Nearbed sediment suspension in the offshore zone of a large scale wave tank

UFL/COEL-95/010

NEARBED SEDIMENT SUSPENSION IN THE
OFFSHORE ZONE OF A LARGE SCALE WAVE TANK

by

Eric D. Thosteson

Thesis

1995

NEARBED SEDIMENT SUSPENSION IN THE OFFSHORE ZONE OF A
LARGE SCALE WAVE TANK

By

ERIC D. THOSTESON

A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA

1995

ACKNOWLEDGMENTS

For providing funding for the experiments mentioned herein, I wish to acknowledge

the generous support of the Office of Naval Research. Also, the invitation from the U.S.

Army Corps of Engineers Coastal Engineering Research Center to participate in the

Supertank project is greatly appreciated. For giving me the opportunity to participate in

this research and the freedom to make my own decisions, I wish to express my gratitude

to Dr. Daniel Hanes. In addition, for contributing to the academic excellence of the

University of Florida's Coastal Engineering Program and for making my experience at U.F.

truly rewarding, thanks to Dr. Robert Thieke and Dr. Peter Sheng. Most importantly, for

her constant encouragement and undying patience I thank my Mom!

Special thanks goes to my brother Pete Thosteson and to Homer Simpson for

keeping me sane at times I thought I shouldn't be. On this same note, thanks to Chris,

Paul, the original wildman Phil, Tim, Mark, Dagwood, Ken, Jill, Melanie, Lynn, Monica,

my dog Sadie, the Hogtown Brewers, Calvin, Opus, Seinfeld, and the Market Street Pub.

TABLE OF CONTENTS

ACKNOWLEDGMENTS...................................................................................ii

L IST O F T A B L E S ................................................................................. ....................................... iv

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

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

A B STRA CT ............. ........................................................................ ................... xi

C H A P T E R S ......................................................... .......................................................... ............. 1

1 IN T R O D U C T IO N .................................................................................... ................... 1
B ackground.............................................. ....................................................... 1
T h eo ry ..................................................................................................................... 3
O bjectiv es ................................................................................ ............. . ........... 6

2 EX PERIM EN T ............................. ........................................................................... 8
Site D escription.................................. ................................................. 8
Equipment and Measurement Capabilities.............................................................. 8
D ata A acquisition ................................................ ........ ........................................ 15
Data Description .................................................................... 16

3 THE CONCENTRATION PROFILE AND GOVERNING PARAMETERS ............... 22
The Influence of Shear Stress on Sediment Entrainment ........................ 22
R reference C concentration .......................................................................................... 27

4 D A T A A N A L Y SIS ................................................................................. ..................... 33
Calibration ................................................................. .................... 33
A analysis .......................... ...................................................... .................... 38

5 EVALUATION, CONCLUSIONS, AND RECOMMENDATIONS .................... 45
Trends in M measured D ata ......................................................................................... 45
Comparison of Measured Reference Concentration to Predictive Models............. 51
Conclusions and Recom m endations.......................................................................... 62

A P P E N D IX ......................................................................................................................................... 6 3
ANALYZED DATA FROM EXPERIMENTS PERFORMED AT SUPERTANK.................. 63

REFEREN CES............ .................................................................................... 134

B IO G RA PH ICA L SK ET CH ............................................................................................................... 136

LIST OF TABLES

Table 2.1 Maximum resolution of measured quantities with Supertank acquisition system............... 15

Table 2.2 W ave conditions during experim ent.................................................................................... 18

Table 4.1 Calibration constants from various instrumentation....................................................... 35

Table 5.1 Experimental results summarized. .......... ............................................................. 61

Table 5.2 Relative errors from various models................................................................................. 62

LIST OF FIGURES

Figure 2.1 Location in tank where experiment was performed...................................................... 9

Figure 2.2 Side view of instrumentation within tank........................................................................... 10

Figure 2.3 Description of acoustic pulse and ensonified volume.................................................... 13

Figure 2.4 Underwater video system and reference grid................................................................ 14

Figure 2.5 Averaging process on ACP data during collection........................................................ 17

Figure 2.6 Calibrated pressure signal............................................................................... 19

Figure 2.7 Calibrated pore pressure sensor................................................................ .................... 19

Figure 2.8 Calibrated u velocity from EM current meter. ............................................................ 19

Figure 2.9 Calibrated O B S sensor.............................................. ........................... ..................... 20

Figure 2.10 Time series of uncalibrated ACP profiles. .................................................................. 20

Figure 2.11 Ripple pattern from video picture............................................................................... 21

Figure 4.1 ACP recirculating calibration chamber ....................................................................... 36

Figure 4.2 Surface elevation spectrum. .................................................................................... 40

Figure 4.3 W ave height histogram .............................................................................. ..................... 41

Figure 4.4 Bottom return histogram ............................................................................ ................... 43

Figure 4.5 Measured concentrations and best fit exponential curve ............................................... 44

Figure 5.1 Comparison of Swart's and Sleath's shear stress estimates............................................ 46

Figure 5.2 Comparison of H andH 1/3 ........................................................ ......... .................... 47

Figure 5.3 ACP bottom return tim e series................................................................ ..................... 48

Figure 5.4 Bed form height as determined from ACP and video measurement ................................. 49

Figure 5.5 Measured reference concentration vs. effective Shield's parameter.................................. 50

Figure 5.6 Nielsen's model compared with measured concentrations.............................................. 52

Figure 5.7 Nielsen's prediction shown with runs with ripple measurements only.............................. 54

Figure 5.8 Smith & McLean's model versus measured results....................................................... 55

Figure 5.9 Bosman and Steetzel's model vs. measured values. ....................................................... 56

Figure 5.10 Engelund and Fredsoe's model vs. measured values ................................................... 58

KEY TO SYMBOLS

a Function used in determination of the wave friction factor by Sleath's
boundary layer model, a= f(lb/UO ,r/A)

A Semiorbital excursion length

A System constant in calibration of ACP

b Function used in determination of the wave friction factor by Sleath's
boundary layer model, b = f(r/A)

c Instaneous sediment concentration, c = + c'
c Time averaged sediment concentration

c' Time varying component of sediment concentration

Cb Concentration of bed

Co Reference concentration

d Grain diameter
do50 Median grain diameter

fw Wave friction factor

g Acceleration due to gravity

G Sediment suspension coefficient in Bosman and Steetzel's reference

concentration model

h Water depth
hp Depth of pressure sensor

H1,3 Significant wave height

Hmo Wave height determined from total energy of spectrum

in Fraction of sediment size class n

k Wave number

ki Constant of integration in solution to Schmidt equation

ki Constant describing attenuation of sound by water

k2 Constant of integration in solution to Schmidt equation

k2 Constant describing attenuation of sound by sediment
K, Pressure correction factor from linear wave theory

n Total number of instances in relative error calculation

p Fraction of grains in bed load in unit area

p(t) Instantaneous pressure at pressure sensor

Q, Suspended sediment flux per unit bed width
Q, Time averaged Q,

r Equivalent roughness length

R Range from ACP over which spherical spreading occurs

s Relative sediment density, p,/p

4S Normalized excess shear stress

T Wave period

U Horizontal velocity component of fluid

U Time averaged horizontal velocity component

U' Time varying component of horizontal velocity component

Uo Amplitude of free stream fluid velocity just outside of boundary layer

Uib Amplitude of fluid velocity deficit at bed

V(z) Voltage returned from ACP at time corresponding to distance z
w, Sediment fall velocity

y, Measured value of instance i used in relative error calculation

A, Predicted value of instance i used in relative error calculation

Z Vertical distance from z0
zo Bed level

ZN Bed level determined in relation to Nikuradse's roughness

a Grain diameters from bed at which --is evaluated in Engelund and
dz

Fredsoe's model

Y o Sediment resuspension coefficient in Smith and McLean's reference

concentration model

A Relative error

e Eddy viscosity

E, Sediment diffusivity

"1 Ripple height

0 Shield's parameter, (0)
p (s- 1)gd

02.5 Grain roughness Shield's parameter

0c Critical Shield's parameter

OR Grain roughness Shield's parameter with ripple induced velocity

enhancement

K Van Karman's constant

X Ripple wavelength
X Bagnold's linear grain concentration

?'b Bagnold's linear grain concentration at the bed

D Tangent of dynamic friction angle, gD = tan(,D)

v Kinematic viscosity of water

p Density of water

p, Density of sediment

T Instantaneous shear stress
S(0) Instantaneous shear stress at z0

T Maximum shear stress at bed
c2.5 Grain roughness shear stress

tc Critical shear stress

0G Bagnold's sediment dispersive shear stress

T ,, Critical shear stress of sediment size class n
( Phase difference of fluid velocity at bed from uo

to Angular wave frequency

Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

NEARBED SEDIMENT SUSPENSION IN THE OFFSHORE ZONE OF A
LARGE SCALE WAVE TANK

By

Eric D. Thosteson

May 1995

Chairman: Daniel M. Hanes
Major Department: Coastal and Oceanographic Engineering

In describing suspended sediment profiles under nonbreaking waves, it has been

shown that a time and bed averaged equilibrium profile exists under given flow conditions.

Ultimately, the total magnitude of the vertically integrated suspended sediment

concentration depends on the amount of sediment entrained from the bed, deposited to the

bed, and advected into and out of the water column from other areas. The time averaged

concentration at the bed, or reference concentration, provides this boundary condition,

and determination of its value both from experimental data and from predictive models is

of the utmost importance. Use of an acoustic sediment profiler with high spatial and

temporal resolution allows examination of details of the profile previously unattainable.

During a laboratory experiment in August of 1991, an acquisition system including such a

profiler was deployed. Wave conditions in a prototype scale wave flume offshore of

breaking ranged from 3 to 10 second periods and 0.2 to 1.5 meter monochromatic, narrow

band random, and broad band random waves. Instantaneous and time averaged profiles

were examined to determine the method of calculating the time-averaged reference

concentration which most adequately describes the profile. Analysis of hydrodynamic data

from the system provided the information necessary to determine the time-averaged

reference concentration from four predictive models. These four models include Nielsen's

1986 model, Bosman and Steetzel's 1987 model, Smith and McLean's 1977 model, and

Engelund and Fredsoe's 1976 model. Upon comparing the predicted values to those

obtained experimentally, it is shown that the reference concentration is best described by

Smith and McLean's empirical model utilizing a linear relation with shear stress.

CHAPTER 1
INTRODUCTION

Background

With the increasing utilization of the oceans resources and coastal regions comes the

need to be able to predict changes in coastal bathymetry. The ability to predict changes in

bathymetry and the resulting evolution of the shoreline enables more careful planning of

coastal development, determination of the impact of structures placed in the coastal

region, and improvement of methods of maintaining navigable inlets. It also eases

determination of methods of coastal protection and their effectiveness in protecting an

already developed coastline. Local wave conditions from both local and distance weather

processes are continuously at work changing the shoreline, the extent of these changes

dependent on the severity of the resulting wave conditions and local composition of the

coast. A model of coastal bathymetric change would provide a prediction of the final

coastal bathymetry when provided with the expected wave conditions over the time period

of interest.

Bathymetric change results from the erosion or accretion of sediment at various

locations. Sediment is eroded from a location and transported elsewhere where it is

eventually deposited. Deposition of sediment at a great enough depth such that transport

by processes typically found on the coast is no longer possible results in a net loss of

2
sediment from the littoral system. Assuming the sediment moves at the same velocity as

the surrounding fluid, the sediment flux per unit bed width is given by

= (ilc)dz (1)
0

In this equation, u is the horizontal component of the sediment velocity and c the

sediment concentration. Decomposing the velocity and concentration into time mean and

fluctuating components

U =u-+U'
c + C'

where the overbar and prime denote the time mean and the fluctuating components,

respectively, allows us to examine the effect of currents and waves on the sediment

transport separately. Making this substitution and time averaging yields

f =(u + u'C'z (3)
0

The term uc describes how the mean concentration is carried by the time-mean current.

In the presence of waves, the flow rate is continuously changing in both magnitude and

direction, and consequently the amount of sediment available for transport changes as

well. Since the sediment tends to move with the water, the relation between these

intermittent processes may govern the transport, as indicated by the term u'c'. In order to

determine the sediment flux, the essential first step is accurate prediction of the time mean

concentration. It is expected that the fluctuating component of concentration will be

related to the time mean.

3
In order to develop new models or evaluate existing models of sediment dynamics,

accurate measurements of the process are necessary. Because of the large number of

factors involved in a study of sediment dynamics, attempting to examine the effects of

changing a single parameter can be extremely difficult with field measurements. For this

reason, much of the work is done in the laboratory under carefully controlled conditions.

Although the laboratory measurements may be only in fair agreement with those obtained

in the field, much insight into the sediment dynamics can be obtained. Variations between

laboratory and field measurements result from neglecting factors normally found in the

field and their subsequent interactions with other processes.

The region of the coast active in sediment transport extends from the uppermost

limit of the swash zone to a substantial distance offshore of the break line. To study

cross-shore sediment processes over the active region in the laboratory then requires

enough space to recreate this region or requires the region to be scaled down

considerably. To retain the accuracy of the prototype, scaling down the region

necessitates scaling all of the processes involved in the sediment dynamics. Unfortunately,

this is not possible, so scaling will lead to increasingly larger errors and inconsistencies

with field observations. Prototype scale laboratory experiments allow examination of

sediment transport processes under readily changed and carefully controlled conditions

with fairly good agreement with field conditions.

Theory

Sediment moves either as bedload or suspended load. When the sediment is

supported mainly by intergranular forces and individual grains inherit enough energy from

4
the fluid to move by sliding, rolling, or making short jumps over other grains, it is said to

be in the bedload regime (Bagnold, 1956). Bedload extends from the lowest moving

grains within the bed to several grain diameters above the bed. When individual grains of

sediment are no longer supported by other grains but instead are supported by fluid forces,

they are in the suspended load regime. Suspended load extends from the bed to the

highest location above the bed where any grain is found. Grains in bedload require a

certain amount of energy to begin moving and once moving lose energy easily through

collisions with other grains. Once grains become suspended load though, they move easily

with the fluid. Both regimes contribute to the total sediment transport, but because of the

differences in the forcing on the particles, the two types of sediment motion must be

described differently.

