• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Dedication
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Abstract
 Introduction
 Theoretical review and backgro...
 Field measurements and instrument...
 Data analysis
 Numerical investigations
 Conclusions
 List of references
 Biographical sketch






Group Title: Technical report – University of Florida. Coastal and Oceanographic Engineering Program ; 128
Title: Two-dimensional time dependent structure of the suspended sediment concentration over rippled seabeds
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Permanent Link: http://ufdc.ufl.edu/UF00075313/00001
 Material Information
Title: Two-dimensional time dependent structure of the suspended sediment concentration over rippled seabeds
Physical Description: xii, 84 leaves : ill. ; 29 cm.
Language: English
Creator: Chang, Yeon Sihk, 1968-
Publication Date: 2001
 Subjects
Subject: Civil and Coastal Engineering thesis, Ph. D   ( lcsh )
Dissertations, Academic -- Civil and Coastal Engineering -- UF   ( lcsh )
Genre: bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (Ph. D.)--University of Florida, 2001.
Bibliography: Includes bibliographical references (leaves 81-83).
Statement of Responsibility: by Yeon Sihk Chang.
General Note: Printout.
General Note: Vita.
Funding: Technical report (University of Florida. Coastal and Oceanographic Engineering Dept.) ;
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Bibliographic ID: UF00075313
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved, Board of Trustees of the University of Florida
Resource Identifier: aleph - 002758068
oclc - 48190524
notis - ANN6020

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Title Page
    Dedication
        Section
    Acknowledgement
        Acknowledgement 1
        Acknowledgement 2
    Table of Contents
        Table of Contents 1
        Table of Contents 2
    List of Tables
        List of Tables
    List of Figures
        List of Figures 1
        List of Figures 2
        List of Figures 3
    Abstract
        Abstract 1
        Abstract 2
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
    Theoretical review and background
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
    Field measurements and instrument calibration
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
    Data analysis
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
    Numerical investigations
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
    Conclusions
        Page 78
        Page 79
        Page 80
    List of references
        Page 81
        Page 82
        Page 83
    Biographical sketch
        Page 84
Full Text




UFL/COEL-TR/128


TWO-DIMENSIONAL TIME DEPENDENT STRUCTURE OF THE
SUSPENDED SEDIMENT CONCENTRATION OVER RIPPLED
SEABEDS








by





Yeon Sihk Chang


Dissertation


2001


i















TWO-DIMENSIONAL TIME DEPENDENT STRUCTURE OF THE SUSPENDED
SEDIMENT CONCENTRATION OVER RIPPLED SEABEDS

















By

YEON SIHK CHANG


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

UNIVERSITY OF FLORIDA


2001


1



























To my wife Eun Young Choi

and my sons, James and Charles
















ACKNOWLEDGMENTS


I would like to express the sincere appreciation and gratitude to Dr. Daniel Hanes,

my academic advisor and the chairman of the advisory committee for his guidance,

encouragement, constructive criticism, and infinite patience over the years without which

this work would not have been possible. From him I have learned how to pursue

academic research as well as how to set up a problem. I also thank Dr. Hanes for the

research trips to Duck, Hannover, Genova, and San Francisco from which I had precious

experience to meet the academic leaders in the areas.

I would like to extend my gratitude to Dr. Robert G. Dean, Dr. Michel K. Ochi,

Dr. Robert J. Thieke, and Dr. Ulrich H. Kurzweg for their guidance and suggestions as

the members of my doctoral advisory committee. Their classes deeply contributed to my

knowledge in the fields of littoral processes, stochastic processes, fluid dynamics, and

mathematics.

I am especially indebted to Dr. Ken Andersen for use of the Dune2d numerical

model and also to Dr. Soren Tjerry and Dr. Diane Foster for their assistance with the

model. I would also like to thank the ONR Coastal Sciences Program for funding this

research.

I wish to thank Sydney and other members at the Coastal Engineering Lab for

their assistance in the preparation of the field experiments. I am grateful to Becky and all


I










other office staff for their hospitality and timely help on my affairs. Thanks also go to

Helen, John, and Kim for the best service in the archive.

Special thanks go to my fellow students. Craig taught me about instrumentation

and helped me get accustomed to life in United States. Eric helped me with the acoustic

instrument calibration, allowing me to use his program. Vadim helped me with the

bedform data. Oleg has provided me with computer help. He also amused me with his

cheerful way of life. I also acknowledge my friendships with the Korean students Jun,

Kijin, and Tae Yun.

I would like to give my special thanks to Pastor Hee Young Sohn and my dear

friends in the Korean Baptist Church of Gainesville for their love and leading me toward

God.

For their constant love and support, I am forever grateful to my mother and

brothers. I would also like to remember my late father. His precept with love has always

guided my life. I also wish to thank my parents-in-law for their support and

encouragement.

My final thanks go to my wife and two sons, James and Charles who let me know

what true love is for they have changed my life into a wonderful and beautiful one.















TABLE OF CONTENTS

page

ACKN OW LEDGM ENTS ..................................................................................... iii

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

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

ABSTRACT....................................................................................................................... xi

CHAPTERS
1 INTRODUCTION ..................................................................................................... 1

2 THEORETICAL REVIEW AND BACKGROUND.......................................................

Sedim ent Trapping by a Vortex ....................................... .............. ......................... 5
Dune2d Num erical M odel......................................................................................... 7
Flow m odule ......................................................................................................... 7
Turbulence module ............................................................................................... 9
Sedim ent transport m odule ..................................................... .......................... 11
Transform ation of the equations in general coordinates........................ .......... 14
Discretization...................................................................................................... 16
Grid generation ................................................................................................... 20

3 FIELD MEASUREMENTS AND INSTRUMENT CALIBRATION........................23

SandyDuck97 Experim ent ........................................................ ............................ 23
Instrum entation System .......................................................................................... 25
Calibration............................................................................................................... 27
ABS calibration................................................................................................... 28
ADV, OBS, Pressure, and TTC calibrations...................................... ............. 37
Field M easurements................................................................................................ 41
Coordinate transform ation of the velocity components......................................... 41
Data processing................................................................................................... 43

4 DATA ANALYSIS..................................................................................................48

Hydrodynam ic Conditions........................................................ ............................ 48
M ean Concentration Profiles ..................................................... ........................... 52
Ensemble Average Technique for Suspension Events.............................. ........... 53
Suspended Sediment Distributions over Large Wave Ripples ................................. 54










5 NUMERICAL INVESTIGATIONS......................................................................58

Non-dimensional Parameters................................................................................ 58
Generation of Wave and Current Conditions......................... ............................ 59
The Effects of Small-Scale Ripples..................................................................... 60
Temporal and Spatial Variations of the Flow, Turbulence, and Concentration ........... 64
Comparison of Model Predictions of SSC with Data................................................. 71

6 CON CLU SION S.......................................................................................................78

LIST OF REFERENCES ............................................................................................. 81

BIOGRAPHICAL SKETCH ....................................................................................... 84















LIST OF TABLES


Table Page

3-1: The basic characteristics of ABS........................................ ....................................28

3-2: The water attenuation (a,), the sediment attenuation (a,), and the sediment
backscatter parameter ( F ). .......................................................................................29

3-3: Concentration levels used in the ABS calibration. The initial volume of the water
inside the tank w as 46.0 liter ..................................................................................... 31

3-4: The results of the ABS Calibration. ....................................................................... 32

3-5: Calibration results of the ADVs ............................................................................. 37

3-6: List of the gains and offsets for Tilt, Temperature and Compass ................................40

3-7: Description of the variables saved in the processed data files .....................................43

4-1: Comparison of the hydrodynamic conditions between Case (A) and (B)....................51















