• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Dedication
 Acknowledgement
 Table of Contents
 List of Figures
 List of Tables
 Abstract
 Introduction
 Description of the Amazon shelf...
 Formulation of 1-D vertical module...
 Mud dynamics in Amazon estuary
 Transport model
 General observations, summary and...
 Reference
 Biographical sketch














Group Title: UFLCOEL-98011
Title: A preliminary examination of amazon shelf sediment dynamics
CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00091088/00001
 Material Information
Title: A preliminary examination of amazon shelf sediment dynamics
Series Title: UFLCOEL-98011
Physical Description: xvii, 155 leaves : ill. ; 28 cm.
Language: English
Creator: Vinzon, Susana Beatriz, 1960-
University of Florida -- Coastal and Oceanographic Engineering Dept
Publisher: Coastal & Oceanographic Engineering Dept., University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1998
 Subjects
Subject: Estuarine sediments -- Brazil -- Amazon River Estuary   ( lcsh )
Sediment transport -- Brazil -- Amazon River Estuary   ( lcsh )
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (Engineer)--University of Florida, 1998.
Bibliography: Includes bibliographical references (leaves 143-154).
Statement of Responsibility: by Susana Beatriz Vinzon.
 Record Information
Bibliographic ID: UF00091088
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 41567289

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Page i
    Dedication
        Page ii
    Acknowledgement
        Page iii
        Page iv
    Table of Contents
        Page v
        Page vi
        Page vii
    List of Figures
        Page viii
        Page ix
        Page x
        Page xi
        Page xii
        Page xiii
        Page xiv
    List of Tables
        Page xv
    Abstract
        Page xvi
        Page xvii
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
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    Description of the Amazon shelf environment
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    Formulation of 1-D vertical module for fine sediment transport modeling
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    Mud dynamics in Amazon estuary
        Page 87
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    Transport model
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    General observations, summary and conclusions
        Page 138
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    Reference
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    Biographical sketch
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Full Text




UFL/COEL-98/011


A PRELIMINARY EXAMINATION OF AMAZON SHELF
SEDIMENT DYNAMICS



by



Susana Beatriz Vinzon




Thesis


1998















A PRELIMINARY EXAMINATION OF
AMAZON SHELF SEDIMENT DYNAMICS








By



SUSANA BEATRIZ VINZON


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


UNIVERSITY OF FLORIDA


1998













To Mauricio and my son, Lucas.













ACKNOWLEDGMENTS


The author would like to express her gratitude to Dr. Ashish J. Mehta, Professor of

Coastal and Oceanographic Engineering, University of Florida, for his advice and

support during the development of this work. The author's appreciation is also extended

to Professor Cliudio F. Neves and Professor Paulo C. C. Rosman, both in the Ocean

Engineering Program, Federal University of Rio de Janeiro, Brazil, for their assistance,

friendship and support during this study.

Acknowledgment is also due to Dr. R. G. Dean and Dr. Y. P. Sheng for their

participation as supervisory committee members and their helpful assistance.

The author would like sincerely to thank Professor Gail Kineke of the University

of South Carolina, who kindly provided the database analyzed in this work, to Professor

Alberto Figueiredo, of the Federal Fluminense University, Brazil, who supplied

sediment samples from the Amazon Shelf, and to Professor Richard Faas of Lafayette

College, Easton, Pennsylvania, who provided data on sediment rheology. The author

would also like to thank Prof. Dimitrie Nechet of the Federal University of Para, Brazil,

and to Dr. Robert Kayen of the U.S. Geological Survey, Menlo Park, California, for

providing supplementary information.

Special thanks are due to the staff members of the Coastal and Oceanographic

Engineering Department. This work could not have been completed without the support









of Jolo C. M. Cassar and Luis A. B. Gusmao from AQUAMODELO, Consultoria e

Engenharia Ltda., in Rio de Janeiro.

This work was made possible by financial support from CAPES, Brazil.











TABLE OF CONTENTS

ACKNOWLEDGMENTS...................................................................... iii

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

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

ABSTRACT........... ... ................................ ..................... ............ xvi


CHAPTERS


1 INTRODUCTION..................................................................................................... 1
1.1 Study Area and Problem Statement........................................................................ 1
1.2 O outline of Chapters........................................................................................... 6


2 DESCRIPTION OF THE AMAZON SHELF ENVIRONMENT................................... 8
2.1 Water and Sediment Discharge ............................................................................... 8
2.2 Tidal Flow ........................................................................................................ 9
2.3 Subtidal Flow .................................................................................................. 10
2.4 W ind and W aves............................................................................................. 10
2.5 Amazon Plume and Salinity Distribution ............................................... .......... ... 11
2 .6 D ata Set................................................................................................................ 14


3 FORMULATION OF 1-D VERTICAL MODULE FOR FINE SEDIMENT
TRANSPORT MODELING................................................................................. 19
3.1 Governing Equation........................................................................................ 19
3.2 Sediment Characteristics............................................................................... 20
3.2.1 Introduction............................................................................................. 20
3.2.2 Sediment composition and cation exchange capacity.................................... 21
3.2.3 Particle size............................................................................................. 23
3.2.4 Flocculation and settling velocity ........................................... .......... .... 25
3.2.5 Settling experiments................................................................................ 27
3.2.6 V iscosity ................................................................................................ 32










3.2.7 Shear strength ......................................................................................... 35
3.2.8 Permeability and effective stress .............................................. .......... 38

3.3 Vertical Flow Structure................................................................................... 42
3.3.1 G general ................................................................................................... 42
3.3.2 Tidal boundary layer approach ............................................... ........... .... 43
3.3.3 Fluid cinematic and eddy viscosities ........................................ ........... .. 45
3.3.4 A model for laminar boundary layer....................................... ........... .... 51
3.3.5 Shear stress from measured velocity profiles............................................. 54
3.3.6 M ass diffusivity.......................................................... ................................ 59

3.4 Bottom Boundary Condition......................................................................... 67
3.4.1 Bed level definition............................................................................... 67
3.4.2 Erosion mechanisms and erosion rate....................................... ........... .. 69
3.4.3 Bed shear strength............................................. ............... .... .. 80
3.4.4 R ate constant................................ ........... ............................................... 81
3.4.5 Deposition and consolidation .............................................................. 83



4 MUD DYNAMICS IN AMAZON ESTUARY.............................................................. 87
4.1 Introduction .................................................................................................... 87
4.2 Long Term Processes: Accumulation Mechanisms......................... ...... 89
4.2.1 General observations.................................................................................. 89
4.2.2 Salt wedge trapping mechanism ............................................. ........... .... 89
4.2.3 Tidal trapping.......................................................................................... 90

4.3 Short Term Processes: Local Balance in the Water Column .................................. 93
4.3.1 Some dynamical features of the suspension over the water column.............. 93
4.3.2 Lutocline dynamics.............................................................. 97
4.3.3 Wave effects ............................................... 101
4.3.4 Time scale of sedimentary processes......................................................... 107

4.4 Validity of 1-D Approach........................................ 109
4.4.1 Introduction......................................................................................... 109
4.4.2 A dvective transport.................................................................................. 110
4.4.3 Turbidity current.................................................... 114

5 TRANSPORT MODEL......................................................................................... 117










5.1 P ream ble............................................................................................................. 117
5.2 Main characteristics of the numerical model ..................................................... 117
5.3 Numerical experiments ....................................................................................... 120
5.4 Modeling Quiescent Settling ............................................................................... 124
5.5 Amazon Shelf Concentration Profiles ............................................................... 129
5.5.1 Objective............................................................................................... 129
5.5.2 Bed level and bottom boundary condition.................................................. 129
5.5.3 Settling velocity .......................................................................................... 131
5.5.4 Mass diffusion coefficient......................................................................... 132
5.5.5 Vertical component of the flow velocity.................................................... 132
5.5.6 Sediment concentration time series............................................................ 133



6 GENERAL OBSERVATIONS, SUMMARY AND CONCLUSIONS....................... 138
6.1 General Observations.......................................................................................... 138
6.2 Summary and Conclusions.................................................................................. 140





REFERENCES.................................................................. ......... 143


BIOGRAPHICAL SKETCH.............................................................. 155












LIST OF FIGURES


Figure Page

1 Velocity, suspended sediment concentration, and sediment flux profiles in the
Amazon Shelf during high discharge at station OS2 (from Kineke, 1993). ...............4


2 Amazon water discharge from daily estimates at Obidos,...................................... 8


3 Seasonal sea surface salinity (psu, i.e., practical salinity units) in the Amazon
Shelf region (from Kineke, 1993)................................................. ............ ..... 13


4 Bottom salinity (psu) in the Amazon Shelf region.............................. ............ .. 14


5 Cross-shelf salinity transects at the river mouth for (a) spring and (b) neap tides
(from K ineke, 1993) ......................................................................................... 15


6 Topographic map of the Amazon continental margin with locations of
AMASSEDS anchor stations (from Kineke, 1993) ............................................. 17


7 Size distribution of the Amazon Shelf bottom sediment for samples 3227 and
3230........................................................................................................ . . ............ 24


8 Size distribution offlocs determined by image analysis of plankton camera
photographs at 35 m depth and high river discharge (from Kineke, 1993)............. 26


9 A schematic representation offlocculation, sedimentation and consolidation
(from Im ai, 1981).................................................................................................... 28


10 An example of temporal evolution of concentration profile in the settling column ..... 31


11 Settling velocity versus concentration obtained from settling experiments through
Equation (7) (small symbols) and from free settling stage (larger black dots). ......... 32










12 Flow behavior of Amazon sediment suspension at different densities (from Faas,
1986). .............................................................................................................. . 34
13 Apparent viscosity vs. shear rate for a core sample from the Amazon Shelf, as a
function of density (from Faas, 1985)............................................... ........... .... 34


14 Schematic of shear stress versus shear rate flow curve, and definition of the upper
B ingham yield stress. ......................................................................................... 36


15 Yield shear stress versus concentration for Amazon Shelf mud (from Dade, 1992,
Table 6.7 and Faas, 1985, Figure 3).................................................. .......... ..... 37


16 Shear strength versus concentration for the Amazon Shelf bed sediment (1) for
incipient motion and (2) for bed destruction. ....................................... ............ 38


17 Effective stress as a function of local density (from Toorman and Huysentruyt,
1994) ......................................................................................................... . .......... 40


18 Effective stress versus void ratio data taken from experiments reported in the
literature (Alexis et al., 1992).......................................................................... 41


19 Permeability versus void ratio data taken from experiments reported in the
literature (Alexis et al., 1992)........................................................... ............... 41


20 v (circles) and vf (asterisks) median values for the tidal cycle, from Equation (25)
and (11), respectively. ........................................................................................ 46


21 Velocity profiles recorded at anchor station OS2 (3419).......................................... 47


22 Boundary layer velocity profiles for increasing and decreasing viscosity with
depth ............................................................................................................... . 49


23 Tidal Reynolds number [Equation (29)] vs. depth............................................... 50









24 Observed (discrete points) and calculated [Equation(30)] velocity profiles over
two tidal cycles recorded at anchor station OS1 (low river flow-as4434)................. 52


25 Absolute velocity errors arising from differences between measurements and
Equation (30) (asterisks) and measurements and logarithmic fit (circles)............... 53


26 Observed velocity (dotted line) and shear stress (solid line) over two tidal cycles
for anchor stations OS1 and CN. ................................................................... 56


27 Observed shear stress [dotted line Equation (35)] and calculated shear stress
[solid line Equation (31)] over two tidal cycles for anchor stations OS1 and
CN ............................................................................. .................................... 57


28 Depth variation of the tidal eddy viscosity at anchor station CN (2428) (dots) and
eddy diffusivity calculated according to Equation (37).......................................... 60


29 Tidal median values of the gradient Richardon number considering density
affected by salinity and temperature (solid line), and salinity, temperature and
sediment concentration (dotted line).............................................. ............ .... 61


30 Gradient Richardson number as a function of depth for anchor stations CN
(2428) and O S2(2418)...................................................................................... 64


31 Tidal median values of the stratification damping function [Equation (41)] versus
depth for anchor stations CN (2428) and OS2 (2418) ............................................ 65


32 Stratification damping function versus depth over the tidal cycle for anchor
station C N (2428).................................................................................................... 66


33 Time-variation of water depth at anchor station CN (2428)...................................... 67


34 Tidal median values of shear stress versus depth for anchor station RMi.................. 72









35 Sediment flux (at z=0.25m) and current velocity for anchor station OS1 (1154).
Top: time-series of sediment flux and velocity. Bottom: sediment flux vs.
velocity after phase adjustment.......................................... ............................ 74


36 Sediment flux (z=0.25m) and current velocity for anchor station OS2 (2418).
Top: time-series of sediment flux and velocity. Bottom: sediment flux vs.
velocity after adjusting for the phase. ................................................................. 75


37 Sediment flux (z=0.25m) and current velocity for anchor station CN (2428). Top:
time-series of sediment flux and velocity. Bottom: sediment flux vs. velocity
after adjusting for the phase................................................. .......................... 76