Two basic problems must be confronted in order to model sediment suspension.

The first of these is determining the distribution of sediment with distance from the bed

and the second, the entrainment of sediment from the bed. The distribution of sediment in

the water column is most commonly described through gradient diffusion. In the process

of gradient diffusion an equilibrium vertical sediment distribution results from the balance

of an upward sediment flux and downward sediment settling. Sediment settles under the

influence of gravity, and an upward sediment flux is sustained through random vertical

mixing. The sediment concentration conservation equation describes this balance.

Sc Jc ( c
-c + c E =0 (4)
at az az Sz

In this equation, w, is the fall velocity of the sediment and e, is the sediment diffusivity.

The sediment diffusivity is analogous to the diffusivity of momentum, or eddy viscosity,

5

used in describing boundary layer flow, but instead represents a mass diffusivity. For this

reason, the sediment diffusivity and eddy viscosity need not be the same, but investigations

by Hunt suggest that the mass diffusivity is only 1.2 to 1.5 times larger than the eddy

viscosity (Hunt, 1969). If the sediment diffusivity is assumed constant, the concentration

is broken into time mean and fluctuating components as in equation 2, and the equation is

time averaged, the following steady-state form of the equation is obtained.

d2c dc
.-T+ w = 0 (5)
N dz2 dz

Two well known solutions to this equation have been presented (Schmidt, 1925; Rouse,

1937). They differ in that Schmidt assumed a constant sediment diffusivity, and Rouse

equated it to an eddy viscosity with a parabolic distribution over depth, used in

determining the velocity profile in steady flow. Recently though, Sleath showed that if the

eddy viscosity is split into wave and current components, the wave component of eddy

viscosity is not depth dependent (Sleath, 1991). Since the tests which will be described in

this text were performed in a wave tank, void of any substantial current, and since the

focus of the study is in the region very close to the bed, the assumption of a constant

sediment diffusivity seems justified. Assuming a solution of the form

S= ke + k2e- (6)

and applying the boundary conditions

c= 0 @z= (7)
c = Co @z=Zo

results in the solution to the equilibrium suspended sediment profile.

S= Ce o)(8)
U= Ce E (8)

6
The concentration Co, the suspended sediment concentration at z = z0, is termed the

reference concentration. Obviously, a strategy for determining z0 must be developed in

order to examine the relation between measured flow conditions and the reference

concentration. Most commonly, z0 is chosen to be at the theoretical origin which is

chosen based on an equivalent roughness of the bed. This will be discussed in more detail

in a later chapter.

This reference concentration ultimately determines the total amount of sediment in

suspension, even if a more complicated method than the one described above is used to

determine the exact vertical distribution of sediment. Although equation 8 was derived for

steady flow, it has been shown to describe the vertical sediment profile reasonably well in

unsteady flow (Nielsen, 1986).

Objectives

A fairly comprehensive set of experiments were performed in a prototype scale wave

tank. In these experiments, measurements were made of instantaneous suspended

sediment profiles and of various flow parameters. These measurements were made with

the objective of increasing the understanding of sediment suspension and the role it plays

in sediment transport (Hanes et al., 1993). In the present text, the time averaged

suspended sediment profiles are determined from time average of the instantaneous

acoustic backscatter measurements. From these profiles, the nearbed concentration or

reference concentration will be determined, and the variation of the reference

concentration will be compared with the various measured flow parameters. Several

models predicting the reference concentration will be evaluated with the measured flow

7

parameters, and their predictions compared with the values obtained by measurement.

Finally, observations of instantaneous suspended sediment concentration profiles will be

examined to determine what insight can be gained towards the development of an

instantaneous model of the reference concentration.

CHAPTER 2
EXPERIMENT

Site Description

In August of 1991, researchers gathered at Oregon State University's wave research

facility to participate in the Supertank data collection project. Experiments were

conducted in a prototype scale, sand bed, wave flume under a variety of wave conditions.

The information in the present text was collected during the first two weeks of the project

(Hanes et al., 1993). During these weeks of the Supertank project, wave conditions were

chosen to simulate accretionary and erosive conditions typically found in the coastal

United States.

Sediment concentration profile data and hydodynamic data were collected offshore

of breaking waves in approximately three meters of water. Figure 2.1 shows the tank and

the location in the tank where the measurements described in the present text were taken.

The instruments used for measurement were mounted to the wall of the tank to prevent

scour of the bed and extended approximately sixty centimeters toward the center of the

tank in order to avoid measurement of side wall effects.

Equipment and measurement capabilities

For use in these experiments, instrumentation was chosen which would provide

information on everything affecting the sediment motion. Instrumentation consisted of

University of Florida
Station 18 \

18'-0"1 I- 40'-0"
Wave Transition
Generator Section
End

SECTION ELEVATION

A-Section B-Section

Figure 2.1 Location in tank where experiment was performed.

30'-0"

10

a pore pressure sensor, two optical back-scatterance sensors (OBS), an electromagnetic

current meter (EM), a pressure sensor, an acoustic concentration profiler (ACP), and an

underwater video camera. The OBS's, pressure sensors and EM were in fixed positions

Station 18
XXX Week I XXX Top of tank

Still water level- varied from 5 7 ft. below top of tank r .." M
c) U rO

m c, *- (N r-

7 3/8 ns

Pressure Sensor

8th boli hole

Data logger package

Mesotech

llth bolt hole : - Bg

A. 2 ft, 3 1/8 ins, ______
B. 2 ft, 3 1/4 ins, C Current meter
C, 2 ft. 2 1/8 Ins,
D,. 2 ft. 3 1/2 Ins.
E. 2 ft. 3 ins, Low O.B.S.
Sand bed

E.

ltth bolt hole Pore pressure sensor

14th bolt hole

Figure 2.2 Side view of instrumentation within tank.

11

and alligned vertically as shown in figure 2.2. At the end of each wave run, the

underwater video camera was lowered into the water and used to view the bedform

geometry in the vicinity of the other instrumentation.

Of the equipment described here, the analysis in the present text will focus on the

measurements from the pressure sensor and the ACP. Concentration measurements from

the OBS's are used only for comparison with those found from the ACP, and flow

measurements from the EM are used to determine the significance of the mean flow and to

verify those quantities calculated from pressure measurements. Video measurements are

used when available to evaluate ripple dimensions, but are available for only about one

quarter of the experiment and as will be detailed later, yield questionable results. For

completeness in describing the actual experiment though, each of the instruments used is

briefly described below.

For determining the wave conditions at the location of the instruments, a Trans

Metrics P21 pressure transducer was used. This pressure sensor was mounted in the off-

shore end of a PVC cylinder which housed much of the data acquisition equipment.

Pressure is determined with strain gauges attached to the diaphragm of the sensor. During

the first week of experimentation, the vertical alignment of this sensor was approximately

thirty centimeters offshore of the remaining instrumentation, but a new mount was built

before the second week which allowed all of the instruments to be vertically aligned.

An additional pressure sensor, the Druck PDCR 81 miniature pore water pressure

transducer, was mounted below the bed. Since it is placed below the bed, a pore pressure

sensor is equipped with a porous filter plate which allows measurement of the fluid

12

pressure while effectively preventing measurement of the pressure from the weight of the

bed.

Flow velocity was measured using the Marsh-McBirney OEM521 current meter

(EM). A magnetic field is generated by the transducer, and as water moves through the

magnetic field, a voltage is produced which is related to the velocity of the water. Voltage

is measured by two pairs of electrodes exposed to the water which allows the velocity to

be resolved in two directions. The EM was mounted above the wave boundary layer and

oriented such that the cross-shore and vertical velocity components were measured.

Measurements from the EM were only available during the first week due to a malfunction

of the instrument during the second week.

Two D & A Instrument Company's OBS-I's were used to determine suspended

sediment concentration at specific locations above the bed. The OBS sensor works by

emitting infrared light and determine the intensity of the backscattered light. The

measured intensity is linearly proportional to the sediment concentration in the vicinity of

the sensor. For comparison with the acoustic concentration profiler (ACP) the OBS's

were mounted just outside of the path of the acoustic beam. Data was not available for

the lower of the OBS's for the second half of the first week due to an intrusion of the

mounting aparatus in the infrared beam.

Sediment profiles were obtained with the Simrad Mesotech Model 810 ACP. The

ACP generates a short pulse of five megahertz sound and then determines the intensity of

the backscattered sound. The time delay between transmission and reception of the pulse

is proportional to the distance from the sensor to the region from which the sound was

13

Pulse width (tp)

j Cutoff Intensity
iSound wave envelope

\J [ v Time axis

Transmitted pulse
Returning portion of sound energy
which will be sampled

/ Ensonilied volume

Time 1=1(0) Time t=t(o)+t(p)/2

Figure 2.3 Description of acoustic pulse and ensonified volume.

backscattered. This region from which the sound was backscattered is termed the

ensonified volume. Close examination of this process in figure 2.3 shows this region to be

half of the length of the pulse. In order to determine the suspended sediment

concentration at a distance x from the transducer, the intensity of the backscattered sound

from the ensonified volume centered at x is measured instantaneously. This intensity is

related to the concentration in the ensonified volume. Backscattered sound from the bed

is of such intensity that the acquisition system becomes saturated if any portion of the

ensonified volume crosses the bed surface. Since the concentration measurement is

actually representative of the concentration from one quarter of the pulse width above x to

one quarter of the pulse width below x, the closest accurate measurement to the bed is

when x is located one quarter of the pulse width from the bed.

'S- Reference Grid

Figure 2.4 Underwater video system and reference grid.

Finally, a Sony Hi-8 CCD V99 video camera was placed in an underwater housing

and used to examine bed forms in the vicinity of the other instrumentation after several

runs. As a horizontal and vertical reference, a grid was mounted on the wall next to the

instrument array as shown in figure 2.4. Cables from the camera to outside of the tank

allowed the video signal to be recorded on a VCR and allowed on-shore control of the

camera features through an interface also packaged in the underwater housing.

Caincra (_'.:,nLjv1 _' Sign!
cable

15

Table 2.1 Maximum resolution of measured quantities with Supertank acquisition system.

Instrument Best resolution
Pressure transducer 0.83 cm of water
Pore pressure transducer 0.75 mm of water
Upper OBS sensor 9.5 mg/1
Lower OBS sensor 5.2 mg/1
EM current meter 1.86 mm/s

Data Acquisition

Due to the large quantity of data generated by the ACP, two separate, but

synchronized, systems were used for data acquisition. Information was acquired from the

slow instruments, all but the ACP, by an Onset Tattletale 6 housed in an underwater

package. This underwater package was designed for field use and houses the Tattletale,

interfaces for each of the instruments, and batteries to power everything. Data is acquired

on the Tattletale through an eight channel, twelve bit, analog to digital converter, giving a

digital range from zero to 4095 for each instrument. The Tattletale was programmed to

acquire data at four hertz per channel. This allows each of the sensors to resolve a change

in the measured quantity as small as the values listed in table 2.1. Note that the pore

pressure sensor is capable of detecting changes in pressure with better than twelve bit

resolution. This is due to an interface with seven software selectable ranges, each range

having twelve bit resolution.

Data is acquired from the ACP by a PC-based Data Translation DT2831G data

acquisition card. The AM signal from the ACP is demodulated and then sampled at 250

kilohertz. One profile of returned acoustic intensity from the ACP consists of 512

samples, or bins, collected at this rate. At this rate, measurements are spaced three

16

millimeters from one another vertically, but as mentioned previously, this is a measurement

of the returned acoustic intensity from a region with a vertical length equal to half of the

pulse width of the ACP. During each one second, 100 profiles are collected from the

ACP, and each 25 consecutive profiles are averaged to reduce the statistical fluctuations in

the profile. Adjacent bins in the upper portion of each profile are then averaged to reduce

the quantity of data to be saved. This averaging process is shown in figure 2.5. Finally,

four profiles of returned acoustic intensity from the ACP averaged both in time and space

are stored each second. The two acquisition systems were connected to insure

synchronization of the four hertz sampling rates from each. Instrument calibration will be

described in chapter 4.

Data Description

As mentioned previously, the wave conditions generated in the wave tank during the

two weeks of experimentation were chosen to simulate erosive and accretive conditions.

Table 2.2 shows the wave conditions during the two weeks with the corresponding run

numbers and data collection lengths. The beach was composed of uniform-size quartz

sand with a median diameter of 0.22 millimeters.

Figures 2.6 through 2.9 show the calibrated signals from the pressure sensor, pore

pressure sensor, U channel of the EM, and the OBS sensor located 56 centimeters from

the bed respectively. The data shown in the figures is from approximately two minutes

into run number 12 and is typical of all of the data runs in that it was collected at four

hertz. In the plot from the pore pressure sensor, figure 2.7, the data actually encompasses

512 points sampled at 250 kHz = 1 profile --"

4 8 12 16 20 24 28 microseconds

Spacial averaging

25 profiles sampled at 100 Hz

10 20 30 40 50 60 70 milliseconds

25 profiles time-averaged at 4 Hz

0.25 0.50 0.75 1.00 1.25 1.50 1.75 seconds

25 Spacially-averaged profiles

Final profile averaged
in time and space.
1 every 0.25 seconds

Figure 2.5 Averaging process on ACP data during collection.

0

SCD"

Spacially-averaged
profile

Table 2.2 Wave conditions during experiment.
Wave period (s) Hm0 Band width* Run time Run number
(m) (minutes)
3.0 0.2 MON 20 54
BBR 20 53
0.4 MON 20 56
BBR 20 55
0.6 MON 20 58
BBR 20 57
0.7 BBR 20 38
0.8 MON 20 14-17,60
NBR 90 1-7,59
BBR 80 10-13,18-20
0.9 BBR 40 39,40
1.52 MON 10 43
4.5 0.15 MON 10 27
0.8 MON 40 33,34
NBR 155 21-26
BBR 135 28-32
0.9 BBR 55 41
5.0 0.7 BBR 60 36,37,42
6.0 0.4 MON 20 80
BBR 20 76
0.8 BBR 20 35
7.0 0.4 MON 20 80
BBR 20 76
0.5 MON 20 81
BBR 20 77
8.0 0.2 MON 40 45,46
BBR 20 78
0.4 MON 55 49
BBR 175 47,48,61-65
0.5 BBR 95 66-68
0.6 MON 20 51
BBR 55 50
0.8 BBR 20 52
9.0 0.4 NBR 135 69-73
0.5 NBR 75 74,75
10.0 0.4 MON 55 83
BBR 20 79
Note: (*) BBR = Broad band random, NBR = Narrow band random,
MON = Monochromatic

19

0.9

0.8

0.7

0.