LIST OF FIGURES


Figure Page

2-1: Description of the behavior of the sediment particles under waves (left) and inside a
vortex (right)............................................................................................................. 6

2-2: Grid cell addresses using compass notation. Cell centers are denoted by upper case
letters, lower case refer to cell faces.................................... ................................. 17

2-3: Grids for model, smooth (upper panel) and rough bottom (lower panel). ...................22

3-1: SandyDuck97 instrument layout at the Army Corps of Engineers Field Research
Facility. The instruments mounted by University of Florida are denoted by "Hanes,
V incent"....................................................................................................................24

3-2: Beach profile and the location of the instruments. Data are provided by FRF ............24

3-3: Instrumentation schematic at SandyDuck'97 field experiment....................................25

3-4: Cumulative size distributions of the sand sample, circles: Sieve analysis data, solid:
log-norm al size distribution...................................................................................... 27

3-5: Configuration of the calibration tank. By circulating the water and sand mixture, a
uniform condition can be maintained inside the tank........................................... ..30

3-6: Measured acoustic signals (left panels) and the converted concentration profiles
(right panels) for each transducer.................................... ...........................................33

3-7: One example of the bottom return in the ABS profiles................................................34

3-8: Application of the bottom determination to a measured data from SandyDuck97
experiment. Data were measured at Sep.27, 1997 by ABS #1.....................................35

3-9: Calibration results for OBS. circle: data, solid: fitted line...........................................39

3-10: Calibration results for pressure. circle: data, solid: fitted line....................................40

3-11: Plan view of the coordinate system during the SandyDuck97 experiment .................42









3-12: One example of the processed data, mean concentration profiles, time series of
velocities and concentration profiles, directional spectrum, and bedform profiles........46

3-13: Two-dimensional images of seabeds measured by RSS. ............................................47

4-1: Time averaged bedform with measurement locations......................................... ...49

4-2: Comparison of the surface elevation spectrum, thicker line: Case (A), thinner line:
Case (B). ....................................................................................................................50

4-3: Vertical profiles of the time-averaged suspended sediment concentration; square:
Case (A ), circle: Case (B).........................................................................................52

4-4: Time series of horizontal velocities in the cross-sectional direction (upper panel) and
the corresponding sediment concentrations at z = 1.02 cab (lower panel). The
displayed time series are the first 200 seconds data for case (B). The selected waves
according to the "concentration events" are also shown with the thicker line (upper
panel). The circles in the lower panel indicate the peak concentrations that exceed
the mean + standard deviation of the concentration (dashed line). ..............................54

4-5: Ensemble averaged data of the horizontal velocities, vertically integrated suspended
sediment concentration (upper panel) and the vertical distribution of the suspended
sedim ent concentrations. ...........................................................................................55

5-1: Horizontal velocity comparison over one wave period, o: data at P1 (Case (A)) and
P2 (Case (B)) solid: Dune2d calculations at P1 (Case (A) and P2 (Case (B), to:
time of offshore to onshore flow reversal of Dune2d calculations ..............................60

5-2: Comparison of velocity fields between the smooth and rough bottom at flow
reversal, Case (A). The flows are shown with arrows and drawn at every third grid
points. ........................................................................................................................61

5-3: Calculated vertical profiles of horizontal velocity at position PI, Case (A), solid:
rough bottom, dashed: smooth bottom ........................................................................62

5-4: Turbulent kinetic energy comparison over smooth and rough bottom, t = to 7/20,
C ase (A )....................................................................................................................63

5-5: Temporal and spatial variation of SSC and TKE over flat bed....................................65

5-6: Time variation of velocity field, Case (A). ti: time of maximum offshore velocity, t2:
time of offshore-onshore flow reversal, t3: time of maximum onshore velocity, t4:
time of onshore-offshore flow reversal. The arrow scale in (b) and (d) is magnified
twice for a better view. ..............................................................................................66

5-7: Time variation of velocity field, Case (B). ti: time of maximum offshore velocity, t2:
time of offshore-onshore flow reversal, t3: time of maximum onshore velocity, t4:









time of onshore-offshore flow reversal. The arrow scale in (b) and (d) is magnified
twice for a better view. ..............................................................................................68

5-8: Temporal and spatial variations of the distributions of the Turbulent kinetic energy,
ti,t2,t3, and t4 are same in Fig. 5-6 and 5-7...................................................................69

5-9: Temporal and spatial variations of the distributions of the suspended sediment
concentrations, tl,t2,t3, and t4 are same in Fig. 5-6 and 5-7..........................................70

5-10: Comparison of TKE between data and model predictions at P1 and P2, solid: model
predictions, circles: measured data .................................................................72

5-11: Comparison of the vertical distribution of the suspended sediment concentration
between data and model results at P2. Case (A) ....................................................74

5-12: Comparison of the vertical distribution of the suspended sediment concentration
between data and model results at P2. Case (B)........................................................75

5-13: Comparison of SSC profiles between measurements and model predictions; the
profiles are determined from the maximum values at each elevation..........................76














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

TWO-DIMENSIONAL TIME DEPENDENT STRUCTURE OF THE SUSPENDED
SEDIMENT CONCENTRATION OVER RIPPLED SEABEDS

By

Yeon Sihk Chang

August 2001


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

A field experiment was conducted to investigate small-scale sediment dynamics

near the seabed in the nearshore region. The SandyDuck'97 experiment took place at the

U.S. Army Corps of Engineers Field Research Facility, in Duck, North Carolina, U.S.A.,

where the seabed typically consists of fine to medium size sand. Acoustic instrumentation

measured the local hydrodynamics, the suspended sediment concentration (SSC) profile,

and the local bedforms.

The vertical distribution of the SSC is investigated over low amplitude wave

orbital ripples in two different data sets with comparable hydrodynamic conditions but

with the sediment concentration measurements located at different cross-shore positions

relative to the bedforms. The bedforms have low steepness and exhibit well rounded

crests compared to classical vortex ripples, so the mechanisms for sediment suspension

are somewhat mysterious. The concentration profiles exhibit different temporal patterns

that relate to their different locations over the bedforms. The vertical and temporal









structures of the concentration profiles indicate significant horizontal advection of clouds

of suspended sediment by the wave induced orbital fluid motion.

The Dune2d boundary layer numerical model is applied to investigate the

structure of the turbulence and suspended sediment concentration over the observed

ripples. The simulations of the flow using Dune2d indicate that a turbulent vortex is

generated at the lee of the ripple crest near the time of flow reversal. This indicates that

the mechanism for sediment suspension above these low amplitude, long wave ripples

(LWR) is essentially similar to the vortex formation process expected over steeper vortex

ripples. The turbulence kinetic energy (TKE) distributions also indicate that high TKE is

concentrated at the location of the vortex. The intensity of turbulent vortex is enhanced if

small wave ripples (SWR) are superimposed on the LWR. Numerical investigations of

the SSC indicate that the sediment is entrained from the bed and a sediment cloud is

formed by the action of the turbulent vortex. This cloud is advected horizontally over the

bed by the wave orbital fluid motion.

The comparison between the data and model predictions shows an agreement with

regard to the time within a wave period of the peak SSC. This indicates that the

generation of the sediment cloud and its movement are well predicted over rippled

seabeds by Dune2d. However, the magnitude of SSC as well as TKE was underestimated

by Dune2d. This disagreement can be explained from the use of the rigid lid surface

boundary condition, which results in the under-estimation of sediment suspension and

vertical mixing of the suspended sediments.