38 Sediment flux (z=lm) and current velocity for anchor station CN (2428). Top:
time-series of sediment flux and velocity. Bottom: sediment flux vs. velocity
after adjusting for the phase.................................. ......................................... 77


39 Sediment flux (z=lm) and current velocity for anchor station RMo (3455). Top:
time-series of sediment flux and velocity. Bottom: sediment flux vs. velocity
after adjusting for the phase................................................. .......................... 78


40 Salinity and sediment concentration time-series for anchor station RMo (2405)....... 79


41 Time-series of sediment flux and current velocity for anchor station RMo (2405)...... 79


42 Time-series of sediment flux and current velocity for anchor station OS1 (4434)....... 80


43 Observed (dotted line) and calculated (solid line) sediment fluxes at an elevation
of 0.25m for anchor stations OS2 (2418) and CN (2428)..................................... 82


44 Turbidity maximum caused by residual circulation (from DYER, 1986) .................. 90


45 Sediment trapping due to tidal asymmetry (from ALLEN et al., 1980)................... 91









46 Examples of water levels and current velocities in the Amazon Shelf area. (a)
OS1 anchor station at the Open Shelf Transect and, (b) RMi anchor station at
the River Mouth Transect (see Figure 6 for locations) ........................................... 94


47 Distribution of sediment accumulation rate (from KUEHL et al. 1986). Contours
are in cm /yr ................................................................................................... . 95


48 Vertical concentration and velocity profiles in high concentration estuarine
environments (after Mehta, 1989).............................. ................................. 97


49 Settling velocity and settling flux as functions of concentration (from Ross and
M ehta, 1989).................................................................................................... 98


50 Suspended sediment concentration profiles (solid line), and water density
gradients including salinity and temperature effects (circles), for anchor stations
in the Amazon Shelf for cases of strong salinity stratification.............................. 100


51 Suspended sediment concentration profiles (solid line), and water density
gradients including salinity and temperature effects (circles), for anchor stations
at the Amazon Shelf for cases of weak salinity stratification................................ 101


52 Influence of waves on shear resistance to erosion ofkaolinite beds in flumes
(from M ehta, 1989). .............................................................................................. 102


53 Time-series of a) pressure and b) velocity measured at OS3 anchor station while
the profiler was positioned on the seabed. The sediment concentration at this
level was about 300 g/l (from Kineke, 1993)....................................................... 105


54 Depth, hourly current speed and sediment concentrations at the GEOPROBE
deployment (from Cacchione et al., 1995)........................................................... 106


55 Hourly wind velocity recorded at Macaph, Amap................................................... 106


56 Current meter, optical backscatter output (OBS) and near-bed orbital velocity at
St. Bees deployment, Irish sea, UK (from Aldridge and Rees, 1995). .................... 108









57 Maximum isoline elevation reached during the tidal cycle versus tidal range (both
made dimensionless by dividing by the local depth) for the 18 anchor stations...... 109


58 Comparison between measured (dashed lines) and simulated (solid line)
suspended sediment concentrations in the Weser estuary within the zone of
turbidity maximum (from Lang et al., 1989). Only advection was simulated. ........ 111


59 Current speed (dashed line) and optical backscatter output (solid line) measured
outside of Morecambe Bay, Irish Sea, UK (from Aldridge and Rees, 1995)........... 112


60 Concentration profiles (left) and time series of salinity and concentration (right)
at anchor station RM i (2444)................................................................................. 114


61 Flood and ebb currents in the Amazon Shelf and residual sediment density
induced currents at anchor stations CN (2428) and OS1 (4434)........................... 116


62 Numerical simulation of tide-induced resuspension with a uniform settling
velocity (W,=lmm/s) and a depth-independent, time-dependent diffusivity.
Hourly concentration profiles over a tidal cycle................................................... 121


63 Simulations similar to Figure 62, but with a smaller settling velocity
(W,=0.5mm/s). Hourly concentration profiles over a tidal cycle.......................... 122


64 Comparison of results for different particle masses. Solid lines: Cm=0.005g/l,
asterisk and circles: C jn=0.02g/l.. ..................................................................... 122


65 Same simulation as in Figure 63 with a constant settling velocity (W,=0.Smm/s),
but a with a non-uniform diffusivity (set equal to zero from 3.5m level up to
surface). Hourly concentration profiles over a tidal cycle .................................... 123


66 Same simulation as in Figures 62 and 63, but with a non-uniform settling
velocity. Hourly concentration profiles over a tidal cycle .................................... 124


67 Observed (dotted line) and modeled (solid line) sediment concentration profiles
obtained in settling experiments in quiescent conditions...................................... 126









68 Observed (dotted line) and modeled (solid line) sediment concentration profiles
with the inclusion of effective stress [Equation (51)]............................................. 128


69 Bottom sediment flux based on measurements at anchor station CN and
calculated by the model, according Equation (38)................................................ 130


70 Dotted lines define the range of the settling velocity considered in the model. ......... 131


71 Mass diffusion coefficient profile included in the model........................................ 133


72 Sediment concentration profiles at anchor station CN (rising river flow- as2428),
measured (solid line) and simulated (circles)....................................................... 134


73 Hysteresis in sediment concentration at 3.25m level at anchor station CN (2428),
measured (top) and simulated (bottom). .............................................................. 136











LIST OF TABLES


Table Page

1 Summary of Amazon Shelf data ........................................................................ 18


2 Cation exchange capacities of three common clay minerals, in meq/100g .................. 22


3 Exchangeable cations and cation exchange capacities for Amazon samples, in
m eq/100g ...................................................................................................... . .......... 23


4 Settling column test conditions .................................................. ........................ 30


5 Tidal mean and maximum shear stresses and shear velocities at the anchor stations... 58










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

A PRELIMINARY EXAMINATION OF
AMAZON SHELF SEDIMENT DYNAMICS

By

Susana Beatriz Vinzon

August 1998

Chairman: Ashish J. Mehta
Major Department: Coastal and Oceanographical Engineering

Experimental data on flow and sediment dynamics on the Amazon Shelf,

previously obtained under AMASSEDS (A Multidisciplinary Amazon Shelf Sediment

Study), have been interpreted with the help of a modeling approach to examine the

vertical structure of flow-sediment interaction. The model solves the sediment transport

equation following the particle tracking method. In this model, sediment settling velocity

is considered to be concentration dependent, and erosion flux function is fitted using in

situ near-bed measurements of velocity and sediment concentration. Salt stratification

damping of turbulence is also included, and the shear strength-bed density relationship

required for the calculation of the erosion flux is derived from laboratory analysis of

Amazon sediment samples.

Measured time-series of suspended sediment concentration are compared with

model-simulations in order to better understand the sedimentary processes occurring in

the water column. It is found that flow-sediment interaction in the bottom one meter of

the water column can be described using an oscillatory viscous flow model. The reason

for this behavior is the significant turbulence-damping role of the high density fluid










mud-like suspension that dominates the lower water column. For the remainder of the

water column, stratified turbulent flow conditions can be assumed.

Long-term accumulation mechanisms as well as short-term processes related to the

tides are examined in the context of the vertical transport processes. As observed in the

AMASSEDS study, the findings of the present investigation corroborate the view that a

combination of density-driven estuarine circulation, salt-induced stratification, and

flocculation enhance the trapping of sediments in fluid mud over the long term. On the

other hand, short-term, namely tidal, signatures indicate that sediment dynamics over

this time scale is strongly influenced by resuspension events governed by tidal forcing.

Sediment spreading over the shelf appears to be dominated by transport processes

which occur within the bottom 2m of the water column. Further measurements are

required to assess fully the role of fluid mud advection within this layer as the key

component of shelf sediment transport in this area. It is also likely that swell activity

contributes to the behavior of the oscillatory boundary layer and therefore to fluid mud

dynamics over the shelf.


xvii














CHAPTER 1
INTRODUCTION


1.1 Study Area and Problem Statement

There are wide ranging engineering problems associated with the transport of fine

sediments. Ship channel filling, and sedimentation problems along quay walls, under

pontoons or in shadow zones in harbors, are well known problems for many port

authorities. Water quality related to the transport of fine sediments is another

engineering problem of increasing interest. The properties of clay-sized sediments,

including large specific area of the particle, net negative electrical charge on their

surfaces, and cation exchange capacity, facilitate the sorption of contaminants (Hayter

and Mehta, 1983). Thus, the movement of fine sediments must be understood in order to

account for contaminant transport and fate.

Amazon River, having by far the largest river discharge on the planet, carries up to

its mouth a great amount of sediment, which is mainly composed of fine sediments.

Fresh and seawater mixing occurs on the Amazon Shelf, far from the river mouth in a

very dynamic macro-tidal environment. High concentration of fine sediment can be

found over an extensive area on the shelf, and a complex interaction between sediment

and hydrodynamics occurs. Detailed measurements of sediment concentration profiles

made recently, and available for further studies, offer the opportunity to take a close look

at the mechanisms governing sediment transport in high concentration environments.









Improving our understanding of the dynamics of these environments is a first step

toward improving our ability to model the relevant processes, the ultimate objective of

this work.

A comprehensive research program of sediment transport on the Amazon shelf

occurred from 1989 to 1991 as part of the AMASSEDS project. AMASSEDS (A

Multidisciplinary Amazon Shelf Sediment Study) was an interdisciplinary research

group, which developed geological, chemical, physical and biological studies undertaken

by oceanographers from Brazil and the United States (AMASSEDS, 1990).

As part of the AMASSEDS project, a suspended sediment transport study was

designed and carried out to measure the flow and suspended sediment characteristics

throughout the water column over several time scales: semidiurnal, fortnightly and

seasonal (Kineke, 1993). Four cruises were undertaken to cover seasonal variability in

the river discharge, wind stress, wave climate and transport of the North Brazil Current.

Profiling from an anchored ship was done to account for the semidiurnal time scales.

Profiling was repeated during both spring and neap tides. This data set was available for

the analysis made in the present work. Also, a coastal profiling study was carried out (in

shallow waters from 2 to 10m), and an instrumented bottom tripod (GEOPROBE) was

deployed in 63m depth and measured boundary layer parameters continuously over 19

days.

Many noteworthy works have reported the main results and findings of the

AMASSEDS project (Kineke, 1993, Beardsley et al., 1995, Cacchione et al., 1995,

Kineke and Sternberg, 1995, Kuehl et al., 1995, Geyer, 1995, Lentz, 1995, Nittrouer et









al., 1995, Trowbridge and Kineke, 1994, among others). Most of these studies are

reviewed in Nittrouer and DeMaster (1986).

One of the more important findings during the AMASSEDS project was the record

of thick layers of mud, which can reach up to 7m in the inner and middle shelf, covering

an extensive region (Kineke, 1993). Careful profiling of current velocity, salinity,

temperature and sediment concentration was carried out over the shelf. The lowermost

measurements were 0.25m above the level where the profiler rested. An interesting plot

of data related to sediment transport is shown in Figure 1, which gives instantaneous

vertical profiles of velocity, concentration and flux (Kineke, 1993). The maximum flux

occurs in the lower 2m, while the suspended sediment flux in the main water column and

surface plume is 1-3 orders of magnitude less. This demonstrates how critical it is to

measure the sediment transport rate as a function of elevation and to model velocity and

sediment concentration distributions near the bottom.

In this study it is intended to formulate a model which accounts for, in the simplest

way, the characteristics and processes that occur in the water column including the near-

bed layers responsible for the larger part of sediment transport. Also, it is sought to bring

further insight into the understanding of the processes responsible for the genesis and

dynamics of sediment concentration profiles in the Amazon Shelf area.

Numerical modeling is one of the most useful prediction techniques meant to solve

hydrodynamic and transport problems in estuaries. Fine sediment transport models solve

the mass transport equation for suspended sediment, and different approaches can be

found in the literature, according to the problem of interest. A review of numerical

models on fine sediment transport can be found in Mehta et al. (1989a) and Mehta et al.










(1989b). With the continuous reduction of computational costs, three-dimensional

models are more and more commonly used (Sheng, 1986; Nicholson and O'Connor,

1986; Lang et al., 1989). Density stratification effects on turbulence and density driven

currents, rheologically controlled near-bed layers in high concentration zones, and

advection of density gradients are some of the aspects in modeling which require three-

dimensionality. However, the use of a simple suitable model to represent the processes

occurring in the water column, in order to reach a better understanding of the physics of

sediment motion in the Amazon Shelf, is the "track" chosen in this work.



14 14 14

12 -- -- 12 ,, -- -I- 12 ( _,--- -- -

S10 -- - 10 - -- 10 -- -- -

4 .--- -- 8 -- -- -




-4 4

2 -- 2 2- ---

o 0 0
0.8 1 1.8 0.01 1 100 0.01 1 100
velocity (Mn) concentraton (gil) edimert flux (km)

Figure 1: Velocity, suspended sediment concentration, and sediment flux profiles in the
Amazon Shelf during high discharge at station OS2 (from Kineke, 1993).