0.5

0.4

0.3
0 5 10 15
Elapsed seconds

Figure 2.6 Calibrated pressure signal.

2.55

2.5 -

2.45

2.4 -

2.35 -

2.3 -

2.25
0 5 10 15
Elapsed seconds

Figure 2.7 Calibrated pore pressure sensor.

i 0.4

0.3 -

a 0.2 -
E

o
S 0-

S -0.1

-0.2

-0.3
0 5 10 15
Elapsed seconds

Figure 2.8 Calibrated u velocity from EM current meter.

20

1.7

S1.6 -

1 .5

S 1.4 -

1 .3

1.2

1 .1
0 5 10 15 20 25
Elapsed seconds

Figure 2.9 Calibrated OBS sensor.

a couple of the possible ranges. The calibration routine, described later, produces a single

high resolution time series after calibrating the raw data in each range independently.

Examination of the OBS plot, figure 2.9, shows intermittent suspension events above a

21

background concentration due to the presence of a background turbidity. The effect of

background turbidity is taken into consideration in the calibration procedure described in

chapter 4.

From the uncalibrated time series of profiles from the ACP shown in figure 2.10,

individual suspension events can be seen close to bed with not a lot of activity present

further from the bed. This is typical of most of the wave runs, even under more severe

conditions. So that the suspension events can be seen, the acoustic return from the bed

0.5 -
0.5

-0.5-

0 5 10 1 5 20 25
Horizontal distance inches
Figure 2.11 Ripple pattern from video picture.

itself is not shown on the plot. Since the location of the sensor is fixed, the location of this

return in the uncalibrated profile is related to the instantaneous local height of the bed.

Finally, a typical diagram of the bedform geometry obtained from the video footage

of the reference grid is shown in figure 2.11. Clearly, the pattern is not very regular.

Direct observation of the bed from above gave no indication of this irregularity, but the

pattern did extend to both walls of the tank. All of the data presented here will be

examined in much more detail in later chapters.

CHAPTER 3
THE CONCENTRATION PROFILE AND GOVERNING PARAMETERS

The Influence of Shear Stress on Sediment Entrainment

The first step in determining the amount of sediment in the flow is examination of

the process of sediment entrainment. When there is water flow, whether the flow is

steady, oscillatory, or a combination of the two, a shear stress acts on the bed. When the

shear stress acting on the bed becomes great enough, the stabilizing forces of the

individual grains in the bed are no longer great enough to prevent their motion. Shield's

developed a non-dimensional measure of the tractive force or shear stress at the bed,

otherwise known as the Shield's parameter.

0 T(o) (3.1)
p(s 1)gd

0 is the Shield's parameter and is the ratio of the disturbing force, the shear stress, to the

stabilizing force, gravity, acting on grains in the bed (Shields, 1936). t(0) is the

instantaneous shear stress at the bed, p is the water density, s is the relative sediment

density, g is the acceleration due to gravity, and d is the sediment diameter. The critical

Shield's parameter is defined as the Shield's parameter at which incipient motion of the

grains in the bed occurs. It seems only natural to extend this theory by assuming after

incipient motion has been reached, any excess shear stress will tend to bring additional

grains into motion. If this assumption is made, accurate determination of the magnitude

23

of the shear stress is necessary to quantify the amount of sediment entrained by the flow at

the bed.

In laminar flow, the shear stress is related to the velocity distribution in the boundary

layer by Newton's formula.

S= pv (3.2)
az

As the flow becomes turbulent and apparent stresses due to turbulent velocity fluctuations

become increasingly more significant, this same formula is commonly used with the eddy

viscosity, E replacing the kinematic viscosity, v. This eddy viscosity relates the intensity

of the turbulent fluctuations to the mean flow velocity. In steady flow, this relation is well

studied, and fairly accurate predictions of the steady stress on the bed can be made. In the

presence of waves, flow in the boundary layer becomes substantially more complex.

When both a steady current and oscillatory flow occur together and additionally, bottom

roughness elements are present, description of the flow in the boundary layer and thus

determination of the shear stress at the bed becomes increasingly more difficult.

Because of the difficulty in describing the flow near the bed theoretically for

oscillatory flow except in the simplest cases, empirically determined friction coefficients

are often used to determine the shear stress at the bed. The maximum shear stress can be

evaluated using Jonsson's formula for shear stress in terms of the wave friction factor, f,

(Jonsson, 1966).

S= pf,(Ao)2 (3.3)

24

In this formula, i is the maximum shear stress occurring over a wave period, A is the

semiexcursion amplitude and co is the angular frequency of the waves. Jonsson showed

fw to be a function of Reynold's number, A20/v, and of the relative roughness, r/A,

where r is the equivalent roughness of the bed.

On the coast, wave periods and heights are usually sufficient to keep the flow in the

turbulent regime. In addition, the bed is commonly rough, enabling the use of Swart's

formula for determine the wave friction factor.
[ ( 0.194
=exp 5.213( ,- 94 -5.977 (3.4)
AI

Swart's formula was developed for evaluation of the wave friction factor in the rough

turbulent regime. The rough turbulent flow regime is bounded by a criterion developed by

Kamphuis (Nielsen, 1992).

f200 r/A 0.01
/2A r/v> 70 r/A -- 0

So long as the criterion is met, Swart's formula provides a reasonable prediction of the

shear stress at the bed.

In relating the shear stress to the near bed concentration, it is important to look

closer at the contributions to the shear stress. In the presence of bed forms, the shear

stress results from the pressure difference between the upstream and downstream sides of

the bedforms and from the skin friction with the individual grains of the bed. Engelund

and Hansen studied the contributions and determined the skin friction to be the dominant

mechanism for inducing sediment motion (Engelund & Hansen, 1972). To isolate the

25

effect of the skin friction in the calculation of the bed shear stress, they suggested using a

value of the equivalent roughness based on the grain size.

r = 2.5d5o (3.6)

Using this value of the roughness based on the median grain diameter, dso, in determining

the Shield's parameter yields the grain roughness Shield's parameter, 02.5.

0 2.5 = 2.5 (3.7)
5 p(s )gd

Commonly, 2.5 is evaluated using Swart's formula to determine the friction factor. There

is some concern in doing so because of the low value of the equivalent roughness

parameter r. At such a low value, the flow at the bed may not be in the rough turbulent

regime. Because the effective shear stress derived with Swart's formula is commonly

used, it will be used in the present text, but a somewhat more theoretical effective shear

stress will be used to form a comparison.

Sleath produced a theoretical boundary layer model for combined wave current

flows (Sleath, 1991). In this model, the turbulent structures of the steady flow and

oscillatory flow are evaluated separately. The turbulent structure of the steady flow is

determined using a conventional mixing length argument where the turbulent velocity

fluctuations are due to random turbulent mixing. However, the turbulent structure of the

oscillatory flow is analyzed in analogy with grid generated turbulence where the turbulent

velocity fluctuations are strongly influenced by vortex shedding from the bed. When the

wave motion is much stronger than the mean current such that the time-mean current is

negligible, an expression for the wave friction factor can be obtained from the model.

26

f = (a2 + b2 + 2ab sin )1/2

a=0.10 Ub (A- (3.8)
Uo. r

b 0.60(A-1
r

In the rough turbulent regime, Sleath suggests using }b = 0.48U0 and ( = 22.5 where Uo

is the amplitude of the free stream velocity, Ub is the amplitude of the velocity defect at

the bed and 0 is the phase difference between the velocity at the bed and the free stream

velocity. Since this friction factor utilizes Engelund & Hansen's equivalent roughness of

r = 2.5d50, it provides only the effective shear stress on the bed, and if the total shear

stress is desired, the stress from form drag on roughness elements and from other means

must be evaluated separately. This calculation of total shear stress can be done the with

the same formulae, but a different equivalent roughness is used.

It should be noted that in both of the methods of shear stress determination

mentioned above, the calculations results in only a single, time-independent value of shear

stress. This value is the peak value of the shear stress over an entire wave period, and also

an average shear stress over a sufficient horizontal distance of the bed since the shear

stress can vary substantially from point to point on the bed, particular in the presence of

bedforms. The use of spatial averaging and of a single time independent value will also be

applied in the analysis of the near bed concentration and of the concentration profile,

because these too are subject to large instantaneous variations and differ from point to

point on real seabeds. Once again, this is true particularly in the presence of bedforms.

27

While this study is concerned only with quantities horizontally averaged over several

bedforms, and Engelund & Hansen's results seem to suggest that bedforms do not

influence the entrainment of sediment from the bed, accurate knowledge of existing

bedforms is still important. In order to determine the location of the theoretical origin, the

equivalent roughness must be evaluated. When bedforms are present, the equivalent

roughness is of the same order as the height of the bedforms. In addition, evidence has

been presented showing the presence of an enhanced velocity at the ripple crest which may

therefore increase the stress at the bed. Finally, several investigators have shown

differences in the form of the suspended sediment profile over flat and rippled beds

(Nielsen, 1992, Lee, 1994)

Reference Concentration

Once the bottom shear stress has been determined from the wave characteristics, one

of several models can be applied to determine the resulting suspended sediment

concentration at the bed. A great deal of controversy has been introduced over whether

the boundary condition at the bed should be given as a concentration or an upward

sediment flux, otherwise known as a pick-up function. It is important to realize in terms

of an equilibrium, time-independent, suspended sediment, concentration profile, that given

a reference concentration, the corresponding pick-up function is easily found, and vise

versa (Nielsen, 1992). The issue becomes more of a concern in the time-dependent

situation, where the total amount of sediment in suspension at any instance can change

dramatically. An increased volume of sediment in suspension results in more sediment

falling out and a higher concentration of sediment near the bed, even though the shear

28

stress at the bed may be very small at that instant. In this case, it seems better justified to

relate the upward sediment flux at the bed to the shear stress as opposed to a near bed,

sediment concentration. But, again, for the case of a time-independent prediction of

sediment entrainment, either approach is well justified, and the choice of a reference

concentration is more readily compared with experimental measurement.

Several models for prediction of the reference concentration are presently in use,

ranging from simple, nearly purely empirical relations to slightly more complicated

empirical relations, and further to still more complicated, but more physically intuitive

models describing the sediment motion. In the simplest models, measurements from one

of more sediment suspension experiments, including various laboratory and field

techniques, are assembled. If the near bed concentration was not directly measured, then

some method of determining this concentration is applied. Finally, a best fit equation is

determined from comparing the known shear stress to these measured concentrations.

This is the process used in Nielsen's nondimensional model of reference concentration

(Nielsen, 1986). Bosman & Steetzel's dimensional model also used this method, but

extended it somewhat by including an adjustment parameter to improve agreement with

any particular sediment (Bosman and Steetzel, 1987). Smith and McLean also proposed

an empirical model, but further extended it to directly account for sand beds composed of

various sediment sizes and to limit the concentration in the case of high shear stress (Smith

and McLean, 1977). Finally, Engelund and Fredsoe took a more theoretical approach in

relating the dispersive stress from grains moving both in bed load and as suspended load to

the total shear stress (Engelund and Fredsoe, 1976).

29

In Nielsen's 1986 model, sediment suspension data from experiments performed by

several investigators is compiled. Suspended sediment concentration data from the

experiments is fit with an exponential profile, and the reference concentration is

determined by extrapolating the resulting equation to the theoretical origin, taken to be the

bed level at the ripple crest. This reference concentration is then fit with the effective

Shield's parameter. In the case of rippled beds, it is related to the effective Shield's

parameter determined from the enhanced velocity at the ripple crest.

C = 0.0050 R3 (3.9)

In equation 3.9, Co is the volumetric concentration at the bed, and therefore is unitless.

The modified effective Shield's parameter, OR, is related to the effective Shield's parameter

by equation 3.10.

R= --(1 0 (3.10)
(1-rn/X)2

In this equation, Ti is the ripple height and X is the ripple wavelength. The general form

of equation 3.9 is shown to be in agreement, at least in the power of the Shield's

parameter, with Madsen and Grant's model of the bed load flux (Madsen and Grant,

1976).

The model of Bosman & Steetzel was developed from data from their own

experiments performed in a wave tunnel. Again, suspended sediment concentration

profiles were measured and fit with an exponential relation, and the reference

concentration was determined by extrapolation to the theoretical origin, this time chosen

to be the mean bed level. Their experiments were performed with only a single median

30

grain size of 0.21 mm and strictly with purely oscillatory water motions. In this model, the

reference concentration is related to the semiorbital velocity and to the wave period, while

all other factors are included in an empirical coefficient, G.

C GU35 (3.11)
T2

Co has the units of kilograms of sediment per cubic meter of water-sediment mixture. It

is mentioned that G is expected to vary with sediment grain size, and for the 0.21 mm

sand used in the study is given as 3000 kg s55/m65.

Once again, in Smith and McLean's model, measured concentration profiles are fit

with an exponential curve and then extrapolated to the theoretical origin to determine the

reference concentration (Smith and McLean, 1977). The location of the theoretical origin,

z0, is chosen based on the roughness, given as a combination of the equivalent roughness

owing to the unevenness of the bed and an additional added roughness due to the presence

of sediment in the flow. This can be expressed as in equation 3.12.

Zo =ZN Tb T,
Tb -c Z (3.12)
zo= :.--+ZN T>b > c
(p, p)g

In this equation, z., owing only to the unevenness of the bed, is the location of the

theoretical origin based on Nikuradse's experiments (Nikuradse, 1933). Smith and

McLean's experiments showed the reference concentration at this location to be a linear

function of the excess shear stress. Furthermore, they realized that at very high values of

the shear stress, the concentration can not exceed the concentration of the bed itself,

leading them to the form of equation 3.13.