CHAPTER 1
INTRODUCTION



The distributions of the suspended sediment concentration (SSC) over seabeds

under wave and current conditions are important to sediment transport in coastal areas

because a considerable portion of the sediment is moved in suspension. As waves

propagate from deep water toward the shoreline, they shoal and their height generally

increases in the near shore region. During this process the waves entrain sediment from

the seabed. The suspended sediment is then transported by the currents. When the

sediment is suspended from the seabed, the shape of the bottom is one of the main factors

to be considered. Hydrodynamic conditions over a rippled seabed vary horizontally on

the scale of the bedforms, but above a flat seabed hydrodynamics are uniform over these

scales. Sediment suspension events should therefore exhibit very different patterns above

flat versus rippled beds.

The distributions of the SSC over various seabeds have been investigated for

several decades. For example, Bagnold (1946) suggested that the sediments are entrained

into a vortex that is formed at the lee of the ripple crest and the vortex is ejected upward

as the flow reverses. During this process, a large amount of sediment falls quickly to bed

but some of the sediment is carried with the vortex forming a cloud of sediment. From an

experiment that was carried out in an oscillatory flow water channel, Sleath (1982)

confirmed the generation of a vortex and its influence on the suspension of sediment over

rippled beds. Through the analysis of the velocity and the SSC measured in the field,






2

Vincent et al. (1999) showed that the suspended sediment distribution is consistent with

vortex entrainment. They found that high sediment concentrations are distributed over the

ripple trough at times of peak wave velocity.

Acoustic instruments for measuring the SSC such as the Acoustic Backscatter

System (ABS) have enabled the measurement of nearly instantaneous concentration

profiles (Lee and Hanes, 1995; Osborne and Vincent, 1996; Thosteson and Hanes, 1998).

The Multiple Transducer Array (MTA) has enabled the measurement of bedforms in one

dimension (Jette and Hanes, 1997). For analysis of the hydrodynamic and the sediment

concentration data, an ensemble average technique is often employed in order to

investigate the temporal and spatial distribution of the suspended sediment. One way of

ensemble averaging is by wave phase (Osborne and Vincent, 1996; Vincent et al., 1999).

The advantage of this technique is that the temporal variation of the concentration

distribution may be compared with the flow at each wave phase. However, since the

concentration events only occur intermittently in the field, the ensemble average over all

waves could smear out the sediment distribution pattern. Another ensemble averaging

technique is to "average by events" by picking suspension events from the whole bursts

and ensemble averaging the concentration and flow after aligning the temporal peaks in

SSC (Dick and Hanes, 1994). The temporal variation in concentration can be seen clearly

by this approach but the relation with the wave phase is not as clearly seen. Here we use a

new technique to avoid these disadvantages. Particular waves are selected only if the

peak concentration is higher than mean plus one standard deviation of concentration, and

then the selected waves and concentrations are ensemble averaged by wave phase.









Sediment suspension and its distribution have also been investigated through

various numerical models. Over a flat bed, Fredsoe et al. (1985) suggested a one-

dimensional time dependent diffusion type model for suspended sediment distribution. In

this model, they used the momentum integral method to derive a time-varying eddy

viscosity that enabled the calculations of the time variation of the SSC. The instantaneous

bed concentration was assumed to be a function of bed shear stress, resulting in the

maximum bed concentration at the time of maximum fluid velocity. Time lags were

found for the peak concentration at different elevations due to the diffusion processes.

Another one-dimensional description of suspended sediment distribution is a convection-

diffusion type model (Nielsen, 1988, 1991, 1992, 1992b). By introducing a "pick-up"

function that describes the instantaneous pickup rate at the bed, the model accounts for

the large scale mixing (convection) as well as small scale mixing (diffusion). Lee and

Hanes (1996) also suggested a one-dimensional, convection-diffusion type model that

combined the eddy diffusivity of Wikramanayake (Wikramanayake, 1993; Grant and

Madesen, 1979) and Nielsen's "pick-up" function.

Several models are also available for the investigations of the two-dimensional,

time dependent suspended sediment distributions over rippled seabeds (Hansen et al.,

1994; Black et al., 1997; Andersen, 1999). The Dune2d numerical model is a boundary

layer numerical model that calculates hydrodynamics and sediment concentration fields

above rippled seabeds (Tjerry, 1995; Andersen, 1999). It resolves the turbulent vortices

around the ripples by using a k- c turbulence closure model.

The purpose of the present study is to investigate the two-dimensional time

dependent structure of suspended sediment distributions over rippled seabeds through









analysis of the measured field data, and through a numerical study using Dune2d. For this

purpose, the theoretical background of the Dune2d model is described in Chapter 2. The

description includes formulation of the flow, turbulence, and sediment transport module,

and also describes the coordinate transformation, the grid generation, and the discrete

equation. The importance of the turbulent vortex in trapping the sediment particles is also

reviewed in this chapter. In Chapter 3, the calibration procedure of the instruments used

in the SandyDuck97 field experiment is described. Data processing procedure is also

explained in this chapter.

In Chapter 4, the ensemble average technique according to the suspension events

is described. The result of the data analysis is then discussed in terms of the timing of the

sediment suspension with relation to the relative location of the SSC measurements. The

movement of sediment clouds over ripples that are generated by the action of the

turbulent vortex is investigated through the use of the Dune2d model in Chapter 5. The

Dune2d model is also evaluated by comparing the model predictions with the

measurements. Chapter 6 presents the main conclusion of the present study and

discussions for future study.














CHAPTER 2
THEORETICAL REVIEW AND BACKGROUND


Sediment Trapping by a Vortex

When the sediment suspensions under waves are discussed in the nearshore

regions, one of the main factors to be considered are the seabed conditions, flat or rippled

bed. When the waves are moving over ripples with their oscillatory motions, the velocity

distributions near the bed are not uniform because of the irregular shape of the bottom.

So, the uniform conditions are no longer satisfied as they are over flat beds. One of the

most distinguishing features over the rippled beds is that the turbulent vortices are

released in the lee of the ripple crest at the time of flow reversal. Those vortices entrain

the sediments from the bed, forming the sediment clouds. The sediment grains inside the

sediment cloud are trapped in the vortices and transported with flows for a considerable

distance. In contrast, a pure oscillatory motion by waves cannot trap the sand grains

though the fluid orbits are also in the shape of circles or ellipses. The mechanism of the

sediment trapping in the vortex will be briefly discussed here based on Nielsen's work

(Nielsen, 1992a).

The velocity vector of the sediment particle, u,, can simply be formulated by a

vector sum of the fluid velocity, u, and the settling velocity, w0, from the zero order

approximation,



u, = u+Wo (2-1)









Since the settling velocity is directed downward, the particle velocity in Eq. (2-1)

is deviated from the orbital motion though the fluid velocity has a closed orbit under

wave conditions. So, the sediment paths under waves are directed downward as shown in

the left panel in Fig. 2-1.


WAVE

-C


Sediment path


VORTEX


Fig. 2-1: Description of the behavior of the sediment particles under waves (left) and
inside a vortex (right).



But, the particle velocity inside a vortex can be found to be different. Since the

fluid motion of a vortex can be simply considered as that of a rigid body, the fluid

velocity, u, is now,


u = u(x,z) = co(-zi+x j)


(2-2)


where co is the angular velocity and x, z are the horizontal and vertical positions.









By applying Eq. (2-2), the sediment velocity is now reduced to



u, = u + wO = C(-z i + x j) + (0 i w0 j) = c(-z i + (x w0 / o) j) (2-3)



So, the particle velocity, u,, is identical to u except for a horizontal shift of

magnitude, w0 / a. As shown in the right panel in Fig. 2-1, the sediment path is trapped

inside the water particle path. So, though the vortices and waves have similar fluid orbital

motions, they differ greatly with respect to their influence on suspended sediments.

As a result, the turbulent vortices play an important role in sediment transport

over rippled beds because they tend to trap sediments and carry them for some distance.