Fine sediment transport models are very demanding of numerical methods. The

quantities usually involved, like settling velocity or diffusion, vary by several orders of

magnitude over the physical domain. In the vertical dimension, strong sediment









concentration gradients can be observed, and these raise severe problems in solving the

transport equation. An alternative numerical method based on what is called the particle

tracking technique is introduced in the present work in order to attempt to overcome

common problems found with the usual methods. Particle tracking methods are being

used increasingly in transport problems, and their introduction into sediment transport

problems may be very useful. The main characteristics of the method are described in

the present work, and its advantages and disadvantages are discussed in order to look for

future improvements.

The choice of the numerical method represents an important first step in the

modeling process, since it must ensure that the numerical results correspond to the

equivalent mathematical model. It should be noted, however, that mathematical models

are always restricted. They are mere representations of physics which require a

knowledge of the underlying processes and of the scales associated with them. Thus,

before the presentation of the proposed model, a comprehensive examination of the

relevant mechanisms which occur in high concentration fine sediment environments is

presented.

It should be noted that one of the conclusions arrived at by Kineke (1993) and

Kineke and Sternberg (1995), concerning the mechanism that explains the presence of

thick layers of fluid mud in the Amazon Shelf, is

The combination of density-driven estuarine circulation, salt induced stratification,
and flocculation enhance the trapping of sediments in fluid muds. Although tidal
currents are very strong on the Amazon shelf and surface waves probably are important
in maintaining fluid muds as a suspension, fluid muds mainly are not the result of
resuspension or erosion from the seabed, but the result of enhanced settling flux. (Kineke
and Sternberg 1995, p.227)









If correct, this assertion precludes the possibility of there existing a local

sedimentary flux balance which could explain the observed sediment concentration

profiles. According to this conclusion, modeling for representing the processes in the

water column must be thought of only in a two- or three-dimensional manner. It is

hypothesized here, that density-driven circulation is a mechanism which acts over long-

term scales, of several months, and may play an important role in the turbidity maximum

formation at the Amazon Shelf. Salinity-induced stratification may exert influence over

the tidal time scale due to the damping of the turbulence. However, the observed

suspended sediment concentration profiles, and particularly the quantity of sediment

found in suspension, can be the result of local sediment flux balances, which can

therefore be explained in a simple way by using a one-dimensional vertical model.




1.2 Outline of Chapters

A general description of the physical environment and a brief description of the

data set are provided in Chapter 2. In Chapter 3 the mathematical model for sediment

transport in the water column is described. A characterization of the native sediments

was necessary for comparative purposes, and also to obtain the sediment dependent

functions to be included in the model, i.e., for settling velocity, for the viscosity of the

water-sediment mixture, for bottom shear strength and for consolidation. This aspect is

presented in Section 3.2. Flow velocity and shear characteristics are also needed for

modeling purposes. Thus, a preliminary analysis of the measured velocity profiles is









provided in Section 3.3, which highlights the main features of the flow. In Section 3.4.2

an estimate of the erosion rate, also a model parameter, is provided.

A discussion of the several long and short-term mechanisms underlying the

transport of fine sediments related to the Amazon Shelf is presented in Chapter 4. The

importance of short period wave and tidal action mechanisms is addressed in Section

4.3.3. At the end of this Chapter, in Section 4.3.1, some of the main features related to

sediment vertical profiles are noted.

In Chapter 5 the numerical model is described briefly. After the presentation of a

few examples showing the response of the model to some of the important modeled

processes, settling experiments in quiescent conditions are reproduced with the model.

The most important results relative to the modeling of a time series of sediment

concentration on the Amazon Shelf are presented and discussed in section 5.4. Finally,

conclusions are provided in chapter 6.














CHAPTER 2
DESCRIPTION OF THE AMAZON SHELF ENVIRONMENT


2.1 Water and Sediment Discharge


Draining an area of 6.9 million km2, the Amazon River is the largest riverine

freshwater source to the oceans (Kineke 1993, Gibbs, 1970). With an average discharge

of 1.8x105 m3/s, it exhibits strong seasonal variations. Figure 2 shows daily estimates of

Amazon River discharge for 1989-1991 based on stage data from Obidos, with an

observed maximum discharge in May of about 2.4x105 m3/s, and a minimum discharge

in November of 0.8x105 m3/s (Figueiredo et al., 1991).


E 1.8

% 1.5
e
g 1.2
*1
0.9

0.6


1989 1990 1991

Figure 2: Amazon water discharge from daily estimates at Obidos,
from Figueiredo et al. (1991).









Relative to the sediment discharge of the Amazon River, Meade et al. (1985)

reported a mean value of 11-13x108 tons/year. Richey et al. (1986) measured sediment

discharge at several locations along the Amazon River. At Obidos, the sediment flow

varied from 2.5 to 19.2x108 tons/year, with minimum and maximum recorded

concentrations of 0.09 and 0.35 g/l, respectively. Most of the suspended material

transported was reported to be fine (<0.063 mm). Gibbs (1967) also reported that 85-

95% of the sediment carried out to the mouth of the Amazon River was silt- and clay-

sized.

In addition to the large input of fresh water, strong tidal currents and wind-driven

currents contribute to one of the most energetic continental shelf environments in the

world.




2.2 Tidal Flow

The tidal forcing is strong, with a range of up to about 5m (Gibbs, 1970), which

generates strong currents with a large fortnightly variability. The dominant tidal

constituent, the M2 (12.42 h), plus other principal semidiurnal constituents, the S2 (12.00

h) and the N2 (12.66 h), account for about 85% of the total tidal elevation variance, and

are the most energetic tides in this region. Beardsley et al. (1995) observed that M2 tidal

currents are oriented primarily across the local isobaths over the shelf.

Over the adjacent shelf north of Cabo Norte, the M2 tide approaches a partial

standing wave, with large amplitudes near the coast due to resonance. One consequence

of the enhanced tide within the Cabo Norte-Cabo Cassipore embayment is the formation









of large tidal bores, locally known as 'pororocas'. Near the Amazon River mouth, the M2

tide propagates as a progressive wave, with decreasing amplitude in relation to the

vertical structure of the M2 tidal current. Beardsley et al. (1995) observed a small

ellipticity with a clockwise rotation. The M2 phase increased with height above bottom,

with flood at the bottom leading that at the surface by about 1 hour.




2.3 Subtidal Flow

Subtidal currents are vertically sheared, moving along-shelf toward the northwest

(Limeburner and Beardsley, 1995). With near-surface currents that reach speeds of 1.5

m/s and near bottom velocities less than 0.2 m/s (Geyer et al., 1991), these currents show

a high degree of coherence with the along-shelf wind stress (Lentz, 1995). The influence

of the North Brazilian Current is not completely determined, but there is evidence that it

could help explain the drift of the Amazon plume in the opposite direction to most

buoyant plumes, with the coast on its left, in the Northern Hemisphere.



2.4 Wind and Waves

The trade winds blowing over the Amazon shelf do not show monsoon-like

reversals of the prevailing wind direction, or hurricanes and tropical storms, as at other

similar latitudes. According to Nittrouer et al. (1995), "winds generally strengthen in

January-March while blowing onshore from the northeast, and weaken and blow along-

shelf from the southeast during June to November". This wind climate causes locally

generated waves that are dominated by short periods coming from the eastern quadrant









(significant height of 1-2 m less than 4m 99% of the year, and dominant periods of 6-7

sec less than 10sec 95% of year, from Kineke, 1993). Nevertheless, observations carried

out in the area along the coast of Ceari (40 S) indicated long period (up to 20 s) swell-

type waves coming from a more northerly direction from December to March. Melo et

al. (1995) asserted that these waves might have as a distal source, namely the extra-

tropical storms in the North Atlantic.




2.5 Amazon Plume and Salinity Distribution

The Amazon River discharge is so large that seawater never enters the river mouth.

The riverine water meets the seawater on the shallow continental shelf 100-200 km

seaward of the mouth (Geyer, 1995). This shelf is oriented in NW-SE direction and

extends from shore to the 100m isobath, between the latitudes of about 0 and 5N.

The Amazon River plume follows the coast northwestward from the river mouth.

Sea surface salinity maps (Figure 3) show the plume spreading in the vicinity of the river

mouth and extending northwestward along the shelf. The lowest salinity in the vicinity

of the river mouth is found near the North Channel, suggesting that this is the strongest

source of fresh water.

Lentz and Limeburner (1995) describe the behavior of the riverine plume as

follows. "The Amazon River discharge forms a plume of low-salinity water that spreads

from the river mouth at the equator, 5m thick layer of relatively fresh water. The plume

intersects the bottom sea water between the 10m and 20m isobaths forming a bottom

front that appears to be locked to the local bathymetry" (Figure 4). Gibbs (1970)









suggested that the North Brazilian Current (referred to as Guiana Current in his work)

carries the plume out into the ocean, while the prevailing trade winds and waves result in

a steady longshore current flowing northwestwardly along the shore. Lentz (1995)

pointed out that the general tendency of the Amazon plume to flow northwestward is

probably related to the North Brazilian Current, but he also observed large variations in

plume width, salinity and currents of time scales of days to weeks due to the local wind

stress. Lentz and Limeburner noted the importance of local winds, asserting that

southeastwardd winds may impede or even block the normal northwestward transport of

fresh water resulting in a pool of fresh water. This process, more frequent in spring,

when the river discharge is large and southeastward winds are most likely, may have

important implications in sediment supply since it results in both longer residence times

and broader areal extent in the vicinity of the river mouth".

Spring-neap variations in vertical density structure on the Amazon shelf have been

observed (Geyer, 1995). During neap tides the water column is strongly stratified,

resembling an estuarine salt wedge. During spring tides, however, stratification is greatly

reduced resembling a partially mixed estuary. In all cases, surface and bottom waters

flow in the same direction during the nearly all-tidal cycle. Figure 5 shows two cross-

shelf salinity transects for spring and neap tides observed at the river mouth. Different

salinity structures in different tidal regimes are apparent.











































Figure 3: Seasonal sea surface salinity (psu, i.e., practical salinity units) in the Amazon
Shelf region (from Kineke, 1993).










354 -



25 8

20-




5 -

0
0 20 40 60 80 100
water depth (m)

Figure 4: Bottom salinity (psu) in the Amazon Shelf region
(from Lentz and Limeburner, 1995).



2.6 Data Set

The data set examined in this study is part of data collected during the

AMASSEDS study (AMASSEDS, 1990). As noted in chapter 1, this program was a

multi-component U.S./Brazil program meant to study physical, geological, and

geochemical processes that control sediment transport and accumulation in the Amazon

Shelf region. The physical oceanographic component included four regional shipboard

Acoustic Doppler Current Profiler (ADCP) and Conductivity-Temperature-Depth (CTD)

surveys timed to sample the shelf during four stages of the Amazon River discharge, an

instrumented bottom tripod deployment (GEOPROBE), and a coastal study. Figure 6

shows the sampling locations.

Measurements were taken seasonally, according to the river stages shown in

Figure 2 along 6 cross-shore transects, at 19 anchor stations with hourly profiles during











one or two tidal cycles, and during coastal profiling, totaling more than 600 profiles.

Synchronous profiles of current, sediment concentration, salinity and temperature over

the tidal cycle were available for the present study.


13 16


17 Is


0 1








30-




45
so 75 100 125 13
Pirran ~I I hn


50 73 100 125 150
(b) Dizmm. Offshom =m)
Figure 5: Cross-shelf salinity transects at the river mouth for (a) spring and (b) neap tides
(from Kineke, 1993).









A detailed description of the collected velocity profiles and data analysis has been

given by Kineke (1993). For completeness of treatment, the main features of the

measurement procedure are reproduced here. The measurements were performed with a

profiling system which included an optical suspended sediment sensor, a

water/suspended sediment pumping system to collect samples, a CTD (i.e.,

Conductivity-Temperature-Depth) sensor, an electromagnetic current meter and a

compass. The profiles were continuous from the sea surface to -0.25m above the seabed.

The profiler was lowered through the water column at -10m min.-' with a sampling rate

of -0.85 Hz, thus yielding a scan every 15-18cm. The up-and-down casts were bin-

averaged in 0.3m bins, and the data were converted to height above the bottom in even-

spaced intervals (0.25m). The bottom reading elevation (0.25m) was an averaged value

over the time the tripod was on the seabed. In addition to bin-averaging, for the velocity

measurements a 17-term cubic/quadratic smoothing function was used to filter out some

of the high frequency oscillations.

Measurements were referenced to the height above the bed where the bed was

considered to be defined by the limit of downward movement of the suspended-sediment

profiler (Kineke and Sternberg, 1995).

Table 1 provides a summary of the main characteristics of each time series

recorded at the 18 anchor stations, identified by a name with reference to its location

(showed in Figure 6) and a number. Note that mean and minimum bottom velocities

denote values recorded at the lower-most elevation, at z = 0.25m, considering z = 0 to be

the resting elevation of the profiler legs. Isoline elevations indicate the maximum









elevation reached by concentrations of 0.lg/1 or lg/l over the tidal cycle. Total mass

denotes the mean total mass in suspension per unit area over the tidal cycle.