31

C, (zo)- ilYObSn (3.13)
1 +YoS,

S0 is the sediment resuspension coefficient, cb is the concentration of the bed, and i, is

the fraction of sediment in size class n. Also, S, is the normalized excess shear stress,

given by equation 3.14.

S,= b b- (3.14)

T,, is the critical shear stress for size class n The final reference concentration is

determined by summing the n concentrations found from equation 3.13.

Engelund and Fredsoe applied the theory of Luque to develop a model which allows

prediction of the bed load transport rate and the near bed concentration (Luque, 1974;

Engelund and Fredsoe, 1976; Fredsoe and Deigaard, 1992). In this theory, grains of sand

in bed load and suspended load exert a reaction force on the fluid, thereby reducing the

total effective shear stress. First, a portion of the total effective shear stress equal to the

critical shear stress is transferred directly to the immobile bed. Next, the number of grains

in bed load is determined, assuming at most, one layer of grains from the bed can be

eroded as bedload. This number is expressed as the the fraction of grains, p, in a single

layer of the bed that are in motion as bed load, as given in equation 3.15.

p= 1+ L- (3.15)

In this equation, gd is the tangent of the dynamic friction angle. The magnitude of the

stress from each grain in bedload is equal to the fluid drag force on that grain. Since the

32

number of grains in bed load and the force on each grain is known, the bedload transport

rate and reduction of the total shear stress from bed load can then be determined. Finally,

what is left of the total effective shear stress is balanced by the dispersive shear stress of

grains in suspension. Using Bagnold's relation, equation 3.16, which relates the dispersive

shear stress to the linear grain concentration stress in the inertial region, the linear

concentration of the suspended load can be determined (Bagnold, 1954).

TG = 0.013ps(d)2( (3.16)
dz

In this equation, X is the linear concentration of sediment, and is the velocity
dz

gradient in the fluid. The volumetric concentration is related to this linear concentration

by equation 3.17.

c= Cb (3.17)
(1+1/A)3

Cb is the maximum value for volumetric concentration, and is equal to 0.65. The final

expression takes into account the stress transferred directly to the immobile bed, the stress

transferred to grains as bed load, and finally, the dispersive stess from suspended sediment.

S0.0133.18)
= 0, +- pd -2SO 2b (3.18)
1C 2 (X

It is from this equation that the reference concentration is determined.

At this point, the parameters assumed to affect the concentration profile have been

presented. Four models relating these parameters to the near bed concentration have been

introduced. In the following chapter, the methods used to determined these parameters

from the measurements taken at the Supertank project will be described.

CHAPTER 4
DATA ANALYSIS

Just as real sand beds seldomly contain grains of only one size, in reality, waves are

of a multitude of frequencies and heights. Also, bedforms vary in size and shape, and

rarely does the sand bed stay at a fixed height in space. Simple representative quantities

are instead chosen to simplify description of physical processes. In addition, easily

measured quantities are not necessarily those of interest. In this chapter, the methods of

determining the appropriate representative measures of hydrodynamic conditions and of

other desired quantities are presented.

Calibration

In order to calibrate the various slow instruments, again, all but the ACP, the

quantity to be measured by the particular instrument is held constant and the digital value

is recorded on the data logger. This is repeated with several different constant values of

either pressure or concentration. Due to the complexity of the electronics in the EM, the

coefficients from the factory calibration are instead used. For calibration of the pressure

sensor, various pressures of compressed air are applied to the transducer face, and for the

pore pressure sensor, various hydrostatic water pressures are applied to the sensor while

maintaining constant back pressure. The OBS's are inserted into a recirculating calibration

chamber which maintains a constant concentration of sediment in the water. From the

34

recorded data the coefficients to the best fit line describing the desired quantity as a

function of the digital value are determined using a least squares approach. To insure the

use of the coefficients from the calibration will provide accurate results with experimental

data, the conditions during calibration are chosen to closely match the conditions in the

wave tank during experimentation. For example, pressures used in calibration are in the

same range as those occurring in the tank during experimentation, cables to the

instruments are those used in the experiment, and sediment concentrations are created

using the same sediment used during experimentation and again are in the same range as

those produced in the experiment. The resulting linear formulae can be used to determine

above-bed pressure, below-bed pressure, and single point concentrations from recorded

time series from the pressure sensor, pore pressure sensor, and OBS's respectively. The

calibration constants for the each of the instruments are shown in table 4.1.

One additional step is required in the calibration of the OBS sensors due to the

presence of very fine sediment and organic material which tend to cloud the water. This

turbidity is transparent to the ACP, but not to the OBS's. Before most of the wave runs,

several seconds of data were recorded before the wave creation began. The value from

the OBS's during this period is then used as a background concentration to be subtracted

from the calibrated value of the concentration, the idea being that this background

concentration results not from the wave conditions during the current run, but instead

results from previous runs. Such a linear addition of this background concentration may

not be entirely correct, but it is assumed that the background concentration is only a small

35

fraction of the sediment in suspension. So, the error incurred from the addition is even

smaller.

Ripple measurements were taken at the end of each run with the video camera as

described previously. Because of the difficulty in acquiring a good image through cloudy

Table 4.1 Calibration constants from various instrumentation.
Regression Number
Instrument Gain Offset Coefficient of
points
OBS at 9 cm 5.1570 mg/1 -1125.7 mg/1 0.9845 20
from the bed
OBS at 56 cm 9.4681 mg/1 -2308.9 mg/1 0.9923 20
from the bed
Pressure 0.0084 -11.0216 1.0000 6
m of H20O m of H20
Current (both 1.861 x 10-3 -3.81 m/sec. -
components) m/sec.
Pore Pressure- 3.6 x 10-3 -1.3350 0.9999 84
low gain ft of H20 ft of H20
Pore Pressure- 7.302 x 10-4 -1.3232 0.9995 12
range 1 ft of H20 ft of H20
Pore Pressure- 7.133 x 10-4 0.9117 1.0000 23
range 2 ft of H20 ft of H20
Pore Pressure- 7.196 x 10-4 3.0889 1.0000 21
range 3 ft of H20 ft of H20
Pore Pressure- 7.564 x 10-4 5.2803 1.0000 17
range 4 ft of H2O ft of H20
Pore Pressure- 7.874 x 10-4 7.5625 0.9999 10
range 5 ft ofH2O ft of H20

water, the nonuniformity of the lighting, and the relatively few images to process, the

ripple pattern was taken from the video footage by direct observation instead of by more

complex image processing techniques. On the average, the location of the bed could be

determined within one sixth of an inch using the wall mounted reference grid.

Measurements from the video are used only as an estimate of the bed roughness and the

Flexible
hosing

Sediment-water
Flow direction mixture

"- r^ Funnel
Pump

Figure 4.1 ACP recirculating calibration chamber.

dimensions of the vortex ripples. The bed was not flattened between runs and it is unlikely

the wave runs were long enough to allow the bed forms to reach equilibrium with the flow

conditions.

Calibration of the ACP is performed by placing it in a calibration chamber designed

to continuously recirculate a sediment and water mixture. This continuous recirculation

results in a constant concentration of sediment throughout the entire chamber. Figure 4.1

shows this calibration chamber. After a sound pulse leaves the transducer, the intensity or

power of the reflected sound returning to the transducer depends on the initial intensity of

the pulse, losses in energy due to spherical spreading and attenuation from water and

sediment, and on the concentration of sediment from which the sound can be reflected.

To relate the returned intensity to just the sediment concentration, the effects of spherical

37

spreading and attenuation are accounted for, and the resulting expression, equation 4.1, is

proportional to the sediment concentration.

Ac(z) = V(R exp(J (k + kc(z'))dz') (4.1)

In this equation, A is a system constant that takes into account such factors as initial

sound intensity and the proportionality between intensity and the measured output voltage

of the ACP, V(z). k, and k2 account for water and sediment attenuation, respectively,

and R is the range over which spherical spreading occurs. Since the concentration in the

calibration chamber is constant, this expression simplifies. By measuring the output of the

transducer with several different constant concentrations, the constants A, k, and k2 can

be determined. Since the strength of reflected sound of a fixed frequency varies with the

size, shape, and other characteristics of the sediment, the ACP is calibrated using sediment

from the region in which the ACP is deployed.

After the constants A, k, and k2 have been determined, equation 4.1 can then be

used to determine concentration from the profiles of measured output voltage from the

ACP. Because of the implicit form of the equation, often it is solved using an iterative

technique. Lee and Hanes produced an explicit solution to this equation which provides

the same result with much improved computational time (Lee and Hanes, in press). Since

in the present text, the focus is on the time averaged sediment concentration profile, the

calibration is performed on a single mean profile of returned ACP voltages. Ideally, the

calibration would be performed on each individual profile in the time series, and then the

mean concentration profile determined from the time series of calibrated concentration

profiles. Since instantaneous voltage profiles tend to contain a great deal more variation,

38

or in other words, are noisier than the time averaged voltage profile, a simple calibration

routine is not always well behaved when applied to instantaneous profiles. Because of the

added complexity and computational time necessary to calibrate instantaneous profiles,

and since the resulting final mean concentration profile is not significantly different in the

simpler approach, this more involved calibration procedure is not applied in this study.

Analysis

Once the measured data is in the form of bedform profiles and calibrated time series,

it can be parameterized in terms of such simple quantities as a representative ripple height

and wavelength, water depth, a representative wave height and period, and further to a

semiorbital amplitude and velocity at the bed. With the assumption of an exponential

concentration profile and an appropriate choice of the theoretical origin, the measured

profile can be expressed in terms of a slope and reference concentration. With this

information in hand, the measured reference concentration is easily compared to that

predicted by each of the models.

The representative wave height and period can be determined by applying linear

wave solutions to either data from the pressure sensor or from the current meter. Due to

the previously mentioned difficulty in the second week of experiments with the current

meter, these quantities are determined from the pressure sensor. The current data is used

only to determine the mean current in each of the first week's data runs. Analysis of these

mean currents shows the mean currents to be small relative to the semiorbital velocity in

each case. Because of this, it is expected that the additional shear stress at the bed due to

currents is small and can be neglected.

39

Because of water depth variations of over half a meter during the course of the

experiments, water depth too is determined for each individual data run. It is determined

by adding the height of the pressure sensor from the bed to the depth of the pressure

sensor, determined by equation 4.2.

hp= p(t) (4.2)
pg

In this equation, hp is the depth of the pressure sensor, and p(t) is the mean value of the

pressure time series.

By use of the fast fourier transform, the pressure time series is readily converted to

the frequency domain, where the pressure power spectrum can then be resolved by

multiplying the complex components at each frequency by their complex conjugates.

Because of pressure attenuation with depth, the pressure power spectrum must be

corrected with the pressure correction factor from linear wave theory in order to

determine the corresponding surface elevation power spectrum (Dean and Dalrymple,

1984).

Kpz) = coshk(h + z) (43)
cosh kh

KP (z) is the pressure correction factor. It is evaluated for each discrete frequency of the

spectrum, then multiplied by that component of the spectrum. The peak frequency of the

resulting surface elevation spectrum, an example of which is shown in figure 4.2, is then

used as the representative frequency for the data run. For monochromatic waves, the

representative frequency is determined instead by calculating the time between wave peaks

in the original pressure time series.

40

After the surface elevation spectrum has been determined, the representative wave

height Hm0 is related to the area under the spectrum. The models examined in this study

are most commonly evaluated with the significant wave height, H11/3. As mentioned in

chapter 2, monochromatic, narrow band and broad band spectra were generated during

the course of the experiments. Since the relation between H,,0 and H1/3 is simple only in

the case of narrow band spectra, the significant wave height is determined directly from

the original time series. This is done by performing a peak to trough analysis on the

Surface elevation power spectrum
100

10-2
10- 1

-o

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Frequency (hz)

Figure 4.2 Surface elevation spectrum.

original pressure time series and then generating a histogram of pressure heights, like that

shown in figure 4.3. From this histogram, the mean height of the highest one third of the

waves gives a pressure height which is then corrected using the representative frequency

from the spectrum and equation 4.3. This resulting significant wave height is then used as

the representative wave height.

o15

0
Z 10

5

0 0.2 0.4 0.6 0.8 1
Wave height meters
Figure 4.3 Wave height histogram.

Since the relative roughness, r / A, and the shear stress depend on the semiorbital

amplitude and velocity at the bed, linear wave theory is again used to determine the

horizontal particle excursion length and velocity given the previously calculated significant

wave height and representative wave frequency (Dean and Dalrymple, 1984).

A H gk 1 (4.4)
2 (o2 cosh(kh)

At this point, all of the variables necessary to calculate the peak effective shear stress by

either Swart's formula or Sleath's boundary layer model, described in chapter 3, have been

found.

As described in chapter 2, the closest reliable measurement of concentration near

the bed is a distance one quarter the pulse width from the bed. Considering the desired

reference concentration is at bed level, it becomes important to know the actual bed level

at each instance with as much accuracy as possible. Also, if the bed level rises during the

42

course of an experiment, it is important to realize the highest location to which the bed

moved so the closest concentration measurements are chosen a sufficient distance from

the bed to prevent contamination of the acoustic signal from the bottom return. The time

series of bottom location can be constructed by examining the original uncalibrated

instantaneous profiles of voltage from the ACP. Because of strong reflection from the

bottom, the returned acoustic pulse is of sufficient strength to saturate the amplifier in the

acoustic receiver, usually making the choice of bottom location in the profile rather

obvious. At times though, very high concentrations of sediment in the acoustic beam also

reflect sufficient acoustic energy to saturate the amplifier, occasionally even blocking

enough of the energy to prevent the bottom return from being clearly seen in the profile.

At these points in time, a false bottom return contaminates the time series of bottom

locations. To remove these spurious returns, a histogram of bottom location, as in figure

4.4, is constructed. Then, the highest five percent of the bottom returns are removed from

the time series. This histogram of bottom return locations is convenient for determination

of the highest bed excursion location and for determination of the mode of bottom

locations. On occasion, the bottom moves completely out of range of the ACP during the

couse of a run for small periods of time. Since in these cases the mean bottom location

from the time series would not truly represent the mean bed location, the mode is a

convenient substitute that is probably not a bad estimate of the mean bottom location.