Dune2d Numerical Model

The numerical model used in the present study is called Dune2D and was

originally developed at the Technical University of Denmark. Dune2D is a boundary

layer model composed of three modules the flow, turbulence, and sediment transport

module. The theoretical background for Dune2D is well described in Tjerry(1995) and

Andersen(1999), and will be briefly reviewed here.


Flow module

A two-dimensional, incompressible flow motion is by the momentum and

continuity equations,









Ou a(u2+p) Ouv (O2u 2u)
-+ --+ = v +
Ot Ox ay &x2 2
Ov auv a(V2+p) ( a2'v (2v-
+ ---+ = v + (2-4)
at ox ay 9x2 2
Ou av
-+- =0
Ox ay



where x and y are the horizontal and vertical coordinates respectively. In Eq. (2-4), the

fluid pressure has been normalized by fluid density. Eq. (2-4) can be divided into two

parts by Reynolds decomposition assuming



u=U+u
v = V + v (2-5)
p=P+p



where U, V, P are the mean values and u', v', p are the fluctuations which have zero

means by definition, u = v = p = 0. The mean values are allowed to vary in time on a

larger time scale than the turbulence fluctuations to reveal wave motions or vortices over

rippled beds. The final governing equations, known as Reynolds-averaged equations, can

be obtained by substituting Eq. (2-5) into (2-4) and then averaging with a time scale that

is large compared to the time scale of turbulence, and small compared to the time scale of

the mean flow.









U a(U2 + '2 +p) 9(UV+uv) (D2U D2U
+ + y = v 7 +y2 )

DV D(UV +u'v') (V2 + p) +(2V 2V"
-+ + = v +-
at Ox Dy x 2 y2
DU av
-+-- =0
Dx 9y (2-6)



Eq. (2-6) includes additional stresses, known as Reynolds stresses, that represent

the momentum transfer caused by the turbulent motions. The equations are closed using

an eddy viscosity expressed in tensor form as




-uu1 = v, + Ks,5 (2-7)




where v, is the eddy viscosity and K is the turbulent kinetic energy (TKE). The trace of

the Reynolds stress tensor in Eq. (2-7) gives the TKE as



.2 .2
K= -- (2-8)
2


Turbulence module

In order to calculate the eddy viscosity, it is necessary to employ a turbulence

closure model. Out of numerous models, the K co model that was developed by Wilcox

(1998) is used in Dune2D. The K ca model has been applied with success in areas with









strong adverse pressure gradients (Andersen, 1999). In K w model, the eddy viscosity

is given from dimensional considerations as the ratio of K and w



v, = (2-9)
CO



Because it has the reciprocal of time dimension, a can be interpreted as a

frequency of turbulent fluctuation.

In order to determine K and co, the following set of model equations is proposed



aK aUK aUK a [9K +K 9 F M +9K 9K
-+-+-=-I (v+ov,)\-+- +- Iv+o vI -+--
at ax ay ax [v x ay) y ax y
SOU 9-U -OV --9V OV
-uu --uv --vu --vv -- fako
ax ay ax Oy
(2-10)
ao9 a) aVCO a O ( a coa
-+--+-=- (v+av,) -+- +- (v+V) --+-
at ax ay 9x ax 9y 9y x ay
cO -- U --9a U -. OV -. tOV 2
+r- -uu ----vv- VV
K ax 9y ax ay



where the closure coefficients are given by Wilcox (1998) as

y=5/9, *'=9/100, f=3/40, o=1/2, a =1/2.

Three types of boundary conditions are needed bottom, surface, and lateral

boundary conditions. At bottom, a no-slip condition is applied for the flow, and the TKE

is assumed to be zero, i.e. U= V = K = 0 at bottom. co is specified at the bottom as a

function of the friction velocity and roughness (Wilcox,1998). In Dune2D, the domain









surface is not allowed to change its shape (rigid lid) and the variables are assigned to

have zero flux. For the lateral boundary condition a cyclic condition is applied by linking

the right boundary to the left boundary such that the solution is periodic.


Sediment transport module

After the flow and turbulence are calculated by solving Eq. (2-6), (2-7), (2-9) and

(2-10), the sediment transport is calculated in two parts, the bed load and the suspended

load. The Meyer-Peter formula (Meyer-Peter and Muller, 1948) and the Eungelund-

Fredsoe formula (Eungelund and Fredsoe, 1976) are employed for the bed load such that

the Meyer-Peter formula is used for 0 < 0.4,




b = 8(0-ph -6)3/2 (2-11)
ax



where b : bed load

0: Shields parameter

Oc: critical Shields parameter = 0.05

u : parameter accounting for the effect of bed slope = 20c

Oh
: bed slope
8x

and the Engelund-Fredsoe formula is applied for 0 > 0.4,


=b = 5p(,/ -0.7 ) 2


(2-12)









in which the probability function is given by




p= + l(2-13)
(O-0c)4



where pd : dynamic friction

The suspended sediment is modeled by the advection-diffusion sediment transport

equation in which the volumetric sediment concentrations are expressed in 'C'. The

derivation of the sediment transport equation starts from the balance between the "change

of the local sediment concentration" and the "divergence of the sediment flux" such that



ac a a
-= -V(U,c)= --uc -- wc (2-14)
at ax ay



The horizontal particle velocity, u,, can be replaced by the horizontal fluid

velocity, u, and the vertical particle velocity, w,, is replaced by the difference of the fluid

velocity and settling velocity, v w.. So, Eq. (2-14) becomes



ac a a
-= --uc--vc +-w c (2-15)
at 9x Qy Qy



Now, by applying the Reynolds decomposition, u = U + u', v = V + v', c = C + c',

and by taking time average of Eq. (2-15),









-+- (UC)+-(VC)=-(woc) (uc) (v'c) (2-16)
at Dx Dy Dy Dx Dy



The turbulent fluxes, uc' and vc can be described by turbulent diffusion such

aC
that uc = -, -
ax

The final sediment transport equation is now reduced to



aC DUC DVC owoC D DC 9 C
-+-+- =-+- --+- (2-17)
at Dx Dy ay Dx ox ) y y(2



where w0 is the settling velocity and e, is the sediment diffusivity that is assumed to be

equal to eddy viscosity. According to Eq. (2-17), the movement of sediment is described

as follows:

1) The sediment is entrained from the bed due to turbulent diffusion.

2) The entrained sediment is advected by the flow and settles back to the bed due

to gravity.

The bottom boundary condition for concentration is applied at the reference level,

y = 2d, where d is the median grain diameter. The reference concentration of Engulund-

Fredsoe is applied for the bottom boundary conditions such that the sediment

concentrations increase with the bottom shear stress (Fredsoe and Deigaard, 1992;

Engulund and Fredsoe, 1976).










C, o (2-18)
(1 +1/2,)



where C,: reference concentration

CO: maximum value for the volumetric concentration =0.65

A : linear concentration

In which the linear concentration, /2, is given by




0~-~6fdp *4K"2
& = 1. (2-19)
0.013s9



where K : von Karman's constant = 0.4

s: relative density of sediment = 2.65

In Dune2D, all the equations are non-dimensionalized by the depth, D, and

maximum velocity outside the boundary layer, Uo. By doing this, the vertical coordinate

ranges from 0 to 1 and all the parameters used in the equation have to be changed to non-

dimension form.


Transformation of the equations in general coordinates

In order to solve the equation over complex geometry such as ripples, it will be

helpful if coordinates are transformed into curvilinear general coordinates. In Dune2D,

the calculations are performed in an orthogonal coordinate. To begin with, it is necessary






15

to understand that the Cartesian coordinates (x,y) are functions of the general ones (, r7)

such that




x = x 7) (2-20)
y = y( ,77)



and the derivatives are obtained by applying the chain rule,



a Ox a ay a
+- (a)
S ax a 0-y (2-21)
a ax a +y a
a-= -+ (b)
a7 aq7 ax aq By



The conservative form of the transformation rules can be easily obtained from Eq.