Figure 6: Topographic map of the Amazon continental margin with locations of
AMASSEDS anchor stations (from Kineke, 1993).
















ell4 -4 1~O -4 0 r


00 Oo.rR0 W0 CD ) W C>cQ )0


"i --0 0 66


~~ o o~ ~V)






~0 0 6 6 4 ,j C4-,t Q

~e







t- tn "t C4 0C4


00
4)~~~~c. rfNQ ( k o 0 k 0 -t qC









NO 0% 0 f 00 N. en IfR \R \R W t- eq CI '.0




C-4e~ 00 'fNoo e c O C 00 0 Q 00 e t O






W)- en I C7 en t- ON '~













CHAPTER 3
FORMULATION OF 1-D VERTICAL MODULE FOR FINE SEDIMENT
TRANSPORT MODELING



3.1 Governing Equation

The governing equation for the vertical suspended sediment transport is the

conservation of mass,

8C \(1)
= -C(W -w) + e,


where C is the suspended sediment concentration, W. is the settling velocity, e, is the

mass diffusion coefficient, andw is the vertical component of the flow velocity. This last

variable is usually neglected, but it may be important where noticeable bathymetry

variations occur, or where tides have high ranges, which is the case in the Amazon Shelf

environment. Vertical velocity values are low, but they can be of the order of the settling

velocity of fine sediments. The vertical velocity was estimated as (Dean and Dalrymple,

1991)

z ah (2)
w h-
h t

where h is the water column depth. Equation (1) requires two boundary conditions, one

at the free surface and another at the bottom level. At the free surface, the boundary

condition corresponds to no net sediment flux. As for the bottom condition, the

conceptual model assumes that bed-suspension sediment exchange occurs only in one









direction, i.e. erosion or deposition. In other words, erosion and deposition are not

considered to occur simultaneously. For erosion, i.e., when the flow bed shear stress, To,

is greater than the shear strength of the overlying bed layer, t,, a linear rate of erosion is

prescribed according to

(3)
z=0, To>r, E=M\ --1(


where M is an empirical erosion rate constant.

When no erosion is occurring, a deposition rate is prescribed according to

z=0, To D = C(W, w) (4)

To solve Equation (1) with the corresponding boundary conditions it is necessary

to prescribe the settling velocity, mass diffusivity coefficient, flow shear stress, bed

shear strength and the erosion rate constant. These parameters depend on the sediment

and flow characteristics, which is the subject matter of this chapter.



3.2 Sediment Characteristics


3.2.1 Introduction
Factors characterizing the physico-chemical properties of the Amazon Shelf

sediment including mineralogy, dispersed particle size, cation exchange capacity and

organic content, are important for comparative purposes. These properties were

determined for two samples obtained from the shelf bottom, and were available for this

work (samples numbers 3227 and 3230). Other properties directly involved in sediment

transport modeling, such as settling velocity, viscosity and shear strength, were also









determined in laboratory, or derived from previous studies of Amazon shelf mud (Faas,

1985, Dade, 1992).




3.2.2 Sediment Composition and Cation Exchange Capacity
The geochemistry of the sediment discharged by the Amazon River is controlled

by the weathering and erosion processes in the mountainous Andes regions of Bolivia

and Peru (Gibbs 1967). Mineralogical composition, organic content and the cation

exchange capacity (CEC) were determined for the two mentioned bottom sediment

samples, in the Department of Soil and Water Sciences of the University of Florida.

Analysis by X-ray diffraction (XRD) was conducted using a computer-controlled

diffractometer. Clay minerals identified from XRD patterns (Whittig and Allardice,

1986) were preponderantly consisted of kaolinite and smectite. Non-clay minerals

included quartz and mica. The mineralogy found in these samples is consistent with that

reported by Barreto et al. (1975), cited in Dade (1992).

The percentage of organic carbon in the samples was determined using Acid-

Dichromate Digestion, with FeS04 tritation (Walkley and Black, 1934). The low

carbonate percentages found (0.81 and 0.83 % for the samples 3227 and 3230,

respectively) suggests poor biological activity, probably due to turbidity and anoxia,

which are known to be unfavorable for the growth of benthic organisms.

Organic matter, determined by loss of ignition (D2974-87 of ASTM, 1987) was

3.0 and 3.1 % for samples 3227 and 3230, respectively. Using the same technique, Dade









(1992) and Faas (Dr. Richard Faas, Lafayette College, Easton, Pennsylvania, personal

communication), reported organic matter ranging from 3.3 to 10.3 %.

Clay minerals have the property of sorbing certain anions and cations and retaining

them in an exchangeable state. The most common exchangeable cations are Ca++, Mg+,

IH, K', NH4+ and Na+. Table 2 gives the CEC ranges for kaolinite, illite and smectite

(Grim, 1968). Note that kaolinite and smectite are also present in the Amazon samples.



Table 2: Cation exchange capacities of three common clay minerals, in meq/100g


The CEC for the Amazon samples were determined using the technique of

Extractable Bases (SOIL CONSERVATION SERVICE, 1992). The CEC values found

in this way are given in the Table 3.


Clay CEC


Kaolinite 3 5


Illite 10 40


Smectite 80-150









Table 3: Exchangeable cations and cation exchange capacities for Amazon samples, in
meq/100g
Sample Ca Mg K CEC

3227 9 12 3 24

3230 12 13 2 27



The Mg ion could have come from the marine source of the samples. If Mg is

reduced in the proportion of the Mg/Na ratio, typical of marine samples, then 5

meq/100g must be subtracted, so that the CEC would reduce to 19 and 22. Since CEC is

a measure of the degree of cohesion, it could be said that Amazon Shelf sediments

exhibit a medium or moderate degree of cohesion.




3.2.3 Particle Size
The dispersed particle size of the Amazon sediment was determined in the Coastal

Engineering Laboratory of the University of Florida using the bottom withdrawal tube

method (for a detailed description of this method see Vanoni, 1975), recommended for

fine sediments. The resulting size distribution curves for the two samples are shown in

Figure 7. The median size, d5o, is 2.5 pm and 3.7 pm, for samples 3227 and 3230,

respectively. Furthermore, the size is less than 10pm for 80% and 70% for the respective

samples. Dade (1992) reported Micrometrics Sedigraph grain size analysis of a

composite sample of dispersed Amazon mud, it being 90 percent less than 10 pm with a

median grain size 1.2 pm, which indicates a slightly smaller particle size than for the

samples analyzed here.














Sediment Size Distribution Amazon Sample 3227
100


80-- -



60-



9o ,
40 -- -


20 -


A I IL


diameter (pim)


Sediment Size Distribution Amazon Sample 3230
100
80 - -

S80-



60 -

40
40--- -- --



20 -----


n


diameter (prm)


Figure 7: Size distribution of the Amazon Shelf bottom sediment for samples 3227 and
3230.









3.2.4 Flocculation and Settling Velocity

Fine particles with diameters less than 2pm (clay) are plate-like having on their

surfaces ionic charges which creates forces comparable to or exceeding the gravitation

force, and cause the particles to interact electrostatically (Dyer, 1986). Consequently,

they do not act as separate or individual particles, but as aggregates of particles called

flocs. In fact, where in situ observations have been made, only rarely has unflocculated

material been found in the clay size range. Salinity modifies the surface ionic charges

by sorption of cations and the formation of an electric double layer. Interparticle

collisions causing flocculation result from Brownian motion, flow shear, and differential

settling velocities of particles (Einstein and Krone, 1962; Dyer, 1986). At low

concentrations a small amount of shearing enhances the collision potential of the

particles, but higher, shear-induced, collisions will tend to disrupt flocs rather than

promote their growth (Van Leussen, 1988; Kranck, 1981). Suspended aggregates often

include a certain amount of organic matter. Organic polymers released by algae and

bacteria are sticky and therefore significantly affect the process of aggregation. Studying

in situ aggregates, Brinke (1997) found that biological processes also affect the collision

efficiency, aggregate strength and density, thus causing seasonal variability of flocs

properties.

Due to flocculation the dispersed particle size is not useful for characterizing the

settling velocity of fine-grained sediment in the marine environment, and settling

velocities of flocs on the Amazon Shelf are unknown. In general, settling velocities of

the flocs can be computed from measured floc size and estimated floc density data,

through the Stokes' particle settling equation. Observations have shown that flocs have









an irregular shape, and are often joined biologically into 'stringers' (Fennessy et al.,

1994). Since the Stokes' equation was formulated for spheres falling within the viscous

regime, it should be used only as a rough approximation of the actual settling behavior in

the field environment.

Gibbs and Konwar (1986) measured floc sizes in the shelf region seaward of the

Amazon River mouth obtaining mean values of 50-100l m, and a maximum of 200nm.

During AMASSEDS, photographs of the in situ suspended materials were obtained

showing that these materials were dominantly present as flocs, with modal size in the

range of 200-500gm (Kineke, 1993). At the Open Shelf Transect, see Figure 6, flocs

with modal sizes of 400-6001im were observed (Figure 8).





I\








I;
100 -







1 'I


I ____...I._____
10 100 1000
Diameter wn)


Figure 8: Size distribution of flocs determined by image analysis of plankton camera
photographs at 35 m depth and high river discharge (from Kineke, 1993).









According to Krone (1986), there occurs "an order of aggregation" in formed flocs,

starting with the most compact and strong flocs (having densities of 1.16 1.27 g/cm3).

Increasing order of aggregation occurs by combination of flocs of the next lower order

resulting in weaker aggregates of decreasing density. Thus, floe density is inversely

related to floe diameter, decreasing with increasing order of aggregation. While Krones'

floc densities ranged between 1.07 to 1.27 g/cm3, Gibbs (1985) reported floe densities of

suspended sediments from the Chesapeake Bay ranging from 1.004 to 1.032 g/cm3, for

floe sizes of 50pm to 500pm. Kineke (1993) reported an estimated value of 1.08 g/cm3

for floe density during AMASSEDS measurements near the Open Shelf Transect.

Kranck and Milligan (1992) found floe densities in San Francisco Bay ranging from 1.04

to 1.48 g/cm3 for floe sizes of 500pm and 50pm. In recent in situ measurements of floe

size and settling velocity in the Tamar River estuary, England, Fennesy et al. (1994)

obtained floe densities ranging from 1.008 g/cm3 to 1.12 g/cm3 for 600gm to 50pgm

flocs. The corresponding settling velocity ranged between 0.1 to 2 mm/s.

Considering the size range for the Amazon Shelf sediment to be 50 to 600pm, with

corresponding densities of 1.3 and 1.01 g/cm3, the settling velocity according to Stokes'

equation would range between 0.02 to 2.8 mm/s.




3.2.5 Settling Experiments
A descriptive model of the processes occurring in a settling column is shown in

Figure 9 (Imai, 1981). In the initial stage flocculation occurs and no measurable settling

takes place. In the second stage, the flocs gradually settle and form a layer of sediment.









At first, when the sediment-water mixture is truly a suspension, i.e., at relatively low

concentrations, effective stresses are absent. As additional material settles on top, the

interparticle spacing decreases with the expulsion of pore water from within and

between the flocs. Consolidation occurs as a result of self-weight of the soil particles. A

highly compressible soil framework develops with associated effective stresses. In the

last stage, all of the sediment deposit undergoes consolidation and approaches an

equilibrium state.


Time

Figure 9: A schematic representation offlocculation, sedimentation and consolidation
(from Imai, 1981).


Settling velocity is a property of the suspension, i.e., it is the relative fall velocity

of the particles or flocs occurring in the settling stage, where they are only fluid-

supported. By carrying out laboratory tests with mud samples from the Amazon Shelf,









the settling velocity was determined in quiescent conditions and considering its

concentration dependence. Further research under non-quiescent conditions should be

conducted to investigate the effects of shear stress or turbulent kinetic energy on the

growth and break-up of flocs.

The bottom withdrawal tube method, typically used for determining the dispersed

particle size, assumes that there are no temporal variations in the settling velocity.

Therefore, during the experiment if flocculation occurs this method is not suitable, and

the multi-depth method (McLaughlin, 1958) must be used instead. Accordingly, for a

quiescent medium, the sediment mass conservation equation is reduced to

C a(wc)_ (5)


Integrating this equation with respect to vertical coordinate z gives

a (6)
(W.C) = f Cdz
t0

where D is a given elevation in the water column. Thus, using the vertical distribution of

sediment concentration tracked through time i.e., C(z,t), W. can be calculated. For each

selected value of elevation D, the integral in Equation (6) can be evaluated for different

times from the measured concentration profiles. Then, the spatially and temporally

discretized equation

S1=P Cdz d (7)

C t,+1 000


where









,+! C'i+ +C' (8)
C 2 z -D
.-D 2

yields the pair, W,C, for each time tj+12. W, is thus obtained, knowing C.

The settling velocity tests were carried out in the Coastal Engineering Laboratory

of the University of Florida. Six settling column tests were performed, with initial

concentrations, Co, ranging between 2.1 to 37 g/1. Conditions of each test are given in

Table 4.