Due to the irregularity of the ripple profiles obtained from the video images of the bed, the

choice of a representative ripple height and wavelength is not obvious. For this reason,

700

600

g 500 -

g 400 -
0
0
300
E
Z 200

100-

o0- --- r l
180 190 200 210 220
Bin number of maximum
Figure 4.4 Bottom return histogram.

the same sort of peak to trough analysis applied to the pressure time series for significant

wave height determination is applied to the horizontal ripple profile. Basically, each crest

and trough in the profile is identified, and the representative height, T is found from the

mean of the individual ripple heights. Similarly, the representative wavelength, X, is the

mean of the individual ripple wavelengths (Jette, 1994).

Examination of the measured profiles shows that at least very close to the bed, the

concentration profile is described well by an exponential curve with a constant mass

diffusivity, -,. This is in good agreement Sleath's observations of the eddy viscosity in

wave dominated flow very close to the bed (Sleath, 1991). Each of the measured profiles,

such as the one shown in figure 4.5 is fit with an exponential curve from a distance of one

quarter of an acoustic pulse width from the highest bottom return to a distance often

centimeters above the mean bed location. Extrapolation of the resulting curve to the mean

bed location yields the reference concentration.

44

At this point, all necessary quantities for application of the shear stress formulae

and for calculation of the near bed concentration from each of the models have been

determined. In summary, the water depth, representative period and wave height and

semiorbital amplitude and velocity are determined from the pressure data. Analysis of the

video images before and after the runs provides an estimation of ripple height and

wavelength. The uncalibrated time series of ACP profiles provides the location of the

80

E 60
E
E

U1)
2 40 -

20

02 03 4
10 10 10
Concentration mg/i
Figure 4.5 Measured concentrations and best fit exponential curve.

theoretical origin and the highest bed location, as well as an indication of the bed

roughness. After calibration, the resulting time averaged concentration profile from the

ACP yields an exponential curve from which the reference concentration can be

determined. In the following chapter, each of the models of reference concentration

prediction described in chapter 3 will evaluated from these quantities and compared with

the reference concentration determined from experimentation.

CHAPTER 5
EVALUATION, CONCLUSIONS, AND RECOMMENDATIONS

Before attempting to evaluate any of the reference concentration models presented

in chapter 3, the reference concentrations determined from the experiments are

investigated. Estimated bed shear stress values determined from Swart's formula and

Sleath's boundary layer model are compared, and general trends in the data in relation to

the stress are examined. Also, additional dependence on such other measured properties

as the location of the theoretical origin and wave spectral width are observed. Based on

these observations, improvements to the measurement techniques and limitations of the

present data set are discussed.

Trends in Measured Data

Most commonly, Swart's formula, presented in chapter 3, is used for estimation of

the peak bed shear stress in oscillatory flow. As seen in figure 5.1, Sleath's boundary layer

model, when time averaged and simplified to the case of purely oscillatory flow, provides

a slightly smaller, but very similar estimate of the peak bed shear stress. Because of the

agreement of each of these estimates with empirically determined shear stresses, and

further due to the agreement between the estimates, either model provides a good estimate

of the peak shear stress at the bed. For this reason, the remaining analysis is performed

5
4.5
4

1 3.5

0
0.5

0 1 2 3 4 5
Sleath's shear stress
Figure 5.1 Comparison of Swart's and Sleath's shear stress estimates.

using Swart's formula only keeping in mind that this may result in a slightly large

estimate of the bed shear stress.

One additional comment concerning the calculation of the shear stress needs

mentioning. As mentioned in chapter 4, the representative wave height is chosen to be the

significant wave height, H,13, calculated directly from the pressure time series, as opposed

to the more readily obtained value, H,,0, determined from the area under the surface

elevation spectrum. Because in a broad band spectrum of waves, the energy is spread

over a wide range of frequencies, the wave height at any particular frequency need not be

very large. Determination of the wave height from the total energy, related to the area

under the surface elevation spectrum, thus results in a value much larger than the

significant wave height determined by the true mean of the highest one third of the waves.

The differences between H,,0 and H11/3 with the width of the surface elevation spectrum

1.8- x Broad band
+ Monochromatic
1.6-

1.4-

1.2 +

i 1 /

0.8-

0.6
+ x
x
0.4 x

0.2-

0
0 0.5 1 1.5 2
Hm0 (m)

Figure 5.2 Comparison of Hmo and H1/3.

can be seen in figure 5.2. Consequently, use ofHmo results in an estimated value of the

peak bed shear stress much larger than what likely is present at the bed.

In these experiments, the theoretical origin is chosen to be at the mean bed level.

The actual determination of the bed level at any instant is accurate within plus or minus

1.5 millimeters. This uncertainty in bed position is due to the 250 kHz sampling rate of

the ACP. Ideally, enough bed forms will migrate under the ACP during the course of a

run such that the mean concentration profile determined from the ACP is representative of

the horizontally averaged concentration profile. Evidence of this migration can be seen by

examination of the bottom return time series shown in figure 5.3, which shows definate

48
movement around the mean bed level over the course of a run. In this figure, the false

bottom returns caused by high suspension events can be seen as downward spikes. If this

ripple migration actually occurs, one would expect the variation in the bottom return time

series to be of the same order of magnitude as the variation in a horizontal profile of bed

forms. After subtracting the corresponding mean values from the bottom return time

series and the horizontal profile of bed forms, the rms values of the two are compared in

figure 5.4. The agreement between the two is not very good, but is at least of the same

order of magnitude in most cases. This disagreement can be explained somewhat by the

irregularity of the bed forms in the horizontal direction, by the tendency for the bottom

282
E
0
0
.0
z80
E
S78

0 100 200 300
Elapsed seconds

Figure 5.3 ACP bottom return time series

i111111111iii, ii

49

return to represent a spatial average due to the width of the acoustic beam at the bed, and

further from the migration of only a small portion of the bedforms under the ACP in the

length of the data collection. Consequently, the theoretical origin determined from the

mean of the bottom return time series may vary slightly from the true mean bed level. It is

not expected that the variation is too severe, but surely this contributes to some of the

scatter observed in the reference concentration measurements.

The reference concentration, determined by extrapolating the best fit curve to the

concentration profile to the theoretical origin, and the grain roughness Shield's parameter,

determined using Swart's estimate of bed shear stress, are shown together in figure 5.5 for

all of the data runs. Because of the previously mentioned uncertainty in bed position due

to the sampling rate of the ACP, this concentration also has an uncertainty of a maximum

of eight percent. This error is determined using the steepest concentration profile found in

the experiments with an uncertainty of 1.5 millimeters in bed position. In addition, the

1.8 -

1.6 -

E 1.2 -

0.8
c l06 K
0.4 M K
0.2 X *

I I I II
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
RMS ripple height from video (cm)

Figure 5.4 Bed form height as determined from ACP and video measurement.

10 +

*) +
Eo
C +

0

x- xo
100
a0 3
0 X X0
0) 00 X
2 xX

10 - 0
10 10 10 10
Effective Shield's parameter

Figure 5.5 Measured reference concentration vs. effective Shield's parameter.

best fit exponential curve is shown in the figure and is given by equation 5.1.

Co = (2.574 x 103)02.51202 (5.1)

In this equation, CO is the measured reference concentration in milligrams per liter.

Because the calibration of the ACP was performed using the dry mass of the sediment,

concentrations expressed in milligrams per liter also relate to the dry mass of the sediment.

Although the plot shows considerable scatter, a trend in the data is certainly apparent,

yielding a regression coefficient for the best fit exponential of 0.7918. To serve as a

comparison with the model evaluations, the relative error, A, in using this best fit curve

for prediction of the reference concentration, calculated using equation 5.2, is 1.9135.

A=exp J(ln(y) lnC2,))2 (5.2)

In this equation, n is the total number of measurements, and y, and 5, are the measured

and predicted values, respectively. Note that in equation 5.1, the power of the effective

Shield's parameter, 1.202, indicates a fit that is nearly linear. Although the spread in the

data is considerable, it does appear that the monochromatic waves tend to raise the

concentration at the bed slightly relative to the spectral waves. No significant changes in

concentration are obvious between the narrow band and broad band spectral types, though

more measurements performed while only varying spectral shape are needed to make an

effective comparison between spectral types.

Comparison of Measured Reference Concentration to Predictive Models

In the sediment conservation equation presented in chapter 2, the assumption was

made that the downward settling flux due to gravity was balanced by an upward flux due

to random vertical mixing. Schmidt's solution to this equation assumed a constant value

of the sediment diffusivity, resulting in an exponential solution to the equation. Since

Hunt showed the sediment diffusivity to be nearly equal to the eddy viscosity and Sleath

showed the eddy viscosity has no vertical dependence near the bed in oscillatory flow, one

would expect Schmidt's solution to describe the concentration profile fairly well near the

bed (Hunt, 1969; Sleath, 1991; Schmidt, 1925). Based on the high values of the

coefficient of determination found for the exponential fits to the concentration profiles in

these experiments, this is indeed the case. It should be noted though that very near the

bed, the upward sediment flux contains contributions other than vertical mixing. These

52

additional contributions, from bedload and saltation, can significantly increase the

concentration very near to the bed. Because the reference concentration determined in

this text and in three of the models presented extrapolates from the region in which

vertical mixing dominates to this region very near the bed, one might expect the

extrapolated value to underpredict the true concentration at the bed. Nonetheless, this

extrapolated value is quite useful and easily found, but extreme care must be taken to

insure this value is not confused with the true bed concentration.

Figure 5.6 shows Nielsen's prediction of reference concentration versus the

effective Shield's parameter. Also shown are the values of the concentration determined

0

o
(D 3
0 10
C
0
C-
0

cc

S -2 0
10 10 10
Effective Shield's parameter

Figure 5.6 Nielsen's model compared with measured concentrations.

53

from the experiments plotted against their corresponding effective Shield's parameters

modified to include the velocity enhancement at the ripple crest. For those runs which no

video footage of the bed is available, a constant ripple steepness, equal to the mean ripple

steepness from those runs with video measurements, was applied. Inspection of figure 5.6

shows that Nielsen's prediction of concentration seems to increase with the stress faster

than do the measured values. The relative error in this comparison is 5.0820. Use of the

mean ripple steepness when no ripple measurements are available may not present an

entirely fair evaluation of the model, so in figure 5.7, the same prediction curve is shown

with only those measured values in which ripple measurements were made. Also shown in

this figure is the best fit exponential to these points, given by equation 5.2.

CO = 2.6034 x 1030l16321 (5.2)

The relative error in comparing Nielsen's prediction to just the runs with ripple

measurements is 2.6121, whereas the relative error using the prediction from equation 5.2

instead is 1.9956. Although this is a significant improvement, Nielsen's prediction still

over estimates the concentration at high stress. Finally, in the present data set, the

measured values of the reference concentration are determined by extrapolating to the

mean bed level. In the original model, the origin was instead chosen to be the level of the

ripple crests. The irregularity of the ripple profile makes this choice of the origin very

difficult. In the most extreme case, using the steepest concentration profile and the

highest ripples, the choice of bed location is off by nine millimeters. This results in a

measured concentration at the mean bed level of 6.4 grams per liter as opposed to 4.5

grams per liter at the assumed ripple crest level. This certainly can introduce significant

103

(-
.2 )K

10
-2 /-

10 10 10 10
Effective Shield's parameter

Figure 5.7 Nielsen's prediction shown with runs with ripple measurements only.

scatter in the data. But, this example is the most extreme case, and the error introduced is

still relatively small on a logarithmic scale. Because extrapolation to a higher bed level

would lower the measured concentrations, the disagreement between the model's

predicted concentration and the measured concentration at high stress values may even

increase.

Smith and McLean's model is evaluated using a single size class of sediment

because of the nearly uniform sediment size used in the experiments. Previous

investigations have shown a great deal of variability in y0, the sediment resuspension

coefficient. Laboratory experiments by Hill et al. have suggested the value to be

10
C

10
I
10 10 1 10

Effective Shield's parameter
10 -2 1 0
10 10 10 10
Effective Shield's parameter

Figure 5.8 Smith & McLean's model versus measured results.

1.3 x 10-4, in good agreement with the value of 1.22 x 10-4 obtained by the best fit of

Smith & McLean's model to the present data set shown in figure 5.8 (Hill et al., 1988).

Assuming the best fit value of the resuspension coefficient applies, the model gives a

relative error of 2.5195 in predicting the measured reference concentration values. Again,

the choice of the theoretical origin in the original model was slightly different than the

mean bed level in the experiments. In the most extreme case in the experiments, the

change in bed location due to the high shear stress is less than a millimeter. Assuming the

steepest concentration profile, this introduces an error in measured concentration

determination of five percent, which is very small on a logarithmic scale. It is expected

10 10 10o
Effective Shield's parameter

Figure 5.9 Bosman and Steetzel's model vs. measured values.

that the model would agree better with the experimental data if this correction was made,

because it would reduce the measured concentrations at high stress values, making these

measured concentrations more linear with shear stress. Again though, because of the

difficulty in accurately determining the bed position and true roughness, the mean bed

level is used. Obviously, this error increases scatter in the measured data and again

reinforces the importance of accurate bed position and roughness measurements.

In figure 5.9, Bosman and Steetzel's predictions are shown for a range of periods

encompassing the wave periods generated in the experiments. The model does not

57

directly relate the reference concentration to the shear stress, but when put in such a form,

it shows an additional dependence on wave period. The measured results in figure 5.8 are

plotted with the wave period generated, and this additional wave period dependence is not

apparent in the measured values. In the prediction, the value of G used was determined

from the best fit to the measured data and was found to be 205 an order of magnitude

smaller than the value of 3000 in the original work for a slightly smaller grain size. This

could possibly be explained by Bosman and Steetzel's use of only monochromatic waves,

as previously it was seen that monochromatic waves seemed to yield higher measured

concentrations. In comparison with the measured results, the predicted values gave a

relative error of 3.4050.

Engelund and Fredsoe's predicted nearbed concentration curve is shown in figure

5.10 with the measured values. Of the models compared so far, this is the first to make an

attempt at describing the sediment concentration based on description of the processes

actually occurring at the bed, rather than simply curve fitting measured data.