(2-21) after some manipulation such as (a) (b) and (b) (a) *





8x J Q TJ J
(2-22)
S 1it is the area of the grid cell. By using Eq. (2-22), the governing equations expressed





in which xi is an expression of th andJ is the Jacobian defined by J = xeoy, xpy


and it is the area of the grid cell. By using Eq. (2-22), the governing equations expressed


i








in Cartesian coordinates (x, y) are transformed to general orthogonal coordinates (5, 7).

For example, the continuity equation is transformed such that



-u+-v =- Y,7 YU u+ -- x7 v
8x ay J By By [ 8
(2-23)
a (y,u -x,v) a (xv yu) 0
= -+ =0




Also, the horizontal component of the Reynolds averaged equation can be

transformed as shown in Eq. (2-24).



aU + (yyU x,V)U -+ L(xV yU)U
at a8 arl
S 2 2 2 u (2-24)
ay p y,p a y, +x U 8 +x 8U
yp y'p +- (v + v,) X + (v +v,)
8r a8 a8 J J J




Discretization

The governing equations are discretized implicitly in time using the finite volume

method (Patankar, 1980) and written in general curvilinear coordinates to allow the grid

to fit smoothly to the boundaries (Tjerry, 1995). Since there is no explicit equation for

pressure, the PISO algorithm is used to find the pressure field (Patankar, 1980). In order

to avoid numerical diffusion, the ISNAS scheme that gives third order accuracy is used

for the discretization (Zijlema, 1996).









In order to obtain the discrete equations, it is necessary to define the grid cell

address first. The cell centers are identified by upper case letters, while cell faces are

denoted by lower case. As shown in Fig. 2-2, the compass notations are used to mark the

neighboring cells around the center cell. For example, Ue represents the horizontal

velocity at the east face of the center cell, while UE represents the velocity in the cell east

of the center cell.




nw "ne
NW N NE -- --


W P E w p e


SW S SWSE--- se
I----------- I--J ----- ^~*

Fig. 2-2: Grid cell addresses using compass notation. Cell centers are denoted by upper
case letters, lower case refer to cell faces.



All the governing equations can be written in the general final discrete form at the

n+1 time step.




a ',,= n +S (2-25)
nb=E,W,S,N




in which 0 s are the variables to be solved such as velocities, turbulent kinetic energy,

and concentration. a s are the coefficients in the discrete equations and S is the source

term.


1









In Dune2d, the discretization is performed separately on the individual terms

instead of treating the whole equations, and the most important terms for this are the

convection and diffusion terms because they are involved in all the governing equations.

If the convection and the diffusion terms are separated from Eq. (2-24), it can be written

as


aCH + ac,= a '- a D
+ =-D -+-iDIa(2-26)


In Eq. (2-26), the horizontal and vertical convection fluxes are defined such that


CH = y, x,v


CV = Xsv Yru


(2-27)


and the diffusion fluxes are defined as


2 2 2 2
y +X yV +Xs
D, =(v + v,) Dx = (v + ,)y
J J


(2-28)


also, the horizontal velocity, U, is replaced by the general variable, 0.

Since A = At = 1 in the general coordinates, the discrete equation of Eq. (2-26)

now becomes


(2-26)









(C "n+l n- l AcA".+l "I"+1+ n+l) n+I +1)l
(CL' -C( -+(7 ,0s = [DJ(E )-Dw (Op (2-29)\
(2-29)
+ [(o; -(P )-4 ,['p o> 1J



by applying the upwind scheme, the convection fluxes at the cell faces are replaced by

the properties at cell center



Ce,"' = p+1 max(Ce,0) "+1 max(-Ce,0)
C, +1 -= C' max(C,, ) max(-C,, 0)
(2-30)
C,,' = +1 max(C,,0) N' max(-C,,,0)
C,."1 = S'+ max(C,, 0) + max(-C,, 0)



by combining Eq.(2-30), Eq.(2-29) is now reduced to



aP~, = a + aE + aS +a = + l= bb+l1 (2-31)



where,

aN = D, + max(0,-Cn) aE = D, + max(0,-C,)
as = + max(0,C,) aw = D, + max(0,C,)

and ap = aN + aE + as + aw

After the convection and diffusion terms are discretized, the next step is the

discretization of the local acceleration term.



_=- J -pt (2-32)
at At








where, J, is the Jacobian at cell center.

By combining Eq. (2-31) and (2-32),



[a, +-A- = a, ,l +~-" (2-33)




If Eq.(2-33) is compared with Eq.(2-25), we get



J J
a,<- a + S A- (2-34)
At At



The other terms such as pressure gradients in the momentum equations or

turbulent kinetic energy production term in the turbulent equations are discretized in the

same way, contributing to the source term or other coefficients.


Grid generation

For a given bedform such as the one used in this study, a grid system is generated

using the hyperbolic grid generator with a high density of grid points near the bed. The

starting points of the grid equations are orthogonal as described by Eq (2-35).



(x Y y= 0 or x x7 + y,y = (2-35)









Since the horizontal derivative, x y,, is known at lower grid level, Eq. (2-35)

only has two unknowns, x,, y,, and another equation is needed to close the system. The

second equation can be obtained by specifying the volumes of grid cells.



xy,, xqy~ = V (2-36)



where V is the volume of the cell and the left side of Eq. (2-36) is the Jacobian. So, by

specifying the volume of the cells at each grid level and by solving Eq. (2-35) and (2-36),

the vertical gradient, x,, y,, can be found at next level.



-Vy, -Vx
x, = -2 V 2 2 2 (2-37)
x2 +. y2 X + y2



Figure 2-3 shows two possible grids for Case (A). Since one of the purposes of

the present study is to investigate the effects of small-scale ripples when they are

superimposed on large-scale ripples, two types of bottom topography are presented in

Fig. 2-3. The upper panel has a LWR with dimension 1 m in length and 0.06 m in height.

SWR with length 7 cm and height 0.5 cm are added on top of the LWR in the lower

panel. In order to investigate the effects of SWR, the grid size should be smaller than the

ripple size, resulting in the decrease of grid size. In this study, 120 horizontal grid points

are used for the domain width 2.39 m and 60 grids points are used in the vertical

direction, which keeps the vertical grid size sufficiently small near the bed.











smooth bottom


0.1


E
C-
0
I 0.05
Ca


rough bottom


0.1

E
C'-
- 0.05

(U


0 0.5 1 1.5 2
cross-shore distance, m


Fig. 2-3: grids for model, smooth (upper panel) and rough bottom (lower panel).














CHAPTER 3
FIELD MEASUREMENTS AND INSTRUMENT CALIBRATION


SandyDuck97 Experiment

The SandyDuck'97 experiment was conducted at the U.S. Army Corps of

Engineering Field Research Facility, in Duck, North Carolina, U.S.A. for approximately

eight weeks from Sepember to November, 1997 (Hanes et al, 1998). During the

experiment, 26 organizations performed their investigations for a better understanding of

nearshore sediment transport with the focused topics on

Small and medium scale sediment transport and morphology (sediment

grains to 100 m scale);

Wave shoaling, wave breaking, and nearshore circulation;

Swash processes including sediment motion.

The instrument layout of the participating organizations is shown in Fig. 3-1.

A series of field data were measured by University of Florida under the

instruction of Dr. Daniel Hanes in order to investigate small-scale sediment dynamics

near the seabed in the nearshore region. An array of instrumentation was deployed about

390 m away from the shoreline and 1000 m north along the shoreline according to the

FRF coordinate system. The water depth is approximately 4 meters, and usually outside

the surf zone. The local bed slope near the instrument array is small and approximately

0.01 as shown in Fig. 3-2.





































