite-differenced equation for A is
.n+1
a"+1-a" e a.
_k k _ 0 35 _z _k
At H2
n
A
Vr
n
r .“k+rv .Vu'V vk+rvk. A+rV .
[ (^r)(^r + 1
+ 0.075Rz q£ + °-6at/
R
+ 0.3 77T
H2 4Act
+k
Aâ„¢ R
k e
/ n nN /An .n+1 .n.n+1.
Aa. . qk+l qk (Ak+lAk+l ' AkAk }
k+1
1 , n n . ..n.n+1 .n .n+1. ,
• (qk+ qk-i} (\Ak • Ak-iAk-i} ]
k
0.375 kz 1 , . n n. ,.n .n,
— H2 16^7 [ (qk+l + qk} (Ak+l + V
qk +k
n v * . ri .n » -.o
• (qk + qk-i} (Ak + Ak-i} ]

195
0. SA^1
k
(A-14)
+
The shear, diffusion, and buoyancy terms are implicit terms and the
remaining terms are explicit. The turbulent velocity is explicit
because the turbulence macroscale is solved before the dynamic q2
equation is solved. Equation A-14 produces a system of tridiagonal
equations. The boundary conditions at the water surface are that
3A/3(7=-0.65 and equations 4-47 and 4-48 are substituted into the shear
production term. The bottom boundary condition is that A equals a
specified minimum value.

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BIOGRAPHICAL SKETCH
I grew up in Los Altos, California, during the 1960s and 1970s.
From 1978 to 1983, I attended the University of California at Davis
where I earned a bachelors and a masters in civil engineering. My
major field of study was open channel flow. I worked for the U.S.
Geological Survey in Bay St. Louis, Mississippi, from 1984 to 1987,
where I primarily developed Lagrangian transport models and applied
them to sediment transport problems. In 1987, I transferred to the
U.S. Geological Survey office in Tampa, Florida, where I was project
chief for a study of sediment resuspension and light attenuation in
Tampa Bay. During the 1988-89 school year I attended classes at the
University of Florida, primarily from the Department of Coastal and
Oceanographic Engineering. From 1989 to 1993 I completed the U.S.
Geological Survey project and my doctoral research. In 1993 I will be
transferring to the U.S. Geological Survey office in Sacramento,
California, and studying sediment resuspension in San Francisco Bay.
215

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Y. Peter sneng, (JJa^Lrman
Erofessor of Coasxal and
Oceanographic Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Robert G. Dean
Graduate Research Professor of
Coastal and Oceanographic
Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Daniel M. Hanes
Associate Professor of Coastal
and Oceanographic Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Ashish J. Mehta
Professor of Coastal and
Oceanographic Engineering

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Louis H. Motz
Associate Professor of Civil
Engineering
This dissertation was submitted to the Graduate Faculty of the
College of Engineering and to the Graduate School and was accepted as
partial fulfillment of the requirements for the degree of Doctor of
Philosophy.
May 1993
A
Winfred M. Phillips
Dean, College of Engineering
Madelyn M. Lockhart
Dean, Graduate School

UNIVERSITY OF FLORIDA
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