Consequently, the concentration predicted is the true concentration at the bed, which is

likely to vary significantly from a value determined from extrapolation of measured

concentrations further from the bed. In comparison of the value predicted using the peak

shear stress with the measured values, the predictions give a relative error of 400. Since

the model actually predicts an instantaneous concentration base on an instantaneous shear

stress, it would be expected that an estimate of the average shear stress should provide a

better time average concentration at the bed. This instead shifts the curve shown in the

figure to the right and increases the relative error to 3560. This strong disagreement

0

10 -

10

Figure 5.10 Engelund and Fredsoe's model vs. measured values.

indicates either the value of concentration determined by extrapolation drastically

mispredicts the true value, or an assumption made in describing the processes at the bed is

resulting in a predicted value which is too large. Also, it is possible that the distribution

between suspended load and bed load in the model may be substantially different, resulting

in part of what is counted as suspended load to be or not to be accounted for in bedload.

To determine the predicted value, -d = tan(Od) was chosen to be 1.0. Of the suggested

values for this parameter, this is rather high, but the relative error becomes larger with

lower values. Because this model was developed to predict the nearbed concentration in

59

steady flow, it is quite possible that the reduction in the velocity gradient due to increased

mixing near the bed from waves is causing the overprediction. Sediment in suspension at

the bed results in a dispersive stress, and this dispersive stress is assumed to be related to

the velocity gradient in the model. Therefore, over-prediction of the velocity gradient will

result in a corresponding over-prediction of the near bed concentration.

Due to the difficulty in accurately determining the size ofbedforms during the

experiment, a portion of the error in comparing the resulting concentration from the model

to that found by experiment can result from a slightly misplaced theoretical origin in the

experiment. Furthermore, the bedforms may not migrate enough within the testing period

for the measured profile to be an accurate representation of the horizontal average. It is

expected the additional error introduced from these factors is relatively small, but indeed

this could contribute to the significant spread in the data.

Conclusions

Experiments performed at the Supertank data collection project in Fall of 1991

with an ACP provide measurements of the suspended sediment concentration profile

under a variety of wave conditions. Previous investigations have shown the nearbed

concentration to be related to the shear stress at the bed, so from pressure time series,

video footage of bedforms and ACP bottom return time series, the effective shear stress at

the mean bed level is determined by both Swart's formula and Sleath's boundary layer

model. Estimates of the peak shear stress from the two models vary only slightly, with

Swart's formula predicting a slightly higher shear stress. Extrapolation to the bed of best

fit exponential curves of the concentration profiles, determined from the time mean of the

Table 5.1 Experimental results summarized.

Run number 02.5 Det. coefficient CO (mg/1)
3 0.445 0.979 1040
4 0.432 0.961 910
5 0.466 0.983 1070
6 0.493 0.990 1470
7 0.481 0.972 1200
10 0.365 0.980 1280
11 0.373 0.990 1180
12 0.341 0.976 1300
13 0.367 0.992 1720
17 0.396 0.985 1650
18 0.397 0.980 1110
19 0.428 0.981 1970
20 0.420 0.973 969
21 0.558 0.963 555
22 0.511 0.967 557
23 0.519 0.934 536
24 0.566 0.984 679
25 0.565 0.987 798
26 0.559 0.937 306
27 0.0452 0.932 136
28 0.433 0.920 329
29 0.471 0.979 557
30 0.457 0.969 497
33 0.641 0.996 3117
36 0.220 0.951 303
37 0.198 0.995 509
38 0.261 0.993 730
39 0.393 0.983 1110
40 0.385 0.996 1130
41 0.520 0.972 539
42 0.362 0.978 456
43 1.13 0.964 10400
44 0.0527 0.122 80.2
45 0.107 0.334 77.8
46 0.114 0.236 80.6
47 0.167 0.447 126
48 0.156 0.855 162
49 0.251 0.990 1060
50 0.300 0.982 645
51 0.425 0.993 1020

Table 5.1--continued.

Run number 02.5 Det. coefficient CO (mg/1)
52 0.411 0.924 187
53 0.0485 0.823 83.0
54 0.0721 0.827 85.5
55 0.156 0.925 132
56 0.231 0.995 677
57 0.280 0.998 800
58 0.406 0.992 6400
59 0.418 0.991 1220
60 0.591 0.963 5650
61 0.151 0.977 248
63 0.170 0.991 233
64 0.176 0.990 250
65 0.122 0.995 240
66 0.228 0.979 510
67 0.211 0.986 618
68 0.238 0.985 400
69 0.111 0.974 222
70 0.0862 0.975 184
71 0.0682 0.980 184
73 0.146 0.997 201
74 0.112 0.996 412
75 0.117 0.981 249
76 0.176 0.985 209
77 0.224 0.985 221
78 0.164 0.992 231
79 0.125 0.962 147
81 0.412 0.984 856

ACP return profiles, gives the reference concentration. Table 5.1 shows the coefficient of

determination from the best fits to the concentration profiles, the effective Shield's

parameter from Swart's estimate of the bed shear stress, and the experimentally

determined value of the reference concentration for each of the runs used. Table 5.2

shows the relative errors from the comparisons of each of the model predictions of the

62

Table 5.2 Relative errors from various models.

Nielsen all runs 5.0820
Nielsen runs with ripple measurements 2.6121
Smith and McLean 2.5195
Bosman and Steetzel 3.4050
Engelund and Fredsoe 400.00

reference concentration to the values determined from analysis of acoustically measured

concentration profiles. Nielsen's, Bosman and Steetzel's, and Smith and McLean's models,

each developed from curve fits to reference concentrations determined by extrapolation of

concentration profile data to the bed, provide the closest predictions to the values

obtained in theses experiments. This result is not surprising since the same method of

determining the reference concentration is employed in this study. Because Engelund and

Fredsoe's model actually describes the processes occurring at the bed in order to predict

the near bed concentration, comparison of the predicted values to values obtained from

extrapolating measurements made a significant distance from the bed may not be justified,

and therefore could explain the high relative error.

Of the three models which agree best with the measured data, Smith and McLean's

model has the lowest relative error. The linear variation of reference concentration with

the shear stress predicted in this model agrees well with best fit exponential curve to the

experimentally determined reference concentrations. Although Nielsen's model provided a

similar relative error in predicting the reference concentration, the experimental reference

concentration values did not increase as rapidly with shear stress as the model predicts.

The additional dependence of wave period predicted by Bosman and Steetzel's reference

concentration model is not seen in the experimentally determined values.

APPENDIX

ANALYZED DATA FROM EXPERIMENTS
PERFORMED AT SUPERTANK

In the following pages, the results from the data analysis from the majority of the

experiments is presented. The results from run numbers 1, 2, 8, 9, 14, 15, 16, 31, 32, 34,

35, 62, 72, 80, 82, and 83 are not presented due to various difficulties during data

collection. In table A-i, each of the variables presented with the runs is described.

Table A. 1 Key to data appendix

DEPTH
HSIG
PT
MEANU
UO
AMP
RE
RIPRMS
BRRMS
STEEP
BB
BT
MENOBS09
OBS090FF

MENOBS56
OBS56OFF

SHEAR_SL

SHLD25_SL
SHLDR_SL

SHEAR SW

Water depth in meters.
Significant wave height in meters.
Peak period from spectrum in seconds.
Mean cross-shore velocity in meters per second.
Maximum semiorbital velocity in meters per second.
Semiexcursion amplitude in meters.
Reynold's number, RE = A2./v
Standard deviation of horizontal bed form profile in inches.
Standard deviation of bed return time series in inches
Ripple steepness.
Bin number of lowest bed location during run.
Bin number of highest bed location during run.
Mean concentration from OBS 9 cm from bed in grams per liter.
Background concentration for OBS 9 cm from bed in milligrams per
liter.
Mean concentration from OBS 56 cm from bed in grams per liter.
Background concentration for OBS 56 cm from bed in milligrams per
liter.
Shear stress as predicted from Sleath's model in Newtons per square
meter.
Grain roughness Shield's parameter from Sleath's stress.
Grain roughness Shield's parameter from Sleath's stress with ripple
crest velocity enhancement.
Shear stress as predicted from Swart's equation in Newtons per

SHLD25 SW
SHLDR SW

BSRC

NRC SW

SMRCSW

EFRC SW

RSQR

RC

M

square meter.
Grain roughness Shield's parameter from Swart's stress.
Grain roughness Shield's parameter from Swart's stress with ripple
crest velocity enhancement.
Reference concentration predicted from Bosman & Steetzel's model
using best fit value of G.
Reference concentration predicted from Nielsen's model using
Swart's estimation of shear stress.
Reference concentration predicted from Smith and McLean's model
using Swart's estimation of shear stress.
Reference concentration predicted from Engelund and Fredsoe's
model using one half Swart's estimation of shear stress .
Coefficient of determination from best fit of exponential curve to
concentration profile.
Reference concentration in milligrams per liter from extrapolation to
mean bed level.
Slope of best fit logarithmic concentration profile with distance given
in millimeters.

Run number: 3 Original data file: a0510bft
Start of data collection: 08/05/91 11:00:00 End: 08/05/91 11:10:00
Shape of survace elevation spectrum: narrow band random
HmO: 0.80 Peak period: 3.0 Quality of concentration profile data: good

Measured hyrodynamic conditions
DEPTH: 2.15
HSIG: 0.71
PT: 2.91
MEANU: 0.03
UO: 0.50
AMP: 0.23
RE: 1.15e+05

Ripples and bottom location
RIPRMS: No data
BRRMS: 0.53
STEEP: estimated 7.32e-02
BB: 204.00
BT: 199.00

OBS concentrations
MENOBS09: 0.174
OBS09OFF: 1.26e+02
MENOBS56: 0.112
OBS56OFF: -1.22e+02
Neor bed concentration & best fit
B0
70 1C 1038 1g/I
m = -0.0195
E 60
050
E 40
0 30

Concentration mg/I

Figure A-I. Near bed concentration and best fit.

Frequency (hz)
Figure A-2. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.312
SHLD25 SL: 0.369
SHLDR SL: 0.622
SHEAR SW: 1.490
SHLD25_SW: 0.445
SHLDR SW: 0.751

Reference concentration model predictions
BSRC: 2.99e+03
NRC_SW: 5.62e+04
SMRCSW: 1.08e+03
EFRCSW: 2.64e+05

Concentration profile fit
RSQR: 0.98
RC: 1.04e+03
M: -1.95e-02

Run number: 4 Original data file: a0512aft
Start of data collection: 08/05/91 12:29:50 End: 08/05/91 12:39:50
Shape of survace elevation spectrum: narrow band random
HmO: 0.80 Peak period: 3.0 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 2.16
HSIG: 0.70
PT: 2.91
MEANU: 0.01
UO: 0.49
AMP: 0.23
RE: 1.1 lle+05

Ripples and bottom location
RIPRMS: No data
BRRMS: 0.94
STEEP: estimated 7.32e-02
BB: 206.00
BT: 199.00

OBS concentrations
MENOBS09: 0.237
OBS09OFF: 1.62e+02
MENOBS56: 0.083
OBS56OFF: -1.98e+01
Near bed concentration & best fit
80-- -
70 C, 910 mg/I
S-0.01668
E 60
E 50

E 40
S so \
-I n

Concentration mg/I

Figure A-3. Near bed concentration and best fit.

10-2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0,8 0.9 1
Frequency (hz)

Figure A-4. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.271
SHLD25 SL: 0.357
SHLDR SL: 0.603
SHEAR SW: 1.445
SHLD25 SW: 0.432
SHLDR SW: 0.728

Reference concentration model predictions
BSRC: 2.81e+03
NRCSW: 5.12e+04
SMRC SW: 1.05e+03
EFRCSW: 2.36e+05

Concentration profile fit
RSQR: 0.96
RC: 9.10e+02
M: -1.67e-02

Run number: 5 Original data file: a0512bft
Start of data collection: 08/05/91 12:55:00 End: 08/05/91 13:05:00
Shape of survace elevation spectrum: narrow band random
HmO: 0.80 Peak period: 3.0 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 2.15
HSIG: 0.73
PT: 2.91
MEANU: 0.03
UO: 0.51
AMP: 0.24
RE: 1.21e+05

Ripples and bottom location
RIPRMS: No data
BRRMS: 1.32
STEEP: estimated 7.32e-02
BB: 201.00
BT: 194.00

OBS concentrations
MENOBS09: 0.335
OBS09OFF: 1.62e+02
MENOBS56: 0.185
OBS56OFF: -1.98e+01
Near bed concentration & best fit

Concentration mg/I

Figure A-5. Near bed concentration and best fit.

Surface elevation power spectrum
10o

10-

0 0.1 0.2 D.3 0.4 0.5 0.6 0.7 0,8 0.9 1
Frequency (hz)

Figure A-6. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.372
SHLD25 SL: 0.386
SHLDR_SL: 0.650
SHEAR SW: 1.558
SHLD25 SW: 0.466
SHLDR_SW: 0.785

Reference concentration model predictions
BSRC: 3.28e+03
NRC SW: 6.42e+04
SMRC SW: 1.63e+03
EFRC SW: 3.05e+05

Concentration profile fit
RSQR: 0.98
RC: 1.07e+03
M: -1.76e-02

Run number: 6 Original data file: a0517aft
Start of data collection: 08/05/91 17:46:00 End: 08/05/91 17:56:00
Shape of survace elevation spectrum: narrow band random
HmO: 0.80 Peak period: 3.0 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 2.14
HSIG: 0.75
PT: 2.91
MEANU: 0.02
UO: 0.53
AMP: 0.25
RE: 1.30e+05

Ripples and bottom location
RIPRMS: No data
BRRMS: 1.32
STEEP: estimated 7.32e-02
BB: 209.00
BT: 200.00

OBS concentrations
MENOBS09: 0.215
OBS09OFF: 6.43e+02
MENOBS56: 0.135
OBS56OFF: 4.94e+02
Near bed concentration & best fit
80
70 C0 = 1470 mg/I
m = -0.01876
E 60
S 50
E 40
30
20
10

Concentration mg/I

10o-
D .1 0.2 O.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Frequency (hz)

Figure A-8. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.455
SHLD25_SL: 0.409
SHLDR SL: 0.689
SHEAR SW: 1.651
SHLD25 SW: 0.493
SHLDRSW: 0.832

Reference concentration model predictions
BSRC: 3.70e+03
NRC_SW: 7.64e+04
SMRCSW: 1.22e+03
EFRC SW: 3.62e+05

Concentration profile fit
RSQR: 0.99
RC: 1.47e+03
M: -1.88e-02

Figure A-7. Near bed concentration and best fit.