Table 4: Settling column test conditions
Test No. Mud Sample Suspension Height (cm) Co (g/l)

1 3230 166- 151 21

2 3230 175.3-163 37

3 3230 179-167.5 8.3

4 3227 166.8- 156.8 8.5

5 3227 173 -164 2.1

6 3227 170.8 161.7 10.7



Figure 10 shows an example of the concentration profiles obtained for an

experiment with the sample 3230 and Co = 21 g/1. In every test, the mud particles were

aggregated, and therefore an interface appeared between the upper water layer and the

top of the suspension. This interface settled with time.

From the settling experiment, the settling velocity can also be estimated as the fall

velocity of the water-mud interface, which is constant during the settling stage










(schematized in Figure 9). These values were also plotted in Figure 11 together with the

results obtained using the Equation (7).

Settling Test Amazon Sample 2730 Co= 21 g/l
1 8 0 0..

160

140 15 min

120 30 min

100
E 56 min
80


40 180min

20

0 20 40 60 80 100 120 140
concentration (g/1)

Figure 10: An example of temporal evolution of concentration profile in the settling
column


The data points indicate an increasing velocity (with increasing concentration)

region due to flocculation effects and a decreasing velocity region (with increasing

concentration) due to hindered settling. The settling velocities derived from floc sizes

measured in the Amazon Shelf and estimated floc densities, 0.02 to 2.8 mm/s, are in

agreement with the settling experiments. As could be expected, the settling velocities

determined in quiescent conditions may underestimate the field-estimated values

(Wolanski et al., 1992). In any event, from the above experiments the following

empirical relationships between settling velocity and concentration are obtained:










W =0.05 (1.35 0.01C).6 mm/s

W, = 0.11C'6 mm/s


for C > 1.7 g/1

for C < 1.7 g/l


which are drawn in Figure 11. These equations are similar to those proposed by Ross

(1988); however, the presently adopted coefficients better reproduced the laboratory

experiments than those of Ross, when included in the numerical model. Details of

numerical simulations are provided in section 5.4.


101




loo + a


a ; + A+ + +
10-0 + + .


0 1



SCo= 2.1 g/
10-3 + Co= 8.3-10.7 g/I
x C 21 g/I
o C0= 37 g/

10-1 100 101 102
concentration (g/l)

Figure 11: Settling velocity versus concentration obtained from settling experiments
through Equation (7) (small symbols) and from free settling stage (larger black dots).



3.2.6 Viscosity

A single viscosity characterizes Newtonian fluids, e.g., water. This value is

obtained from the slope of a linear plot of shear stress vs. shear rate. Fine sediment

suspensions at high concentrations behave differently from pure water. Clay particles are


(10)









mostly flat in shape and, if the concentration is high, build a net-like structure. This

structure causes the suspension to exhibit non-Newtonian characteristics (Mignot, 1968,

Wang and Wang, 1994). Thus, the viscosity is not constant, but is a function of the shear

rate, shear stress and time. Thus, the term 'apparent' viscosity is used to refer to this

property.

Faas (1985, 1986) analyzed dense suspensions of Amazon sediment taken from

tops of box cores. Figure 12 shows the flow diagram for one of the analyzed samples, at

several densities. With the log of shear rate on the horizontal axis and the log of shear

stress on the vertical axis, the diagram shows how the flow behavior changes between

successive increments in shear rate. Low density mud (<1200 kg/m3) exhibits a shear-

thinning (pseudoplastic) behavior. At densities > 1200 kg/m3, the behavior changes from

shear-thinning to shear-thickening dilatantt). This behavior can be also observed in

Figure 13, which is a plot of the apparent viscosity vs. shear rate, showing the complex

behavior of shear-thinning at low densities and shear-thickening, in certain ranges of

shear rate, for denser suspensions.

This change enhances the resistance of mud to resuspension of dense suspensions

with increasing shear stress and, as was pointed out by Faas (1986), this effect in turn

can control sediment resuspension, reducing or preventing further resuspension. It is

interesting to note that in the AMASSEDS profiles, the maximum measured

concentration was 321 g/l, which is just below the limit found by Faas above which the

mud behaved as shear-thickening or dilatant.

























01

*O (1.1 1)

,l "(1.0
I.


M (1.052)






.01 -----
1 10 100
SHEAR RATE (se"')


Figure 12: Flow behavior of Amazon sediment suspension at different densities (from
Faas, 1986).







10 -

---------------------.






I-I


A 10


10 60 100
SHEAR RATE (use1)


Figure 13: Apparent viscosity vs. shear rate for a core sample from the Amazon Shelf, as
a function of density (from Faas, 1985).











In order to obtain analytical equations to fit the data in the range of concentrations

found in movement at the Amazon Shelf (< 1200 kg/m3), the data set obtained by Faas

were fitted to the power-law model (Sisko, 1958)

v,(C) = Cexp(-0.78--10.24) for < 3.9 sec-'
az za

v,(C) = Cexp(-0.017 12.95) for a- 3.9sec_1
az az






3.2.7 Shear Strength

Following Migniot (1968), Otsubo et al. (1986) and Dade (1992), among others, it

is considered here that the yield stress represents a measure of the interparticle bond

strength per unit area. Thus, the bed shear strength, T, can be determined from its

correlation with the yield stress measured from Amazon sediment samples. The upper

Bingham yield stress, Ty,, is defined from the stress-versus-shear rate flow curve by

extrapolation from the low values of shear rate, as indicated in the Figure 14.

Migniot (1968) and Otsubo et al. (1986) performed extensive experiments to relate

shear strength to the yield stress for sediments of different mineral compositions and

water contents. Migniot suggested the following relations:






















az


Figure 14: Schematic of shear stress versus shear rate flow curve, and definition of the
upper Bingham yield stress.


For consolidated mud

T, = 0.25-tPa ty >1.6 Pa (12)

and for weakly cohesive mud

= Oly Pa Ty <1.6 Pa (13)

In the experiments of Otsubo et al. (1986), the tested materials were grouped in

two categories, depending on the type of exchangeable cation. The Amazon samples fell

within the first group corresponding to natural clay mixtures. The functional

relationships obtained by Otsubo between shear strength t. and yield stress ry for the

first group is

T,1 = 0.27%6Pa (14)










,2 = 0.79%tPa (15)

depending on the threshold states in mud transport considered; these being, according to

Otsubo, sT for incipient mud particle movement and T2 for the onset of bed failure.

Faas (1985) made yield stress measurements on superficial sediments of the

Amazon Shelf bottom obtained from box cores during a June-July 1983 cruise (during a

high discharge period in the river). Similarly, Dade (1992) studied two samples collected

by a pump 20cm above the limit of downward instrument penetration in the bed. Using

both sets of data, Ty as a function of sediment concentration, is presented in Figure 15.


102





o o
10 o (o o0
S10 0








Figure 15: Yield shear stress versus concentration for Amazon Shelf mud (from Dade,
1992, Table 6.7 and Faas, 1985, Figure 3).
10o
Concentration (g 1)

Figure 15: Yield shear stress versus concentration for Amazon Shelf mud (from Dade,
1992, Table 6.7 and Faas, 1985, Figure 3).


The best fit line for the combined data is

ty= 2.02x10 l C2.6233 (16)









Thus Equations (12) through (13) and Equation (15), provide relationships

between shear strength and concentration, which are plotted in Figure 16. The choice of

the appropriate relationship for modeling purposes will be examined in connection with

the current induced shear stress and associated erosion flux (see section 3.3.5).












10-1
..-Otsubo(2)
10" ---..--- -Otsubo -l




110
Concentration (g/I)

Figure 16: Shear strength versus concentration for the Amazon Shelf bed sediment (1)
for incipient motion and (2) for bed destruction.



3.2.8 Permeability and Effective Stress

When fine-grained particles deposit on the bottom they form an open network

structure. Under the weight of the accumulating particles above, this network slowly

collapses during which pore water is expelled. Consolidation models solve the mass

balance equation for the solid particles, and for that purpose additional information

related to momentum exchange between the fluid and the solid phase is necessary

(Toorman and Huysentryt, 1997). Thus, two parameters are introduced, namely the









permeability, k, and the effective stress, o', for which empirical relationships must be

found for each particular case. Through Darcy's law, permeability relates seepage

velocity to the excess pressure head in the soil element, provided the interstitial flow

remains laminar. The effective normal stress, o', is defined as

o' = ot w, (17)

where at is the total stress and w,, is the pore water pressure. It represents the part of

the total stress supported by grains. Effective stress is usually associated with sediment

concentration (or void ratio in soil mechanics) but creep (i.e., time dependent change in

concentration without any change in effective stress) can influence the results (Sills,

1997).

Consolidation tests with sediment from the Amazon shelf have been carried out

(Dr. Robert Kayen, U.S. Geological Survey, California, personal communication).

However, in those tests, performed using the Constant Rate of Strain method (CRS), the

initial void ratio was always below 5. The void ratio, e, is related to sediment

concentration, C, through the granular density of the sediment, p., according to

C = p (18)
e+1

Thus, for a void ratio of 5 a sediment concentration of 441 g/1 is obtained. Since it

is of interest to analyze the set of data from at the Amazon Shelf where the maximum

recorded sediment concentrations reached 321 g/l, the experiments of Kayen do not

provide useful information for the purpose of this work.

Effective stress is usually obtained (in settling columns through self-weight

consolidation tests) as the difference between the total normal stress, computed from









measured density profiles, and the pore pressure, measured with capillary tubes or pore

pressure transducers (Berlamont et al., 1992, Been and Sills, 1981). Since the accuracy

of the effective stress measurements depends on the accuracy of the measured pore

pressures, in the beginning of consolidation, when the effective stress tends to be small,

the error in the effective stress measurement can reach 100%. Figure 17 is an example of

experimental data obtained by Toorman and Huysentruyt (1997) showing the spread of

results at low densities.

2000..





1200 ,.
1800 ,-.-



S100




200

1 1.05 1.1 15 11 115 1.25 1.3 1.535 4 1.45 1.5
DENST (*1000 kg/m3)

Figure 17: Effective stress as a function of local density (from Toorman and
Huysentruyt, 1997).


From the literature, we noted that Alexis et al. (1992) gathered data on the

effective stress and the permeability as functions of the void ratio, which are reproduced

in Figure 18 and Figure 19, respectively. Both figures will be used to obtain approximate

values of permeability and effective stress for the Amazon mud.







41





20


*
e

15-
.. :*.


O :
L- 10 '. 1*

52-I



5 9 */ ... .




0- rl -rm -i-rlriln q -rT hlnq--rri 1111--i-rrunql--r-'mnn*
10 *' 10' I0"' I 10 10' (0'
Effective stress (kPo)


Figure 18: Effective stress versus void ratio data taken from experiments reported in the
literature (Alexis et al., 1992).




52
507
48-
46
44
42'
40-
38-
36

30- ;
a 28 -
276-
922-
O 20 P.9
>18 1."
16 : /
12 :
10 g .B U
8 *

2-
0'
0 -us n" rq- rn..... .qr..- .. ....q ....q, ... .
10 10 10 10 10 10 10 10 "
PERMEABILITY (cm/s)


Figure 19: Permeability versus void ratio data taken from experiments reported in the
literature (Alexis et al., 1992).









3.3 Vertical Flow Structure


3.31 General

Having in mind the development of a vertical transport model for fine-grained

sediment applicable to the Amazon Shelf, it was necessary to examine the structure of

the tidal boundary layer at the study site.

High concentrations of fine suspended sediment induce two particular structural

features that affect the flow, both with stabilizing effects: density gradients and increased

fluid viscosity. The stability of flows in which both viscosity and buoyancy are

important is not a well-understood matter; hence each issue needs to be addressed

separately.

Clay suspensions at very high concentrations can possess a yield stress and a high

viscosity, and may exhibit a laminar behavior even at higher velocities, which is quite

different from similar hydrodynamic conditions in clear water, or low concentration

suspensions (Wang and Plate, 1996). Comparisons with non-cohesive suspensions have

indicated that a change in viscosity plays an important role in governing the boundary

layer structure. In laboratory experiments with a suspension of clay in seawater, Gust

(1976) reported noticeable thickening of the viscous sublayer, and a reduction of the

friction velocity. The laminar character of the near-bed flow in high concentration

environments has been recognized by many investigators (Ross and Mehta, 1988,

Kineke and Stenrberg, 1995). On the other hand, in turbulent flows, wherever there is a

density gradient, turbulence is required to do more work to entrain the denser fluid









upwards. Thus, the presence of the density gradient tends to damp turbulence and reduce

the boundary shear stress (Sheng and Villaret, 1989).

Recorded velocity profiles in the Amazon Shelf region are examined here, and the

above two effects are evaluated. Current-induced bed shear stress and shear velocity as

well as diffusivity through the water column are calculated for that purpose.