Fig. 3-1: SandyDuck97 instrument layout at the Army Corps of Engineers Field Research
Facility. The instruments mounted by University of Florida are denoted by "Hanes,
Vincent".




beach profile at 97/09/27





0 --------------------------------------------
1
0 -i
(9
Z -2

o

-< Frame
-4

-5

-6
100 150 200 250 300 350 400 450 500
cross-sectional distance (m)


Fig. 3-2: beach profile and the location of the instruments, Data is provided by FRF.










Instrumentation System

The instruments measured the local hydrodynamics using a pressure sensor and

two Acoustic Doppler Velocimeters (ADV). The SSC was measured with a three

frequency Acoustic Backscatter System (ABS). The local bedforms were measured with

a Multiple Transducer Array (MTA) in one dimension over 2.385 m at frequency of 2 or

3 sec. Except the MTA data that were collected in separate system, the data sampling

frequency had the range from 1 to 4 Hz. A schematic of the instrumentation is shown in

Fig. 3-3, where the coast is located to the right of the figure.



--- Cross shore


-- .1 C, ---50.0M, -------- 98.19 ----- S
Soar

Sea bed

Fig. 3-3: Instrumentation Schematic at SandyDuck'97 field experiment.



More detailed description of the instruments used in SandyDuck97 experiment is

as follows;

Two Acoustic Doppler Velocimeters (ADV): three components of

velocities were measured at the frequency of 1, 2 or 4Hz. Most of the









data collected at 2 Hz. The control volumes of each sensor were

approximately betweenl0 cm and 30 cm above the bed. The horizontal

distance between two sensors was 53 cm along the cross-shore direction

and the vertical distance was 6.3 cm. The two ADVs are designated by

ADV #1 (right in the figure) and ADV #2 (left).

Three-frequency Acoustic Backscatter System (ABS): Concentration

profiles were measured from three different frequency sensors, 1.07,

2.28 and 4.80 MHz. The vertical range of the sensor is approximately

90 cm. The data were collected at the same frequency with ADV.

* Multiple Transducer Array (MTA): One-dimensional bedform profiles

were measured by MTA over 2.385 meters every 2 or 3 second. As

shown in Fig. 3-3, the spatial resolution is 1.5 cm at MTA #1 (center)

and 6.0 cm for MTA #2 and MTA #3.

Rotating Scanning Sonar (RSS): The planform acoustic images of the

seabed with a radius of 5 to 10 m were recorded on videotapes through

RSS.

Optical Backscatter Sensor (OBS): Time series of sediment

concentrations at one position were measured by OBS approximately 50

cm above the bed. Sampling frequency is same with ADV.

Pressure sensor: Time series of pressure was measured at the same

frequency as ADV.










Tilt, Temperature, and Compass (TTC): Tilt meter and compass was

used for the calibration of the frame coordinates. Temperature meter was

used for the estimation of the speed of sound.

Underwater video camera


Calibration

The instruments described in the previous section were calibrated in order to

convert the measured signals into engineering units. The methods and the results of the

calibration for data sets collected during the SandyDuck97 experiment were described in

this section. The purpose of this section is to have an official record of the experiment

data for any reader who is interested in utilizing the data. So, the readers may skip this

section if he is not interested in the calibration procedures.





0.8 mean = 2.6717()
Std. dev. = 0.4375(o)

S0.6-
0


|~0.4


0.2


-2 -1 0 1 2 3 4 5
Phi

Fig. 3-4: Cumulative size distributions of the sand sample, circles: Sieve analysis data,
solid: log-normal size distribution.









Before the calibration, it is necessary to obtain the correct information on the

sediment size. For this, sand samples were captured near the instrumentation frame by

scuba divers. Then, the sand samples were sorted by the Sieve analysis to give the

median diameter, 2.672 and the standard deviation, 0.438 in phi units. The sand grain size

is well described by the log-normal distribution as shown in Fig. 3-4.


ABS calibration

As already mentioned, a three-frequency Acoustic Backscatter System (ABS) was

employed for the measurement of the suspended sediment concentration during the

SandyDuck97 experiment and the basic characteristics of ABS are listed in Table 3-1.




Table 3-1: The basic characteristics of ABS.
Manufacturer CEFAS (MAFF) CEFAS (MAFF) CEFAS (MAFF)
Serial number ABS 1, Fl(3676) ABS 1, F2(3677) ABS 1, F3(3679)
Frequency (MHz) 1.07 2.17 4.80
Crystal radius (mm) 5.0 5.0 5.0
Pulse width (,ps) 13 13 13
Gain offset parameter tO (,us) 600 600 600
Sampling frequency (KHz) 100 100 100
Sampling delay ( us) 30 30 30


ABS recorded the vertical profiles of the acoustic signals that can be converted

into the volumetric concentration. Each vertical profile consists of 120 bins, and since the

distance of the adjacent bins is 0.74 cm, the maximum vertical range of the measurements

is (120-1)*0.74 = 88.02 cm.

The equation that relates the intensity of the backscattered acoustic signal to the

concentration is given as









AF(z)C(z)= V2(z)z2 exp(4z(a, +a,(z))) (3-1)



where A: System constant

z : Distance from transducer

F : Backscatter parameter

C: Mass concentration

V : Voltage read from transducer

a,: Water attenuation parameter

a,: Sediment attenuation parameter

In Eq.(3-1), the values of the F, a,, and a, can be determined theoretically.

Since all the theories and the procedures for the determination of the concentration from

the ABS measurements are well described in Thosteson and Hanes, 1998, the theoretical

backgrounds for the determination of the sediment concentration are omitted in this

paper. Instead, the calibration results and the parameters used for the data processing are

described here for a future user of the SandyDuck97 data sets. The values of the

determined F a, and a, are listed in Table 3-2.




Table 3-2: The water attenuation (a ), the sediment attenuation (a,), and the sediment
backscatter parameter ( F ).
1.07 MHz 2.17 MHz 4.80 MHz
a, 0.022641561 0.093123281 0.455639408
a, 0.017527177 0.188007003 1.151454408
F 0.119725938 0.762769079 2.511386331








The ABS calibration was performed in a calibration tank that was designed to

maintain the uniform sediment concentration by circulating the water with a considerable

speed.


Calibration Tube

Fig. 3-5: The configuration of the calibration tank. By circulating the water and sand
mixture, a uniform condition can be maintained inside the tank.


As shown in Fig. 3-5, the water and sediment mixture near the bottom of the

calibration tank are supplied to the top portion of the tank by the water pump through the

thin tubes connecting the bottom and the top. By keeping a high speed of the circulation,

a uniform concentration of the water-sand mixture can be reached though out the

calibration tank. So, the concentration inside the calibration tank is determined by









measuring the weight of the water and added sand. For the calibration task, 15 levels of

the concentration were varied from 0 to 5 g/1 and ABS measured the concentrations

inside the tank for 3 minutes at each level as described in Table 3-3.


Table 3-3: Concentration levels used in the ABS calibration. The initial volume of the
water inside the tank was 46.0 liter.
Designed Mass of dried sand Mass of dried sand Time of sand
concentration, g/1 (added), g cumulatedd), g addition, min
0 0
0.1 4.600 4.600 3
0.2 4.601 9.201 6
0.3 4.601 13.802 9
0.4 4.601 18.403 12
0.5 4.601 23.004 15
0.6 4.602 27.606 18
0.7 4.603 32.209 21
0.8 4.602 36.811 24
0.9 4.603 41.414 27
1.0 4.603 46.017 30
2.0 46.052 92.069 33
3.0 46.087 138.156 36
4.0 46.094 184.250 39
5.0 46.185 230.435 42


The three-minute measurements at each level were averaged to give 15 total

vertical profiles of the acoustic signal. Based on the known values of concentration(C),

acoustic signal (V), and other parameters in Eq. (3-2), the system constants (A) can be

determined. The determination of the system constants was performed for each

transducer through a program named "ABSolution" and the algorithm of this is described

in Thosteson and Hanes, 1998.