Run number: 7 Original data file: a0517bft
Start of data collection: 08/05/91 18:12:00 End: 08/05/91 18:22:00
Shape of survace elevation spectrum: narrow band random
Hm0: 0.80 Peak period: 3.0 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 2.14
HSIG: 0.74
PT: 2.91
MEANU: 0.02
UO: 0.52
AMP: 0.24
RE: 1.26e+05

Ripples and bottom location
RIPRMS: No data
BRRMS: 1.23
STEEP: estimated 7.32e-02
BB: 201.00
BT: 194.00

OBS concentrations
MENOBS09: 0.302
OBS09OFF: 6.43e+02
MENOBS56: 0.162
OBS56OFF: 4.94e+02
Near bed cancentrotion & best fit

Concentration mg/I

Frequency (hz)

Figure A-10. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.419
SHLD25 SL: 0.399
SHLDR_SL: 0.672
SHEAR SW: 1.610
SHLD25 SW: 0.481
SHLDRSW: 0.812

Reference concentration model predictions
BSRC: 3.51e+03
NRC SW: 7.09e+04
SMRC SW: 1.18e+03
EFRCSW: 3.37e+05

Concentration profile fit
RSQR: 0.97
RC: 1.20e+03
M: -1.72e-02

Figure A-9. Near bed concentration and best fit.

Run number: 10 Original data file: a0608aft
Start of data collection: 08/06/91 08:11:00 End: 08/06/91 08:21:00
Shape of survace elevation spectrum: broad band random
HmO: 0.80 Peak period: 3.0 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 2.12
HSIG: 0.62
PT: 2.91
MEANU: 0.02
UO: 0.44
AMP: 0.20
RE: 9.07e+04

Ripples and bottom location
RIPRMS: No data
BRRMS: 0.84
STEEP: estimated 7.32e-02
BB: 208.00
BT: 199.00

OBS concentrations
MENOBS09: 0.275
OBS09OFF: 7.10e+02
MENOBS56: 0.095
OBS56OFF: 6.72e+02
Near bed concentration & best fit
80
70 Co = 1284 mg/l
m = -0.0193
E 60
E 50
so
E 40
0 30

Concentration mg/I

Figure A-11. Near bed concentration and best
fit.

Surface elevation power spectrum
100

-o

10-
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Frequency (hz)

Figure A-12. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.071
SHLD25_SL: 0.301
SHLDR_SL: 0.508
SHEAR SW: 1.220
SHLD25_SW: 0.365
SHLDR SW: 0.615

Reference concentration model predictions
BSRC: 1.97e+03
NRC SW: 3.08e+04
SMRC SW: 8.60e+02
EFRCSW: 1.15e+05

Concentration profile fit
RSQR: 0.98
RC: 1.28e+03
M: -1.93e-02

Run number: 11 Original data file: a0609aft
Start of data collection: 08/06/91 09:45:00 End: 08/06/91 09:55:00
Shape of survace elevation spectrum: broad band random
HmO: 0.80 Peak period: 3.0 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 2.13
HSIG: 0.63
PT: 2.91
MEANU: 0.02
UO: 0.45
AMP: 0.21
RE: 9.32e+04

Ripples and bottom location
RIPRMS: No data
BRRMS: 0.70
STEEP: estimated 7.32e-02
BB: 205.00
BT: 198.00

OBS concentrations
MENOBS09: 0.219
OBS09OFF: 7.64e+02
MENOBS56: 0.034
OBS56OFF: 7.26e+02
Ne.r bed concentration & best fit

Concentration mg/I

Figure A-13. Near bed concentration and best
fit.

10-

0 0 0.2 0.3 0.4 0.5 0.6 0.7 D.8 0.9 1
Frequency (hz)

Figure A-14. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.097
SHLD25_SL: 0.308
SHLDR_SL: 0.520
SHEAR SW: 1.248
SHLD25 SW: 0.373
SHLDRSW: 0.629

Reference concentration model predictions
BSRC: 2.07e+03
NRC SW: 3.30e+04
SMRC SW: 8.84e+02
EFRCSW: 1.29e+05

Concentration profile fit
RSQR: 0.99
RC: 1.18e+03
M: -1.52e-02

Run number: 12 Original data file: a061 laft
Start of data collection: 08/06/91 10:59:50 End: 08/06/91 11:09:50
Shape of survace elevation spectrum: broad band random
HmO: 0.80 Peak period: 3.0 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 2.12
HSIG: 0.60
PT: 2.91
MEANU: 0.03
UO: 0.43
AMP: 0.20
RE: 8.38e+04

Ripples and bottom location
RIPRMS: No data
BRRMS: 0.52
STEEP: estimated 7.32e-02
BB: 205.00
BT: 199.00

OBS concentrations
MENOBS09: 0.199
OBS09OFF: 8.61e+02
MENOBS56: 0.045
OBS56OFF: 7.98e+02
Neor bed concentration & best fit

Concentration mg/1I

0.1 0.2 D.3 0.4 0.5 0.5 0.7 0.8 0.9
Frequency (hz)

Figure A-16. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.002
SHLD25_SL: 0.282
SHLDR SL: 0.475
SHEAR SW: 1.142
SHLD25 SW: 0.341
SHLDRSW: 0.576

Reference concentration model predictions
BSRC: 1.72e+03
NRC SW: 2.53e+04
SMRC SW: 7.96e+02
EFRCSW: 8.22e+04

Concentration profile fit
RSQR: 0.98
RC: 1.30e+03
M: -1.95e-02

Figure A-15. Near bed concentration and best
fit.

Run number: 13 Original data file: a061 lbft
Start of data collection: 08/06/91 11:23:00 End: 08/06/91 11:33:00
Shape of survace elevation spectrum: broad band random
HmO: 0.80 Peak period: 3.0 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 2.12
HSIG: 0.63
PT: 2.91
MEANU: 0.02
UO: 0.44
AMP: 0.21
RE: 9.15e+04

Ripples and bottom location
RIPRMS: No data
BRRMS: 1.18
STEEP: estimated 7.32e-02
BB: 205.00
BT: 199.00

OBS concentrations
MENOBS09: 0.182
OBS09OFF: 8.61e+02
MENOBS56: 0.040
OBS56OFF: 7.98e+02
Neor bed concentration & best fit

Concentration mg/I

Surface elevation power spectrum

Frequency (hz)

Figure A-18. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.080
SHLD25 SL: 0.304
SHLDRSL: 0.512
SHEAR SW: 1.229
SHLD25 SW: 0.367
SHLDRSW: 0.620

Reference concentration model predictions
BSRC: 2.01e+03
NRC SW: 3.15e+04
SMRC SW: 8.68e+02
EFRCSW: 1.20e+05

Concentration profile fit
RSQR: 0.99
RC: 1.72e+03
M: -2.13e-02

Figure A-17. Near bed concentration and best
fit.

Run number: 17 Original data file: a0615aft
Start of data collection: 08/06/91 16:03:00 End: 08/06/91 16:13:00
Shape of survace elevation spectrum: broad band random
Hm0: 0.80 Peak period: 3.0 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 2.11
HSIG: 0.65
PT: 2.91
MEANU: 0.04
UO: 0.46
AMP: 0.22
RE: 1.00e+05

Ripples and bottom location
RIPRMS: No data
BRRMS: 0.88
STEEP: estimated 7.32e-02
BB: 211.00
BT: 203.00

OBS concentrations
MENOBS09: 0.448
OBS09OFF: 8.61e+02
MENOBS56: 0.274
OBS56OFF: 7.98e+02
Near bed concentration & best fit
80 --------- 1 1 1 --- -- r
70 Ca- 1652 mg/I
,m -0.01966
E 60
E 50
E 40
a 30

Concentration mg/I

Surface elevation power spectrum

0 D.1 0.2 0.3 0.4 0.5 0.5 0.7 0.8 0.9 1
Frequency (hz)

Figure A-20. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.165
SHLD25_SL: 0.328
SHLDR SL: 0.552
SHEAR SW: 1.325
SHLD25_SW: 0.396
SHLDR_SW: 0.668

Reference concentration models
BSRC: 2.35e+03
NRC SW: 3.95e+04
SMRC SW: 9.48e+02
EFRCSW: 1.68e+05

Concentration profile fit
RSQR: 0.98
RC: 1.65e+03
M: -1.97e-02

Figure A-19. Near bed concentration and best
fit.

Run number: 18 Original data file: a0617aft
Start of data collection: 08/06/91 17:24:50 End: 08/06/91 17:34:50
Shape of survace elevation spectrum: broad band random
HmO: 0.80 Peak period: 3.0 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 1.91
HSIG: 0.59
PT: 2.91
MEANU: 0.03
UO: 0.47
AMP: 0.22
RE: 1.00e+05

Ripples and bottom location
RIPRMS: No data
BRRMS: 0.73
STEEP: estimated 7.32e-02
BB: 209.00
BT: 200.00

OBS concentrations
MENOBS09: 0.310
OBS09OFF: 1.06e+03
MENOBS56: 0.121
OBS560FF: 1.04e+03
Neor bed concentration & best fit

70 C 1111 ii /
nn -0.01703
E 60
S 5
S 430

k5 \

Concentration mg/I

Figure A-21. Near bed concentration and best
fit.

Surface election power spectrum

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 D8 0.9 1
Frequency (hz)

Figure A-22. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.169
SHLD25_SL: 0.329
SHLDR_SL: 0.554
SHEAR SW: 1.330
SHLD25_SW: 0.397
SHLDRSW: 0.670

Reference concentration model predictions
BSRC: 2.36e+03
NRC_SW: 3.99e+04
SMRC SW: 9.51e+02
EFRCSW: 1.71e+05

Concentration profile fit
RSQR: 0.98
RC: 1.1 lle+03
M: -1.70e-02

Run number: 19 Original data file: a0618aft
Start of data collection: 08/06/91 18:22:30 End: 08/06/91 18:42:30
Shape of survace elevation spectrum: broad band random
HmO: 0.80 Peak period: 3.0 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 1.92
HSIG: 0.62
PT: 2.91
MEANU: 0.02
UO: 0.49
AMP: 0.23
RE: 1.10e+05

Ripples and bottom location
RIPRMS: No data
BRRMS: 1.37
STEEP: estimated 7.32e-02
BB: 206.00
BT: 200.00

OBS concentrations
MENOBS09: 0.358
OBS09OFF: 1.06e+03
MENOBS56: 0.150
OBS56OFF: 1.04e+03
Neor bed concentration & best fit

Concentration mg/I

0 0.1 0.2 D.3 0.4 0,5 0.B 0.7 0.8 0.9 1
Frequency (hz)

Figure A-24. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.261
SHLD25 SL: 0.354
SHLDR SL: 0.598
SHEAR SW: 1.433
SHLD25_SW: 0.428
SHLDRSW: 0.722

Reference concentration model predictions
BSRC: 2.76e+03
NRC SW: 5.00e+04
SMRC SW: 1.04e+03
EFRCSW: 2.29e+05

Concentration profile fit
RSQR: 0.98
RC: 1.97e+03
M: -2.13e-02

Figure A-23. Near bed concentration and best
fit.

Run number: 20 Original data file: a0618bft
Start of data collection: 08/06/91 18:45:00 End: 08/06/91 18:55:00
Shape of survace elevation spectrum: broad band random
HmO: 0.80 Peak period: 3.0 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 1.91
HSIG: 0.58
PT: 3.20
MEANU: 0.02
UO: 0.49
AMP: 0.25
RE: 1.22e+05

Ripples and bottom location
RIPRMS: No data
BRRMS: 0.61
STEEP: estimated 7.32e-02
BB: 203.00
BT: 197.00

OBS concentrations
MENOBS09: 0.353
OBS09OFF: 1.06e+03
MENOBS56: 0.180
OBS56OFF: 1.04e+03
Neor bed concentration & best fit
BC
70 Co 969.4 mg/I
-0.01B04
E 60
50
E 40
u 30

Concentration mg/I

Figure A-25. Near bed concentration and best
fit.

Surface elevation power spectrum

D 0.1 0.2 D3 0.4 0.5 0.B 0.7 0.8 0.9 1
Frequency (hz)

Figure A-26. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.500
SHLD25 SL: 0.422
SHLDR SL: 0.711
SHEAR SW: 1.702
SHLD25 SW: 0.420
SHLDR_SW: 0.709

Reference concentration model predictions
BSRC: 2.82e+03
NRC SW: 4.72e+04
SMRC SW: 1.26e+03
EFRC SW: 2.14e+05

Concentration profile fit
RSQR: 0.97
RC: 9.69e+02
M: -1.80e-02

Run number: 21 Original data file: a07 10aft
Start of data collection: 08/07/91 10:24:00 End: 08/07/91 10:44:00
Shape of survace elevation spectrum: narrow band random
HmO: 0.80 Peak period: 4.5 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 2.13
HSIG: 0.66
PT: 4.57
MEANU: 0.00
UO: 0.61
AMP: 0.45
RE: 2.75e+05

Ripples and bottom location
RIPRMS: No data
BRRMS: 0.47
STEEP: estimated 7.32e-02
BB: 100.00
BT: 96.00

OBS concentrations
MENOBS09: unusable
OBS09OFF: unusable
MENOBS56: unusable
OBS56OFF: unusable
Near bed concentraion & best fit

Concentration mg/I

Figure A-27. Near bed concentration and best
fit.