3.3.2 Tidal Boundary Layer Approach

The tidal boundary layer is characteristically considered to be essentially

horizontal (w w 0), and horizontally uniform [u=u(z,t)]. For such an oscillatory boundary

Bu 24A Du
layer, the relevant advective acceleration term can be written as u. 2- =,
ax L at

where u. is the flow velocity outside the boundary layer, A is the water particle semi-

excursion length and L is the tidal wavelength. This term can be neglected depending on

the ratio 2xA/L. Thus, for example, for tidal movement in 15m depth, this value is of

order of 10'1.

Under the assumption of a hydrostatic pressure distribution, and considering that

the shear stresses vanish outside the boundary layer, the equation of motion, valid for the

boundary layer, becomes

a u (19)
P (u u,) = -
at az

where u(z,t) is the velocity at elevation z above the bed level, u. is the velocity outside

the boundary layer and T is the shear stress at level z. Equation (19) can also be written

as









O(u u) ( )(20)


where v is a characteristic viscosity. If the flow regime is laminar, v is the fluid

kinematic viscosity, an exclusive fluid property. However, if the flow is turbulent, v

represents the eddy viscosity, which is dependent on the flow characteristics. In both

cases it represents a momentum diffusion coefficient.

Nielsen (1992) subdivided horizontally uniform models for oscillatory boundary

layers in two categories: quasi-steady models, which assume that the velocity

distribution is at all times logarithmic, and unsteady models, based on the above

boundary layer approach. However, as it will be seen next, quasi-steady models can be

considered as a sub-class of unsteady models, by solving the non-steady oscillatory

boundary layer problem with a suitable viscosity function.

Expressing the tidal velocity profile as u(z,t) = u(z)e', where a is the tidal

frequency, Equation (20) becomes

d ( du (21)
v(z) = ia(u -u( )(
dz\ dz)

A usual functional form found in the literature for the flow viscosity in turbulent

boundary layers is the linear dependence with depth, i.e., v(z) = K u. z, where K, is the

von Karman constant. Substitution of this relation in (21) yields a homogeneous, Bessel-

type differential equation of zero order, known as the Kelvin's differential equation:

d2u 1 du (22)
+-- + u= 0
Ss ds










where X=2 -- is imaginary and s = -z
KU.

With the boundary conditions u = 0 at z = 0 and u = u at z oo, the general

solution of (22) has the form


u = u 1+aker 2 (23


where

-1 (24)

kerf2f


and where ker is one of the Kelvin functions. For small arguments of ker, this velocity

profile approaches the logarithmic form (Abramowitz and Stegun, 1972) as would be

expected for a turbulent boundary layer.




3.3.3 Fluid Kinematic and Eddy Viscosities

To evaluate the form of the viscosity function suitable for flow over the Amazon

Shelf, it is necessary to emphasize the difference between the fluid kinematic viscosity

and the eddy viscosity, especially in the case of a flow which contains a very high

concentration of suspended sediment, and flow regime which is turbulent. Thus, the

momentum diffusion coefficient, v, combines a fluid, whose viscous properties change

gradually, with a flow regime which tends to vary from laminar to turbulent over the

water column. For the present case, v was determined from the boundary layer approach,

Equation (20), using measured velocity profiles, as follows:










(25)


-P p (u u,)dz
v(z, t) =


az

Median values of v over the tidal cycle, obtained according to the Equation (25) in

the water column for each station, are plotted in Figure 20. Also, median values of the

fluid kinematic viscosity, vf, obtained from concentration profiles and Equation (11), are

plotted in Figure 20 as functions of depth.


10-7


10-6


10-5 104 10-3
Kinematic Viscosity (m's)


Figure 20: v (circles) and vf (asterisks) median values for the tidal cycle, from Equation
(25) and (11), respectively.


It is interesting to note that both sets of data converge around the same range of

values in the lower part of the profile. In that zone, about Im above the bottom, high

mud concentrations were observed and, accordingly, a change in the behavioral trend of

momentum diffusion is noticeable in Figure 20.


mw mWam a M aHBi
NeK W xW K xW iBWaB
3 UN "m M WK ( 00100
3 N NUUU NENE(E 1)mmm

3ME WKE XN N E XW W

mm mmm m XI @ sEoD
W2 eK NE i alQ

W NE NKE W on BB)
m am w x a asgi
NE 3I KN m @NH B
N1 E mm *B-ag


ofok@fy @OE agWJ
rili93_. Q@WH wasgiHQ
~~ ~~~~~~ ~ CeW.. .... .... .. ...... ....... ....









A noteworthy feature of the velocity profiles near the bottom of the Amazon Shelf

32u
is the concavity ( > 0), a feature uncommon to estuaries in which logarithmic
az

profiles are observed. Figure 21 shows details of the velocity profiles, enhancing the

portion near the bottom.

OS2 (high river flow- as3419)


0.5 1 1.5 2
Velocity (m/s)


Figure 21: Velocity profiles recorded at anchor station OS2 (3419).


Near-bed layer velocity and concentration profiles measured in the Avon River

(U.K.), a macrotidal and high concentration environment, also showed a similar trend in

the velocity profile. Ross and Mehta (1988) numerically modeled the near-bottom

horizontal velocity of the Avon River as an unsteady Couette-type flow driven

predominantly by the shear stress imposed at the level of the lutocline. The result









confirmed the observed concavity. They explained this trend to Raleigh flow effect

arising from momentum diffusion into the fluid mud layer due to shear flow in the water

column above the lutocline.

Considering a viscosity which decreases linearly with elevation (z) above the

bottom, v(z) = c, -cz, where c, and c2 are constants, Equation (21) can be rewritten

as

d =du u ,. (26)
(ci c z)- = i(u-um)
dz dz)

Through a change of variable, s = c cz, a differential equation is obtained with the


parameter = 2 /- The solution, compatible with the boundary conditions u=0 at
VC2

z=0 and u = u. at z -> oo, is


u= u 1+b bei(2 (c 1 -c2z) (27)


where

-1 (28)

bei(22C


and where bei is one of the Kelvin functions. The resulting velocity profile is shown in

Figure 22, and is compared with the result obtained from Equation (23). Note that the

top of the figure at 8m does not represent the free surface, but is well below it. This

simple analytic result implies that the adopted decreasing viscosity model generates










concave velocity profiles, a characteristic found in the measured profiles, as was

mentioned earlier.



7 T=12 hs
z u= 1 m/s
(m) 6 k=0.4 ,
u 2 cm/s (z)=0.001- 0.0001 z /
5-

4-

3 /
2 /
./. izV)=-u4k z
0 ...................
0 0.2 0.4 0.6 0.8 1
velocity (m/s)

Figure 22: Boundary layer velocity profiles for increasing and decreasing viscosity with
depth.


Wang and Plate (1996) studied the turbulent structure of clay suspensions as a

non-Newtonian fluid following the Bingham equation. They defined a characteristic

Reynolds number as

4puh (29)
1 r+ zh


where p is the fluid density, rT is the rigidity coefficient defined from the shear stress

versus shear rate curve (see Figure 14), -, is the yield stress, h is the flow depth and u

is the average velocity in the water column. Following this definition, they found that

turbulence developed in the entire channel only for Reynolds numbers above 10,000.












Figure 23 shows the median values of the characteristic Reynolds number calculated


over the tidal cycle, and as functions of depth, for the 18 anchor stations.


0
0 0 0 0
00 00 C 0 0
S

a oW M
00 000oc

00 0 m 000

ao a 0m Go

0 0 MO 0

0 00 000 00


O 0cm 000 0
S 0 0000 0
0 0 0Oa 0
a O 0 000 a

0 0 0


10 104 106 108
Reynodls Number


Figure 23: Tidal Reynolds number [Equation (29)] vs. depth.



It should be noted that the threshold of Re=10,000 for the turbulent regime was


established for laboratory conditions. The Amazon Shelf data, however, do provide


evidence of values for R& below 10,000 within a well-defined, Im thick, layer near the


bottom. This evidence, as well as the concave form of the velocity profile, supports the


suggestion of the presence of a thick layer of viscous flow in the near-bed zone due to


the enhanced viscosity of the sediment suspension.


I I --









3.3.4 A Model for Laminar Boundary Layer
Assuming the local validity of Equation (19) with uniform viscosity, an analytical

solution for the velocity profile has been given by Nielsen (1985) as


u(z,t)=Aae'it l-exp(-[1+ i] (30)

from which the bottom shear stress is obtained as

,(0, t)= Aoe'" (1+i) V (31)

and the corresponding shear velocity as

ru =- 12 (32)
[Ae l- 2v/a
Here, Equation (30) is applied to tidal motion, and the kinematic viscosity depends

on the local concentration according to Equation (11), a is the semi-diurnal tidal

frequency, and Aa = u., is the velocity at the outer edge of the boundary layer.

Following Geyer (1995), who considered the boundary layer in the Amazon Shelf region

to be confined between 3 to 5 m for neap and spring tides respectively, the top of the

boundary layer was considered here at z = 4 m for all measured profiles.

Figure 24 compares Equation (3) with measured hourly profiles along two tidal

cycles for the anchor station OS1 (4434). A measure of the agreement between the

observed and the calculated velocity profiles is given in Figure 25, where the absolute

error was computed according to

er(z) = li(z) u(z) (33)










Here, ii is the calculated velocity according to Equation (30), and u is the observed

velocity. For comparison purposes, the absolute error is also calculated for the

logarithmic fit, i.e.,

u., z (34)
u = -U In (34)
K z

where u* was calculated from the velocity profiles as described in section 3.3.5. The

values of the roughness height, Zo, was obtained by matching the measured velocity at

the top of the boundary layer, considered to be at z=4m. In both cases the errors are

tidally averaged.

OS1 (low river flow)


0 0 0 >
0 0 0 0 0 0 0
0 0 0 0

\U 1 U I. U I U0 I


-1. O -1. O -1. O -1. O -1. O -1.


U 1. U 1. U 1.
Velocity (m/s)


flood -> ebb

Figure 24: Observed (discrete points) and calculated [Equation(30)] velocity profiles
over two tidal cycles recorded at anchor station OS1 (low river flow-as4434).


1. U 1. U i. U 1.













OS1 (lowriver flow- a4434)
It
3.5 M
(K
3 K
Of
2.5
S2 o


0
1.5 K
oo

0.5X 0
0
0.5 -X 0

0 0.2 0.4 0.6 0.8 1
absolute error (m/s)


Figure 25: Absolute velocity errors arising from differences between measurements and
Equation (30) (asterisks) and measurements and logarithmic fit (circles).



For the logarithmic profile, a noticeable increase in error can be observed below

lm level. It should be noted, however, that the model was over-extended in the upper

layer where turbulence was present merely to simplify the imposed boundary condition,

namely the free stream velocity. Since the objective of these calculations was to estimate

bed shear stress and the shear velocity from the velocity profile, the relevant results are

those obtained in the neighborhood of the bottom.

The high concentration near the bottom found in the Amazon Shelf, and the

associated enhanced fluid viscosity, inhibit turbulence development in the near-bed

layer. This effect markedly affects the boundary layer structure, including velocity

profiles in a region of extreme importance for sediment transport evaluation. As was

mentioned in the introductory chapter, most of the total sediment transport in the water

column was concentrated in the first meters from the bottom, where the concentrations

were around 10 g/1 or higher (Kineke, 1993). Above this elevation there was an evident









deviation from the laminar model, and, therefore, a turbulent profile must be adopted for

the upper column (from about Im to the total height of the boundary layer).



3.3.5 Shear Stress from Measured Velocity Profiles

Integrating Equation (19) between z and oo, and recalling that T, = 0, the shear

stress can be calculated from

S8 <(35)
W(z) = pf-(u -u.)dz


and the shear velocity, u., can be then expressed as

,_ . 1 (36)
u. = = p (u u.)dz


In this formulation, no assumption regarding the momentum diffusion coefficient is

made. However, it should be noted that oo refers to the top of the boundary layer and this

level, or the thickness of the corresponding boundary layer, 6, must be determined

carefully. A crude estimate of 6 was obtained from the measured velocity profiles by

determining the height at which the first local maximum in flow speed occurred, starting

from the bottom.

Table 5 gives the results of the bottom shear stress calculated from Equation (35)

(setting z=0), and referred to as 'observed', while the bottom shear stress using Equation

(31), is referred to as 'calculated'. Also included are observed, Equation (36), and

calculated, Equation(32), shear velocities. Observed values of shear stress and shear

velocity were obtained entirely from the measurements, so that the effects of viscosity,









stratification etc. on the momentum diffusion coefficient are already included. The

boundary layer thickness, used in the calculations of the observed shear stress and shear

velocity at each anchor station, is also included in Table 5. In Equation (31), the free

stream flow velocity was taken from the measured velocity at 4m level, and the near-bed

concentration was the lowermost measured value.

Even though the shear stress calculated from data and that obtained using the

analytical expression appear to be in reasonable agreement in some cases, in general

there is an under-estimation of the shear stress, and, also, a discrepancy in phase. Note

that Equation (31) predicts that shear stress should lead velocity by about 45 degrees.

While the observed shear stress lags velocity by about the same value for anchor station

OS1, the lag is greater for anchor station CN, as is observed in Figure 26. Figure 27

shows comparisons between calculated and observed shear stresses, after adjusting for

the phase lag.