Before this process starts, two decisions must be made based on the experimental

configuration, "nearfield limit" and "maximum test concentration". As shown in the left









panels in Fig. 3-6, the measured acoustic signals increase rapidly near the transducers

because of the contamination of the signals due to saturation. These contaminated parts

are not recommended to be included for the calibration, and it is done by setting a

nearfield limit that determine a range of profiles to be included in the calibration. The

nearfiled limits are chosen to be 15 cm, 25 cm, and 33 cm for 1.07 MHz, 2.17 MHz, and

4.80 MHz transducers respectively. Based on the chosen nearfield limits, the maximum

test concentration must be determined for each transducer. According to the calibration

procedure by "ABSolution", the concentration at the first point in the profile (at the

chosen nearfield limit) must be determined first using an iterative technique. This

iterative technique produces two concentration solutions, and those concentrations lower

than the maximum value of the first solution are only considered for the calibration.

These maximum concentrations are found to be 5 g/l, 3 g/l, and 0.5 g/1 for the 1.07, 2.17,

and 4.80 MHz transducers respectively.

The calibration results such as system constants and DC offsets are listed in Table

3-4. Also, the errors are calculated based on the differences between the designed

concentration and the converted concentration profiles.




Table 3-4: The results of the ABS Calibration.
Instrument ABS #1 ABS #1 ABS #1
Frequency 1.07 MHz 2.17 MHz 4.80 MHz
Near field limit 15 cm 25 cm 33 cm
Maximum test concentration 5.0 g/1 3.0 g/1 0.5 g/1
System const. (all data) 0.048 0.111 0.273
D.C. offset (all data) -0.010 -0.009 0.013
Errors 17.0% 15.6% 8.4%




U-


33




1.07 MHz 1.07 MHz
1500 8


I4








2000 21-
o1500 1.

O- 0 --- --=--
02

0 0
0 50 100 0 50 100
2.17 MHz 2.17 MHz
2000 2

1500 1.5




500 0.2

0 0
C-




0 -- 0
0 50 100 0 50 100
4.80 MHz 4.80 MHz
1500 0.5

"g 50.3



o s 0.2
S1000
a) 0.1

0
0 50 100 0 50 100
bin bin




Fig. 3-6: The measured acoustic signals (left panels) and the converted concentration
profiles (right panels) for each transducer.




The measured acoustic signals and the converted concentration profiles are also

shown in Fig. 3-6. Because of the maximum test concentration is set to be 3 g/l for 2.17

MHz transducer, first 13 profiles out of 15 profiles are used in the calibration. For the

4.80 MHz transducer, only first 6 profiles are used according to the maximum test










concentration, 0.5 g/1. From the results of the converted concentration profiles shown in

the right panels in Fig. 3-6, it can be seen that the acoustic signals are converted into

concentrations with reasonable agreements, especially in the low levels of the

concentration. The errors are as low as 8 % for the 4.8 MHz transducer and increase up to

17 % for 1.07 MHz transducer. A possible reason for the error is from not accurately

knowing the concentration and distributions in the calibration tank, and this results in

incorrect calculations of the attenuation parameters.


2500


2000


1 1500


0 1000-
'u


500
0 -- --




60 70 80 90 100 110 120
bin number

Fig. 3-7: One example of the bottom return in the ABS profiles.



After all the parameters are determined, it is also necessary to determine the

location of the bottom from the measured profiles. Since ABS measured the returned

sound that are backscattered by the sediment particles, the backscattered signal will be

high near the bottom location because of the high bottom return. In Fig. 3-7, one example

of the acoustic signals measured by ABS 2.17 MHz shows that high acoustic signals are










detected at the bin numbers from 90 to 100, which indicates the possible bottom location

at these positions.


1.07 MHz


2.17 MHz


10

10

10

10

10

0<
8

10

10

10

10

10

08
8


250

-7 200
C
150
0
100
o
m 50



250

-7 200
-C
150
o
( 100
o
m 50



250

- 200

-u 150
4J 100
0
. 50


Fig. 3-8: Application of the bottom determination to a measured data from SandyDuck97
experiment. Data were measured at Sep.27, 1997 by ABS #1.



In order to determine the bottom location precisely, an experiment was set up in a

tank in which the distance between the bottom and ABS sensors are known precisely.

The bottom was then determined by measuring the distances of the acoustic signals. The


90 95 100
4.80 MHz


IU ------- I ------ -1 ------- I --------I------
0
0 -

-0 bottom
10- location peak

'0 "2.62'-

85 90 95 100 105 11
bin number









results showed that the exact locations of the bottom were several bins ahead of the

maximum bottom returns. In order to get the exact bottom location for 1.07 MHz

transducer, 4.67 bins should be subtracted from the bin number of the peak acoustic

signals. For example, if the maximum signal occurs at the bin number of 95, the bottom

is located at 95.0-4.67 = 90.33 bin. For the 2.17 MHz and 4.8 MHz transducers, the

offsets to be subtracted are determined to be 3.42 and 2.62 bins respectively.

In Fig. 3-8, these bottom determinations are applied to a data set, where the

determined bottom locations as well as the measured acoustic signals are shown along the

bin number. Though the location of the maximum signals are different for each

transducer, the determined bottom locations are well agreed each other when the offsets

are subtracted. In order to get the first bin number of the usable concentration

measurements, it is necessary to adjust the measuring point to the center of the acoustic

pulse and it can be done by subtracting the number of bins corresponding to a distance of

one quarter of the pulse width, 13/4 um = 0.48 cm = 0.649 bin. Since those numbers are

floating point quantities, it is also required to round down to the next lowest bin.

For example, the first usable bins can be determined in the following way if the

maximum acoustic signals occur at the bin number of 95 for all 3 transducers. By

subtracting the offsets and one quarter of the pulse width, we get



95.0 4.67 0.649 = 89.681 bin for 1.07 MHz

95.0 3.42 0.649 = 90.931 bin for 2.17 MHz

95.0 2.62 0.649 = 91.731 bin for 4.80 MHz.









Then, by rounding down these bin numbers to the next lowest bins, the first

usable concentrations are at 89 (1.07 MHz), 90 (2.17 MHz), and 91 (4.80 MHz) bins.

From these results, the lowest elevations of the concentration measurements are

determined to be 0.98 cm above bed (cab), 1.17 cab, and 1.02 cab for the 1.07 MHz, 2.17

MHz, and 4.80 MHz transducers respectively.


ADV, OBS, Pressure, and TTC calibrations

The ADV calibration equation is given by



V = 2.5* (M 0)/(4096 / 2) (3-2)



where V : velocity, m/s

M: measured signal

0: offset

Since M is the measured signals, it is only necessary to determine the offset, 0,

for the calibration. In order to determine O, a still water condition was set up at a

calibration tank, in which the velocity, V is designed to be 0. By measuring M of the

still water, the offsets are easily determined by Eq. (3-2). The results of the calibrations

are listed in the Table 3-5 for the ADV #1 and ADV #2.




Table 3-5: Calibration results of the ADVs
Velocity components Offset, counts (ADV #1) Offset, counts (ADV #2)
X1 2022.8 2028.0
X2 2026.3 2025.0
X3 2023.5 2020.7









In Table 3-5, the components, xl, x2, and x3 are not corresponding to the cross-

shore, the longshore, or the vertical velocities yet. They will be converted into those

components using the tilt and compass measurements, and will be discussed in the next

section.