Surface elevation power spectrum

10-
0 D. 0,2 0.3 0.4 0.5 0.5 0.7 D.8 0.9 1
Frequency (hz)

Figure A-28. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.813
SHLD25 SL: 0.510
SHLDR SL: 0.860
SHEAR SW: 2.049
SHLD25 SW: 0.558
SHLDR SW: 0.941

Reference concentration model predictions
BSRC: 2.77e+03
NRC SW: 1.10e+05
SMRC SW: 1.54e+03
EFRCSW: 4.88e+05

Concentration profile fit
RSQR: 0.96
RC: 5.55e+02
M: -1.93e-02

Run number: 22 Original data file: a071 laft
Start of data collection: 08/07/91 11:19:50 End: 08/07/91 11:39:50
Shape of survace elevation spectrum: narrow band random
HmO: 0.80 Peak period: 4.5 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 2.13
HSIG: 0.63
PT: 4.57
MEANU: 0.03
UO: 0.58
AMP: 0.43
RE: 2.48e+05

Ripples and bottom location
RIPRMS: No data
BRRMS: 0.45
STEEP: estimated 7.32e-02
BB: 100.00
BT: 96.00

OBS concentrations
MENOBS09: unusable
OBS09OFF: unusable
MENOBS56: unusable
OBS56OFF: unusable
Near bed concentration & best fit

70 C = 556.8 mg/I
rn = -0.01919
E 60 \
E 50
E 40
30

Concentration mg/I

Frequency (hz)

Figure A-30. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.661
SHLD25 SL: 0.467
SHLDR SL: 0.787
SHEAR SW: 1.876
SHLD25 SW: 0.511
SHLDRSW: 0.862

Reference concentration model predictions
BSRC: 2.32e+03
NRC_SW: 8.48e+04
SMRC_SW: 1.40e+03
EFRCSW: 3.98e+05

Concentration profile fit
RSQR: 0.97
RC: 5.57e+02
M: -1.92e-02

Figure A-29. Near bed concentration and best
fit.

Surface eleva-on power spectrum

Run number: 23 Original data file: a0713aft
Start of data collection: 08/07/91 13:04:50 End: 08/07/91 13:24:50
Shape of survace elevation spectrum: narrow band random
HmO: 0.80 Peak period: 4.5 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 2.13
HSIG: 0.64
PT: 4.57
MEANU: 0.01
UO: 0.59
AMP: 0.43
RE: 2.53e+05

Ripples and bottom location
RIPRMS: No data
BRRMS: 0.40
STEEP: estimated 7.32e-02
BB: 100.00
BT: 95.00

OBS concentrations
MENOBS09: unusable
OBS09OFF: unusable
MENOBS56: unusable
OBS56OFF: unusable
Near bed concentration & best fit

Concentration mg/I

Figure A-31. Near bed concentration and best
fit.

0 0.1 0.2 D.3 0.4 D.5 0.6 0.7 0.8 0.9 1
Frequency (hz)

Figure A-32. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.687
SHLD25_SL: 0.474
SHLDR_SL: 0.800
SHEAR SW: 1.905
SHLD25 SW: 0.519
SHLDR_SW: 0.875

Reference concentration model predictions
BSRC: 2.39e+03
NRC SW: 8.89e+04
SMRC SW: 1.42e+03
EFRCSW: 4.14e+05

Concentration profile fit
RSQR: 0.93
RC: 5.36e+02
M: -1.79e-02

Run number: 24 Original data file: a0715aft
Start of data collection: 08/07/91 15:02:00 End: 08/07/91 15:57:00
Shape of survace elevation spectrum: narrow band random
HmO: 0.80 Peak period: 4.5 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 2.13
HSIG: 0.67
PT: 4.57
MEANU: 0.01
UO: 0.62
AMP: 0.45
RE: 2.80e+05

Ripples and bottom location
RIPRMS: No data
BRRMS: 0.64
STEEP: estimated 7.32e-02
BB: 100.00
BT: 91.00

OBS concentrations
MENOBS09: unusable
OBS09OFF: unusable
MENOBS56: unusable
OBS56OFF: unusable
Neor bed concentration & best fit

70 Co 679.3 mg/I
m -0.01623
E 60
E 50
E 40
30
o" 20

Concentration mg/I

Figure A-33. Near bed concentration and best
fit.

10-1

10

0 D.1 0.2 0.3 0.4 0.5 0.5 0.7 0.8 0.9 1
Frequency (hz)

Figure A-34. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.840
SHLD25 SL: 0.517
SHLDR SL: 0.872
SHEAR SW: 2.078
SHLD25 SW: 0.566
SHLDRSW: 0.955

Reference concentration model predictions
BSRC: 2.86e+03
NRC SW: 1.15e+05
SMRC SW: 1.57e+03
EFRC SW: 5.03e+05

Concentration profile fit
RSQR: 0.98
RC: 6.79e+02
M: -1.62e-02

Run number: 25 Original data file: a0717aft
Start of data collection: 08/07/91 16:59:50 End: 08/07/91 17:19:50
Shape of survace elevation spectrum: narrow band random
HmO: 0.80 Peak period: 4.5 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 2.14
HSIG: 0.67
PT: 4.57
MEANU: 0.01
UO: 0.62
AMP: 0.45
RE: 2.79e+05

Ripples and bottom location
RIPRMS: No data
BRRMS: 0.63
STEEP: estimated 7.32e-02
BB: 100.00
BT: 91.00

OBS concentrations
MENOBS09: unusable
OBS09OFF: unusable
MENOBS56: unusable
OBS56OFF: unusable
Near bed concentration & best fit

70 Co = 798.2 rng/I
m = -0.01694
E 60 \
E 50
E 40
u 30
I5 .o

Concentration mg/1

Figure A-35. Near bed concentration and best
fit.

0.1 0.2 0.3 0.4 0.5 0 5 0.7 0.8 0.9
Frequency (hz)

Figure A-36. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.835
SHLD25_SL: 0.516
SHLDR SL: 0.870
SHEAR SW: 2.073
SHLD25 SW: 0.565
SHLDRSW: 0.952

Reference concentration model predictions
BSRC: 2.84e+03
NRC SW: 1.14e+05
SMRC SW: 1.56e+03
EFRCSW: 5.01e+05

Concentration profile fit
RSQR: 0.99
RC: 7.98e+02
M: -1.69e-02

Run number: 26 Original data file: a0717bft
Start of data collection: 08/07/91 17:53:00 End: 08/07/91 18:13:00
Shape of survace elevation spectrum: narrow band random
HmO: 0.80 Peak period: 4.5 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 2.14
HSIG: 0.67
PT: 4.57
MEANU: 0.00
UO: 0.62
AMP: 0.45
RE: 2.76e+05

Ripples and bottom location
RIPRMS: No data
BRRMS: 0.32
STEEP: estimated 7.32e-02
BB: 97.00
BT: 90.00

OBS concentrations
MENOBS09: unusable
OBS09OFF: unusable
MENOBS56: unusable
OBS56OFF: unusable
Near bed concentration & best fit
80
70 Co 305.8 mrg/I
m = -0.01153
E 60
i 50
E 40
S30
20 lC
10

Concentration mg/I

Figure A-37. Near bed concentration and best
fit.

Surfoce elevation power spectrum

o10-

10-

0 D.1 0.2 0.3 0.4 0.5 0.5 0.7 D.8 0.9 1
Frequency (hz)

Figure A-38. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.818
SHLD25 SL: 0.511
SHLDR SL: 0.862
SHEAR SW: 2.053
SHLD25_SW: 0.559
SHLDRSW: 0.943

Reference concentration model predictions
BSRC: 2.79e+03
NRC SW: 1.1 lle+05
SMRCSW: 1.55e+03
EFRCSW: 4.91e+05

Concentration profile fit
RSQR: 0.94
RC: 3.06e+02
M: -1.16e-02

Run number: 27 Original data file: a0719aft
Start of data collection: 08/07/91 19:07:30 End: 08/07/91 19:17:30
Shape of survace elevation spectrum: monochromatic
HmO: 0.15 Peak period: 4.5 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 2.16
HSIG: 0.15
PT: 4.57
MEANU: 0.00
UO: 0.14
AMP: 0.10
RE: 1.38e+04

Ripples and bottom location
RIPRMS: No data
BRRMS: 0.18
STEEP: estimated 7.32e-02
BB: 199.00
BT: 196.00

OBS concentrations
MENOBSO9: unusable
OBS09OFF: unusable
MENOBS56: unusable
OBS56OFF: unusable
Near bed concentration & best fit
80
70 C0 13,61 mg/I
m = -0.00125
E 60
E
S50
E 40

20
o5 20

10

D10 10W
Concentration m/l

Figure A-39. Near bed concentration and best
fit.

s 10-

10 - i - i - i - i i

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Frequency (hz)

Figure A-40. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 0.143
SHLD25_SL: 0.040
SHLDRSL: 0.068
SHEAR SW: 0.166
SHLD25_SW: 0.045
SHLDR SW: 0.076

Reference concentration model predictions
BSRC: 1.47e+01
NRC SW: 5.86e+01
SMRC SW: 0.00e+00
EFRC SW: 0.00e+00

Concentration profile fit
RSQR: 0.93
RC: 1.36e+02
M: -1.25e-03

Run number: 28 Original data file: a0808aft
Start of data collection: 08/08/91 08:29:50 End: 08/08/91 08:49:50
Shape of survace elevation spectrum: broad band random
HmO: 0.80 Peak period: 4.5 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 2.20
HSIG: 0.59
PT: 4.57
MEANU: 0.01
UO: 0.53
AMP: 0.39
RE: 2.05e+05

Ripples and bottom location
RIPRMS: No data
BRRMS: 0.45
STEEP: estimated 7.32e-02
BB: 95.00
BT: 89.00

OBS concentrations
MENOBS09: unusable
OBS090FF: unusable
MENOBS56: unusable
OBS56OFF: unusable
Near bed concentrold n & best fit

Concentration mg/I

Figure A-41. Near bed concentration and best
fit.

Surface election power spectrum

10-1

10-
0 0.1 0.2 0.3 0.4 0.5 0.5 0.7 0.8 0.9 1
Frequency (hz)

Figure A-42. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.407
SHLD25_SL: 0.396
SHLDRSL: 0.667
SHEAR SW: 1.590
SHLD25_SW: 0.433
SHLDR SW: 0.730

Reference concentration model predictions
BSRC: 1.66e+03
NRC SW: 5.16e+04
SMRC SW: 1.17e+03
EFRC SW: 2.39e+05

Concentration profile fit
RSQR: 0.92
RC: 3.29e+02
M: -9.04e-03

Run number: 29 Original data file: a0809aft
Start of data collection: 08/08/91 09:49:50 End: 08/08/91 10:44:50
Shape of survace elevation spectrum: broad band random
HmO: 0.80 Peak period: 4.5 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 2.18
HSIG: 0.61
PT: 4.57
MEANU: 0.02
UO: 0.56
AMP: 0.41
RE: 2.26e+05

Ripples and bottom location
RIPRMS: No data
BRRMS: 0.56
STEEP: estimated 7.32e-02
BB: 97.00
BT: 88.00

OBS concentrations
MENOBS09: unusable
OBS09OFF: unusable
MENOBS56: unusable
OBS560FF: unusable
Neor bed concentration & best fit
80 -
70 Co = 557.5 mg/I
S -0.01673
E 60
50
E 40
30 -
0 "

Concentration mg/

Surface elevation power spectrum
100

10-

0 0.1 0.2 D.3 0.4 05 06 0.7 0.8 0-9 1
Frequency (hz)

Figure A-44. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.532
SHLD25 SL: 0.431
SHLDR SL: 0.726
SHEAR SW: 1.731
SHLD25 SW: 0.471
SHLDR SW: 0.795

Reference concentration model predictions
BSRC: 1.97e+03
NRC SW: 6.66e+04
SMRC SW: 1.28e+03
EFRC SW: 3.17e+05

Concentration profile fit
RSQR: 0.98
RC: 5.57e+02
M: -1.67e-02

Figure A-43. Near bed concentration and best
fit.

Run number: 30 Original data file: a0812aft
Start of data collection: 08/08/91 12:40:00 End: 08/08/91 13:00:00
Shape of survace elevation spectrum: broad band random
HmO: 0.80 Peak period: 4.5 Quality of concentration profile data: good

Measured hydrodynamic conditions
DEPTH: 2.18
HSIG: 0.60
PT: 4.57
MEANU: 0.01
UO: 0.55
AMP: 0.40
RE: 2.18e+05

Ripples and bottom location
RIPRMS: No data
BRRMS: 0.47
STEEP: estimated 7.32e-02
BB: 97.00
BT: 86.00

OBS concentrations
MENOBS09: unusable
OBS09OFF: unusable
MENOBS56: unusable
OBS56OFF: unusable
Neor bed concentration & best fit

Concentration mg/I

Surface eleaion power spectrum

10o-3
D D.1 0.2 0.3 0.4 0.5 0.5 0.7 0.8 0.9 1
Frequency (hz)

Figure A-46. Surface elevation power spectrum.

Shear stress estimates
SHEAR SL: 1.486
SHLD25_SL: 0.418
SHLDRSL: 0.704
SHEAR SW: 1.678
SHLD25_SW: 0.457
SHLDR SW: 0.771

Reference concentration model predictions
BSRC: 1.85e+03
NRC SW: 6.07e+04
SMRC SW: 1.24e+03
EFRC SW: 2.88e+05

Concentration profile fit
RSQR: 0.97
RC: 4.97e+02
M: -1.65e-02

Figure A-45. Near bed concentration and best
fit.

MILLISECOND	CLASS.METHOD	MESSAGE
0	sobekcm_page_globals.constructor
0	sobekcm_page_globals.constructor	Application State validated or built
0	sobekcm_database.verify_item_lookup_object
0	sobekcm_page_globals.constructor	Navigation Object created from URI query string
0	sobekcm_database.verify_item_lookup_object
0	sobekcm_page_globals.display_item	Retrieving item or group information
0	sobekcm_page_globals.get_entire_collection_hierarchy	Retrieving hierarchy information
0	sobekcm_assistant.get_entire_collection_hierarchy
0	cached_data_manager.retrieve_item_aggregation
0	cached_data_manager.retrieve_item_aggregation	Found item aggregation on local cache
0	item_aggregation_builder.get_item_aggregation	Found 'all' item aggregation in cache
0	system.web.ui.page.page_load (ufdc.page_load)
0	sobekcm_page_globals.constructor.on_page_load
0	html_echo_mainwriter.add_style_references	Adding style references to HTML
0	html_echo_mainwriter.add_text_to_page	Reading the text from the file and echoing back to the output stream
38	html_echo_mainwriter.add_text_to_page	Finished reading and writing the file