The discrepancies between predicted and observed shear stresses were found to be

enhanced when the measured near-bed velocity flow was far from zero (stations 1154,

4438, 4441 or 2420), or when the assumed thickness of the boundary layer was greater

than 4m (stations 2418, 2405 and 3442). It should be remarked, however, that there are

many underlying uncertainties in the calculations [Equations (31), (32), (35), and (36)].

It should be noted, for example, that measurement technique used were not filtered for

turbulence (for details of the measurement technique see section 2.6), the boundary layer

thickness estimation is crude, viscosity-concentration relationship was taken from

laboratory experiments, and the concentration at the bed level was taken as the

lowermost measured concentration, which may not be truly representative of the near-










bed zone. In fact, if the bed concentration were fixed at 320g/l, the maximum

concentration at which mobile fluid mud occurs, the observed and calculated values of

u* approach each other adequately, as can be seen from a comparison of shear velocities

listed in Table 5, in the 7" and the last columns, respectively. This consideration would

thus reduce the difference between the observed and the calculated shear stresses.

Accordingly, the proposed model given by Equations (30) and (31) can be considered

appropriate for describing the lower region of the Amazon velocity profiles.

OS1 (4434)
















4 3
S-- ----/ ------


-31
0 5 10 15 20 25
time (h)
CN (2428)












8 -- 10 15 20 25


Figure 26: Observed velocity (dotted line) and shear stress (solid line) over two tidal
cycles for anchor stations OS1 and CN.











OS1 (4434)
n-;


e 0

-0.1


.n4 I


0 5 10 15
time (h)


CN (2428)


15
time (h)


20 25 30


Figure 27: Observed shear stress [dotted line Equation (35)] and calculated shear stress
[solid line Equation (31)] over two tidal cycles for anchor stations OS1 and CN.












Table 5: Tidal mean and maximum shear stresses and shear velocities at the anchor
stations
Stn. 8 Mean Max. Mean Max. Mean Mean Mean calc. u.

obs. T obs. rT calc.T. obs. u. obs. u. calc. u. Cb=320 g/l

(m) (Pa) (Pa) (Pa) (m/s) (m/s) (m/s) (m/s)

1154 6.25 0.20 0.45 0.001 0.021 0.014 0.001 0.013

4434 2.50 0.21 0.42 0.15 0.020 0.014 0.016 0.017

4438 2.50 0.17 0.33 0.01 0.018 0.013 0.002 0.014

4441 2.50 0.12 0.22 0.002 0.015 0.011 0.001 0.011

4413 3.50 0.18 0.38 0.09 0.019 0.013 0.015 0.015

2420 2.25 0.09 0.19 0.01 0.014 0.010 0.003 0.014

2418 4.50 0.43 0.67 0.08 0.026 0.021 0.010 0.017

2415 2.50 0.14 0.27 0.06 0.016 0.012 0.010 0.012

2428 3.75 0.25 0.52 0.10 0.022 0.016 0.015 0.017

2444 2.75 0.12 0.22 0.06 0.014 0.011 0.012 0.015

2445 3.75 0.18 0.30 0.06 0.017 0.013 0.013 0.014

2405 4.50 0.63 1.07 0.07 0.032 0.025 0.010 0.019

3420 2.50 0.22 0.43 0.08 0.020 0.015 0.010 0.018

3419 3.75 0.39 0.87 0.17 0.028 0.019 0.018 0.019

3418 2.50 0.11 0.21 0.06 0.014 0.010 0.011 0.012

3442 5.00 0.52 1.04 0.07 0.032 0.023 0.010 0.020

3455 2.50 0.18 0.33 0.06 0.018 0.013 0.010 0.018

3405 2.50 0.25 0.62 0.08 0.025 0.016 0.011 0.019











3.3.6 Mass Diffusivity
In the lower part of the suspension, where the flow behavior is viscous, molecular

mass diffusivity is negligible, considering that molecular diffusion, usually small,

decreases with increasing fluid viscosity. In this layer, however, shear caused by wave

action can enhance mixing. Under quiescent conditions, or during tidal slack water, an

effective stress developed by virtue of contact between particles can be of greater

importance in preventing complete deposition than molecular diffusion. In contrast with

the lower zone, in the upper suspension mass diffusivity is directly related to the

momentum diffusivity, which can be large.

There is a general agreement among researchers that the simple eddy viscosity

model, following the parabolic distribution, is adequate for homogeneous fluids

v(z) = KU.Z 1 (37)

which applies above the viscous layer. Figure 28 shows an example of the momentum

diffusivity taken from the velocity profile according to Equation (25), and calculated

with Equation (37), above the 1 m level.

Stable gradients of density caused by suspended sediment concentrations, salinity

or temperature can affect flow dynamics, because work must be done on the fluid to mix

it, and to raise its potential energy. Many researchers have considered turbulence

damping due to density gradients caused by sediments, salt or temperature (Soulsby and

Wainwright, 1987; Geyer, 1995; Trowbridge and Kineke, 1993) by modifying the

universal logarithmic velocity law (Adams and Weatherly, 1981, Green and McCave,

1995; Glenn and Grant, 1987, Wolanski and Brush, 1975). The relative magnitudes of









the stabilizing density forces and the destabilizing shear-induced turbulence can be

measured by the gradient Richardson number:

CN (2428)


:10


01 i 1 i l i i IIl i
104 10-3 10-2
diffusivity (rf/s)


Figure 28: Depth variation of the tidal eddy viscosity at anchor station CN (2428) (dots)
and eddy diffusivity calculated according to Equation (37).


g p (38)





where g is the acceleration due to gravity, p is the mixture density and u is the local

horizontal flow velocity. High Ri indicates high stratification, while low values indicate

well-mixed conditions. Figure 29 shows an example of the tidal median value of the

gradient Richardson number calculated according to Equation (38). Density was










considered to be affected by salinity and temperature, and also by suspended sediment

concentration. The adopted equation of state is given by the Eckart formula:

Al = 5890+38 T-0.375 T2 +3S
A2 = 1779.5 +11.25 T- 0.0745 T2 -(3.8+0.01 T)S (39)
1+A1
p(S,T) = 1000-----
A2 + 0.698 Al

where S is salinity in practical salinity units (psu), and T is temperature in degrees

Celsius. Sediment concentration, C, effect on density is calculated according to


p(S,T,C) = CI + p(S, r)
Pa (40)




OS1 (4434)
10


8-


6-


4-


2-



10-3 102 10-1 100 101 10 103
Richardson number

Figure 29: Tidal median values of the gradient Richardon number considering density
affected by salinity and temperature (solid line), and salinity, temperature and sediment
concentration (dotted line).









It can be seen that the effect of suspended sediment is more important near the bed,

while salinity stratification affects the upper suspension. A similar correlation is found

for all the profiles in which high concentrations of sediment were measured. As stated

before, it is not clear if laminar flow in the lower layer, where high concentration

sediment exists, was due to the increased fluid viscosity, or if it was due to the density

step. In any case, it can be considered that turbulence develops mainly in the upper layer,

where the effect of salinity-induced stratification also plays an important role.

Cacchione et al. (1995) adjusted the logarithmic velocity profile to measured

profiles obtained from the GEOPROBE deployment at 63m depth. The results, after

corrections due to accelerating and decelerating flows, showed an average shear velocity

of 0.017 m/s, with a mean value of zo =2.7 mm. The effect of tidally induced

acceleration and deceleration resulted in changes in shear velocity of 10%. In

Cacchione's data the stratification effect was comparatively less important. The

considered velocity profiles were measured 15 cm from the bottom, where suspended

sediment concentration did not exceed 2 g/1.

Mass diffusivity is related to the momentum diffusivity by the turbulent Schmidt

number

v (41)

While Schmidt number for sediment mass diffusion varies from 0.5 to 1 for low

concentration, homogeneous fluids, in stratified conditions, Teisson et al. (1991) found

variations in the turbulent Schmidt number ranging from 0.7 to 10. Costa and Mehta

(1990) reported values ranging from 0.94 to 2.4, from measurements in Hangzhou Bay,

China, while Yamada (1975) reported values of 0.8 to 2.









The mass diffusion coefficient in stratified fluids can be written as (Teisson, 1992)

v (42)
6, = --(Z)
s,
oeh
where 4 accounts for stratification effects over the water column. A simple relationship

for 4 based on the gradient Richardson number is the well known function proposed by

Munk and Anderson (1948)

= (1+ aRib (43)

with a=3.33 and b=-1.5, for mass diffusion. The gradient Richardson number variation

over depth was calculated for anchor stations CN (2428) and OS2 (2418), and the

median values over the tidal cycle are plotted in Figure 30. Both effects, i.e. due to

salinity and sediment stratification, are again evident (see also Figure 29). The

stratification damping function 4 was calculated for both anchor stations according to

Equation (43), and the median values over the tidal cycle are shown in Figure 31.

In order to have an insight into the time variation of the stratification damping

function over the tidal cycle, the damping function is plotted in Figure 32 for the high

and low-water stages as a function of depth for anchor station CN (2428). Figure 33

shows the time series of depth at this site. An interesting observation is that the damping

function follows the up- and down-water movement, increasing somewhat its effect

during slack water.













CN (2428)





S....-- -
20









:o
b





nc


10-1 100
Richardson number


2 OS2 (2418)






......-.0 .... . .... .. .. ..... .
0 C C
t 0


10 ---- -- - ...... ..

Si111


10



0
10-3 10(2 101 100 1
Richardson number


101 102


Figure 30: Gradient Richardson number as a function of depth for anchor stations CN
(2428) and OS2(2418).









CN (2428)
20


0 i i--i |



10-3 -2 1101 1 101







I Ii'S I 241I)
i1 ...... --- ...... .-...










---C
S10 ..-.. ........... ...... .. ..-- ...






) C


5 1 --- ----- -- 1 -4 -
103 -2 10-1 101
stratification function


08 d 2 (2418)
i11111 i I 111
i I I it ti i iii
i i i i II I i l
I io i i I

I I I i I

i i !,t" iii i
I 0 ,,," I' i I

iIo 0 i i







i10-2 10-1 100
stratification function

Figure 31: Tidal median values of the stratification damping function [Equation (41)]
versus depth for anchor stations CN (2428) and OS2 (2418).

































10-2 100
stratification function

16 h


stratification function

21 h


104 10-2 100 104 10-2 100
stratification function stratification function

Figure 32: Stratification damping function versus depth over the tidal cycle for anchor
station CN (2428).


0I-
104












'1oQ-


I J


ias


17.


165


15.5
0 5 10 15 20
tirre(h)



Figure 33: Time-variation of water depth at anchor station CN (2428).


3.4 Bottom Boundary Condition


3.4.1 Bed Level Definition

For modeling purposes, the bed level is considered following one of the earliest

bed definitions (Krone, 1972) as the level where the current is not appreciable within the

time-scale of interest. Naturally, this is a dynamic definition that will depend on the flow

condition, the sediment characteristics and the time-scale of analysis, as it is locally

determined by the time-varying balance between the applied fluid shear stress and the


A


t I


5. .- 1.....4..... *..... *..............


.. ....... ... ...- -. .
......... .......I .... ... ..t........ ...


L....4*.......t... l**.... ..................I ... ........................*.........* .* ...4*-.t .* *.. .....


^


J

^


P


_ 1"









shear strength of the bed. Also, this level should preferably be time-invariant in the

context of the time scale of analysis.

Another bed definition is based on the transition from where the sediment is fluid-

supported to sediment supported by its own continuous framework, with a transition

zone which is partly fluid-supported, and partly framework-supported (Sills and Elder,

1986). Following this criterion, the bed level is taken where particles begin to develop an

effective normal stress, a', defined by Equation (17). Fluid mud at sufficiently high

sediment concentrations can develop a measurable effective stress, which is also a

mechanism that prevents it from depositing. In the measurements of Toorman and

Huysentruyt (1997), appreciable effective stresses were found for sediment

concentrations as low as 80 g/l. Been and Sills (1981) measured pore pressures in

laboratory consolidation experiments and concluded that there is no unique correlation

between sediment concentration and the development a of non-zero effective stress.

However, effective stress was always apparent in concentrations above approximately

220 g/l. In the Amazon data, mobile fluid mud was detected with concentrations up to

320 g/1. Thus, a bed definition based on classical soil mechanical definition of effective

stress, as proposed by Been and Sills, may not be in agreement with the concepts

mentioned here. Interesting discussions regarding the bed level definition can be found

in Parker (1989) and Mehta et al. (1989).

Finally, it should be noted that the bed definition adopted during the AMASSEDS

survey followed a criterion dependent on the depth reached by the profiler (Kineke and

Sternberg, 1995).












3.4.2 Erosion Mechanisms and Erosion Rate

Two distinct mechanisms for the entrainment of the near-bed sediment by the

current can be recognized (Mehta et al., 1989). If the mud develops a measurable shear

strength, erosion of the mud layer occurs. For a newly placed fluid mud subjected to

shear flow, the interface between mud and water, with no measurable shear strength, can

be warped by flow and entrained by mixing into the upper layer.

Erosion of the bed can occur particle-by-particle, as mass erosion, or by

liquefaction. Particle-by-particle and mass erosion occur when failure occurs where the

shear strength is exceeded by the fluid stress; in the former case the characteristic shear

strength is dependent on the interparticle cohesive bonds, and in the latter case the shear

strength is a bulk property of the soil defined by Coulomb's law for failure.

As noted, particle-by-particle, or surface erosion, is an individual floc breakup

process that begins when the flow stress exceeds the critical shear strength of the bed

surface. Mass erosion occurs by bed failure when the applied stress exceeds the bulk

strength of the material, and the failed material is instantaneously suspended up to the

depth where failure occurs, i.e. where the bed shear strength equals the applied shear

stress (Mehta et al., 1989, Wright and Krone, 1989).

Surface erosion occurs at low to moderate values of the excess shear stress,

T, ;,, where to is the applied shear stress and r, is the shear strength, as discussed in

section_3.2.7. T, is also referred to as the critical shear stress for erosion, in analogy with

cohesionless sediment transport.









The erosion rate, E, i.e., the mass of sediment eroded per unit bed area per unit

time, depends on the excess shear stress as well as on the erosion shear strength. For

uniform, consolidated beds the erosion function suggested by Kandiah (1974) is often

used:


E=MI (44)
E=M


where M is a rate constant. A relationship between M and c, can be found in Lee and

Mehta (1994). According to Equation (44), for a given applied stress, C., the erosion

rate remains constant because the shear strength is uniform within the bed. Mud layers

formed by deposition, however, show a gradual decrease of the erosion rate with time

due to an increasing strength with depth, caused by consolidation. Parchure and Mehta

(1985) proposed an erosion rate function of the form

E( v\(45)
InE = a (z ()]'


where a (PaP) and y (=0.5) are sediment dependent constants, Ef is the floc erosion rate

(kg/m2s) and r,(z) is the shear strength profile (Pa).

When the excess shear stress becomes large mass erosion prevails. In such a case,

erosion can be approximately described by an expression of the form of Equation (44),

but with a constant M much greater than for surface erosion (Mehta et al., 1989).

Entrainment is a basic concept in free turbulent flows and represents mixing of

bottom fluid with turbulent flow. Fluid mud entrainment following slack water has been

compared qualitatively with the entrainment of a stratified layer of salt water underneath









flowing fresh water (Mehta and Srinivas, 1993). When entrainment occurs from the top

of a quiescent lower layer, the upper layer deepens and resembles salt-stratified layer

entrainment. If turbulence is produced at the base of the bottom layer the layer thickens

with entrainment, as for example clear water entrainment by turbidity or density

currents. In the work of Kranenburg (1994), the complete equations to solve both

entrainment process, based on the turbulent kinetic energy balance, can be found.

The entrainment process implies enhanced mixing driven by shear at the interface.

The existence of highly sheared layers in the Amazon Shelf area has been pointed out by

Geyer and Kineke (1995). The shear stress can be calculated according to


S du (46)
r(z)= vp

where vf is the kinematic viscosity of the mixture, calculated according to Equation (11),

and p is the mixture density. The shear stress is maximum within the viscous near-bed

layer, and decreases upward rather abruptly. Figure 34 shows an example of tidal median

values of the shear stress for anchor station OS1 (4413) plotted against depth. It is

interesting to note that a maximum was reached at the 0.75m level, and then the stress

decreased downward. At this site, near-bed sediment concentrations in excess of 200g/l

along with appreciable horizontal motion were recorded.










OS1 (low water


4-0
0
0
3 0

I o
12
1-


0 0 I
108 10,6 104 10-2 100
shear stress (Pa)

Figure 34: Tidal median values of shear stress versus depth for anchor station RMi.


From Figure 34 it can be seen that entrainment may occur above the primary

lutocline, around the elevation of z=lm. At this elevation, due to the lower

concentrations, it is likely that the mud does not develop an appreciable shear strength.

However, a model with a boundary condition at the top of the fluid mud layer

prescribing entrainment in the Amazon Shelf would not account for an important part of

the transported sediment, namely fluid mud below the boundary. Given this, if the bed

level were set at z=0, i.e., at the bottom of the fluid mud layer, the entrainment process

would have to be accounted for in the mass diffusion function established for the water

column, and the prescribed flux boundary condition would correspond to a bed erosion

rate, examined in the next section.

The sediment flux over the tidal cycle was calculated for the available 18 time-

series as the time-derivative of the total mass in suspension, and was correlated with a

characteristic "free stream" velocity as a measure of tidal action. Considering the flux at









the lower-most measured elevation (z=0.25m) a degree of correlation was found, as can

be seen in Figure 35, 36 and 37 for anchor stations 1154, 2418 and 2428, respectively.

Poor correlation found in other cases (not shown) were due to imprecision in the

measurements. In fact, the correlation improved when the flux was calculated

considering the bottom level at higher elevations, as can be seen for anchor stations 2428

and 3455 in Figure 38 for the flux calculated at z=lm. At these stations the maximum

resuspension flux occurred in association with the movements of the lower lutocline

(below about the 2.5 m level for all the anchor stations). The high gradient of sediment

concentration and the high rate of erosion occurring in this near-bed zone can thus easily

lead to errors in measurements, especially when the profiles are recorded with non-fixed

stations as in the AMASSEDS profiling surveys.

The occurrence of a phase difference between the sediment flux and the velocity

cannot be explained in a straightforward way. In some cases the velocity led the

sediment flux (for example, station RMi 3455 in Figure 39), while in others velocity

lagged sediment flux (as at station OS2 1154). As mentioned in section 3.3.5, the flow

velocity at the top of the boundary layer does not always present a consistent phase

relationship with the bed shear stress. However, the analysis is retained here in terms of

the flow velocity because it is the model input parameter from which the shear stress is

calculated.

The above type of resuspension behavior was not found at the station RMo (2445),

which showed the highest stratification level of all the measurements, with the lowest

vertical sediment fluxes. At RMo (2405), an event that could be characterized as

sediment advection from the shallower zone arriving at the anchor station at the end of






74




the ebb tide could have interfered with the cyclic behavior (compare Figures 40 and 41).

Stations 4434 and 4441 also showed unusual responses with respect to resuspension (see

for example Figure 42).


QA









> 0.:


x 104


OS2 (1154)


- .. .7 .7 .7-


0 5 10 15 20 25



'---- ------
0 5 10 15 20 25
time (h)

8 .......... .... .................................................................................................. ...................................


I. ... ............ ... ......... . .. ......



0 5 10 15 20 25
time (h)


1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
n


0
0 0
0





0


0 0


-1.5 -1 -0.5 0 0.5 1 1.5
sediment flux (kg/m's) x 10"


Figure 35: Sediment flux (at z=0.25m) and current velocity for anchor station OS1
(1154). Top: time-series of sediment flux and velocity. Bottom: sediment flux vs.
velocity after phase adjustment.


00 O0

0


-E
X














x 103


S2 (2418)


0 .-.... . -.......-..... ........ ---....



5 .- ..... ............ ......................... ...- ........................ ................. ... ............ ..
I I I
0 -i---.V-, .. - -


5------rs-- ------- ---i----- ----------


time (h)
[ ------!II------I-----!------------
-i 2T 7Ti


S.. ......... .......................... -- '-, ..1............... 2"*"" ............ ............. "-. -'-


5 10 15 20 25
time (h)



1.8 0
0


0 ,8

o0.8
13


0 0
0 o
o
S o





0 0o
0
O


0 0


-10 -8 -6 -4 -2 0 2 4 6 8
sediment flux (kg/rrs) x 10


Figure 36: Sediment flux (z=0.25m) and current velocity for anchor station OS2 (2418).
Top: time-series of sediment flux and velocity. Bottom: sediment flux vs. velocity after
adjusting for the phase.


1






a)


t .


i.


I


w


LIJ











CN rising river flow (Stn 2428)


x 103


E






0.




I 0.


0 5 10 15 20 25
time (h)


1

o0.8

0.6


0 2
sediment flux (kg/mrns)


6
x 10


Figure 37: Sediment flux (z=0.25m) and current velocity for anchor station CN (2428).
Top: time-series of sediment flux and velocity. Bottom: sediment flux vs. velocity after
adjusting for the phase.


0 5 10 15 20 25
time (h)


O
11I I


R _










CN (2428)


0 5 10 15 20
time (h)
e----------------------------------


1171.


SI i I


time (h)


A


i1

S0.8

1,0.6


0.2 -


-4 -3 -2 -1 0
sediment flux (kg/nms)


1 2 3
x 10


Figure 38: Sediment flux (z=lm) and current velocity for anchor station CN (2428). Top:
time-series of sediment flux and velocity. Bottom: sediment flux vs. velocity after
adjusting for the phase.


Ch


/oo o
0 0o


1 .. .


III I 1


x 103


4













..... .- ...... .-.-. ....... . ....... . ..... .




4- I. ... i .
!~ \ / | \


2




I-2


0 2 4 6
time (h)


8 10 12


0 2 4 6 8 10 12
time (h)



1.6 0 o

1.4 -

1.2 O 0

0.8 O

0 0.8- 0 0

0.6

0.4 0
0

0.2
-4 -3 -2 -1 0 1 2 3
sediment flux (kgfm2s) x 10


Figure 39: Sediment flux (z=lm) and current velocity for anchor station RMo (3455).
Top: time-series of sediment flux and velocity. Bottom: sediment flux vs. velocity after
adjusting for the phase.


RMo (3455)


x 103











RMo (rising river flow-as2405)


saliny (pau)

30
25
20
15
10
5
0




time (h)


Figure 40: Salinity and sediment concentration time-series for anchor station RMo
(2405).


x 103
5

0


. -5
.s


RMo (2405)


0 2 4 6 8 10 12 14 16
time (h)

1.5.... ............





-ii
0.5 --- ---- 6-- --- --- --- 4--- ----
0 2 4 6 8 10 12 14 16
time (h)


Figure 41: Time-series of sediment flux and current velocity for anchor station RMo
(2405).






80





x 10 OS1 (4434)



.5 -. ..-- ...-

-5 .... . -------------------- .


1.

0.
0.
0.
0.


0 5 10 15 20 25
time (h)

2..........-...-.. -.-..-,- -.-.-.

2-. -. .. ... ...-..
.I .- .....1 .... ................ .. ............ .... ..... ..... ...
.
6

2 .-- ... ..... - - -


0 5 10 15 20 25
time (h)


Figure 42: Time-series of sediment flux and current velocity for anchor station OS1
(4434).




3.4.3 Bed Shear Strength

Bed shear strength can be calculated using the expressions derived in section 3.2.7

as a function of sediment concentration. For the maximum concentration of 321 g/1

observed in the study (Table 1, anchor station OS1), one would obtain a shear strength of

0.91Pa according to, for example, Otsubo's criterion for incipient motion given in Figure

16. However, the estimated current-induced bed shear stress reached a maximum value

of 0.42 Pa at this site (see Table 5), which would not be enough to move a mud layer

which, for instance, had a horizontal velocity of 7 mm/s. Beside the assumptions made in

obtaining both the shear strength and the shear stress, other physical environmental

factors may also change the properties determined in the laboratory. Thus, it is highly









likely that in the prototype environment, wave action measurably lowers bed shear

strength, as well as enhances current-induced bottom shear stress, as was seen in section

4.3.3. With the purpose of incorporating these effects a coefficient, 091, will be included

and evaluated from the measurements. Considering the empirical equation given by

Otsubo for incipient movement, the bed shear strength is obtained from Equations (14)

and (16) as follows

S= 01.03xO-4C1.57 (47)




3.4.4 Rate Constant
Selecting anchor stations OS2 (2418) and CN (2428) as examples, the erosion rate

constant M in Equation (44) and the coefficient 0 were determined. The erosion rate is

defined with respect to the positive sediment flux. Bottom shear stress was calculated

according to Equation (31). The best fit between the excess shear stress (r. r,) and the

erosion rate for anchor station CN (2428) gives a coefficient [in Equation (47)] 0 =0.4

and a erosion rate constant M=0.02 r kg m'n2sPa'1. Similarly, for anchor station OS2

(2818) M=0.027 c, kg m'2s'Pa-' was obtained, using the same value of 9.

Thus, taking the calibrated M values, the observed and calculated erosion rates at

z=0.25m for anchor stations 2428 and 2418 are as given in Figure 43. Note that negative

flux values, i.e., when the bed shear stress is lower than the bed shear strength, should be

treated as deposition, which will be considered later.













x 10 OS2 (2418)











i \ / /
6-

4-



x 0


-4 2-


-6 '
4-4

-8

-10
0 5 10 15 20 25
time (h)


x 1 0 CN (2428)


4-

2
4 -2
I a,








-6
-4



-8
-8
0 5 10 15 20 25
time (h)


Figure 43: Observed (dotted line) and calculated (solid line) sediment fluxes at an
elevation of 0.25m for anchor stations OS2 (2418) and CN (2428).




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