OBS were calibrated using a linear regression method. By measuring the signal of

the known concentrations inside the calibration tank, the gain and offset were found from

a linearly varying function.



C=G*X+O (3-3)



where C : Concentration

X: Measured signal

G: Gain

0: Offset

The known concentrations are

C = [0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2.0 3.0 4.0 5.0] g/1

and the measured signals are

X = [131.9 143.6 153.5 164.8 175.9 183.5 197.2 214.5 223.5 244.9

242.3 361.6 466.5 613.9 694.3] signal

From the known values of C and X and from the equation (3.3), the gain (G) and

the offset (0) are determined to be

G = 0.0086695 g/l/signal, O = -1.1343 g/1


















o
C'3
-3


0
2

1-
O



0 200 400 600 800
signal

Fig. 3-9: Calibration results for OBS. circle: data, solid: fitted line.



In Fig. 3-9, where the measured signal and the concentrations are shown with the

fitted line according to equation (3-3), the line is well fitted to the data.

The pressure sensor was also calibrated in the similar way to OBS calibration, in

which the measured signals are directly related to the depth of the sensor instead of the

pressure. The known values of the depth (Z) and the signal (X) are as follows.

Z= [0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 ]m

X= [163.0 186.6 210.1 234.1 257.0 280.8 303.7 327.5 350.0 374.0

397.1 420.7 444.2] signal

The gain and the offset is then determined to be

G = 0.0042744 m/signal, O = -0.69833 m.










1.4

1.2

1-

E 0.8

0.6

0.4

0.2

0
150 200 250 300 350 400 450
signal

Fig. 3-10: Calibration results for pressure. circle: data, solid: fitted line.



The calibration of TTC was also performed in the similar way to OBS and

pressure calibrations, that is, the engineering units are determined from the signals

through the gains and offsets. The resulting gains and the offsets for TTC are listed in

Table 3-6.


Table 3-6: List of the gains and offsets for Tilt, Temperature and Compass.
Gain (degree/signal) Offset (degree)
Tilt 1 0.0153 -34.949
Tilt 2 -0.0146 29.421
Compass 0.241 -23.474
Temperature 0.122 -272.894









Field Measurements


Coordinate transformation of the velocity components

The data sets measured during the SabdyDuck97 experiments are converted into

the engineering units using the calibration results. Most of the variables are processed

directly except for the velocities. The three components of the velocities that were

calibrated through Eq. (3-2) have the coordinates related to the instrument frame. These

coordinates are required to be transformed into a fixed coordinate so that the three

velocity components are related to the cross-shore, longshore, and the vertical directions.

The transformation can be performed using the calibrated tilt and compass data. For the

coordinate transformation, the right-handed rule are employed such that the +U

designates the onshore direction, +V designates the downward direction along the

coastline, and +W means upward. Since the coastline is directed 352.510 from the true

north, the direction of+U is 262.510 and +V is 172.51. The plan view of the coordinate

system is shown in Fig. 3-11.

Before the transformation, the angles between the frame coordinates and the fixed

coordinates are needed to be set such that

0 = ir /180 tiltl
= / 180 tilt2 (3-4)
P =r / 180* (352.51 compass)

In Eq. (3-4), 0 is the angle in radian between the instrument frame and the fixed

coordinate in the cross-shore direction and b is the angle in the longshore direction. P is

the angle between the frame and coastline so that the new coordinated are related to the

coastline.












N
82.51

N +U


Coastline


Fig. 3-11: The plan view of the coordinate system During the SandyDuck97 experiment.



So, the conversion processes consists of the three steps according to the three

angles defined. The first step is the conversion in the cross-shore direction,


U = xl cos() x3 sin(O)
W = x3 cos() + xl sin(O)


(3-5)


in Eq. (3-5), xl and x3 is the velocities in the frame coordinates (Table 3-5).

Next step is the conversion according to 0,


V = x2 cos(O) W sin(q)
W = W cos() + x2 sin(O)


(3-6)


The final step is the conversion according to f,









U= V cos() + U sin()
V = -U cos(q) + V sin(q)


(3-7)


The U, V, and W calculated through Eq. (3-5) (3-7) are now the velocity

components related to the fixed frame representing the cross-shore, longshore, and the

vertical velocities respectively.


Data processing

After all the calibration coefficients are determined, the raw data are processed.

The data processing procedure includes the conversion of the raw data into the

engineering units, saving the converted data in the compact disks, plotting the processed

results, and making summary files. The name of the saved variables and their

descriptions are listed in Table 3-7.


Table 3-7: Description of the variables saved in the processed data files.

Name Size Description
HmO 1xl HmO in meter. HmO = 4 area under Sxx
Tpeak 1xl Wave period in seconds
bintsl 1x4096 Time series of bottom location in bin number, ABS 1.07
MHz
bints2 1x4096 Time series of bottom location in bin number, ABS 2.17
MHz
bints5 1x4096 Time series of bottom location in bin number, ABS 4.80
MHz
coast 1xl The direction of the coast line, 352.510 true north
coni 4096x120 Time series of concentration profile in g/l, ABS 1MHz.
Rows : time, Columns : bin
con2 4096x120 Time series of concentration profile in g/l, ABS 2MHz.
Rows : time, Columns : bin
con5 4096x120 Time series of concentration profile in g/l, ABS 5MHz.
Rows : time, Columns : bin
con125 lx120 Combined concentration profile in g/1. Calculated from the









h
h_abs
h advl
h_adv2
h_mta
h obs
h_pres
hdrl

infile
jdstart



jdend
pres
profx

r
sampfreq
seabedl

seabed2

seabed5

std_profmod








ul


u2


vl


v2


lxl
1xl
lxl
lxl
lxl
lxl
lxl
11xl

1x8
lxl



lxl
1x4096
1x64

lx120
lxl
1x4096

lx4096

lx4096

680x67








1x4096


lx4096


lx4096


1x4096


RMS value of ABS raw data.
Water depth in meter
Distance from bottom to ABS in meter
Distance from bottom to ADVI in meter
Distance from bottom to ADV2 in meter
Distance from bottom to MTA in meter
Distance from bottom to OBS in meter
Distance from bottom to Pressure sensor in meter
'hdrl' includes the information of the data collection.
Start date, time, ABS bin number, etc
Input file name
Elapsed day of starting time of data collection.
Eg. jdstart = 0.5 -* 12:00 at Jan. 1. 1997 (EST)
jdstart = 294.9519 -> 22:50:42 at Oct. 22. 1997
(EST)
Elapsed day of ending time of data collection
Time series of pressure in meter
Horizontal scale of MTA data in cm, onshore toward
higher number
Vertical scale of ABS data in meter
Data sampling frequency except MTA data in Hz
Time series of seabed distance from ABS 1MHz sensor, in
meter
Time series of seabed distance from ABS 2MHz sensor, in
meter
Time series of seabed distance from ABS 5MHz sensor, in
meter
Processed MTA data.
Column(l:64) : distances from MTA to bottom.
Column(65) : start time of MTA data collection,
elapsed day.
Column(66) : Time for the each MTA profile, elapsed
day.
Column(67) : Number of raw MTA profiles taken to be
processed
Horizontal(Cross-shore) velocity from ADVI in m/s,
positive value in onshore direction, 262.510 from the
true north
Horizontal(Cross-shore) velocity from ADV2 in m/s,
positive value in onshore direction, 262.510 from the
true north
Horizontal(Longshore) velocity from ADVI in m/s,
positive value down along coastline, 172.510 from the
true north
Horizontal(Longshore) velocity from ADV2 in m/s,
positive value down along coastline, 172.510 from the





I I_ _









wl lx4096 true north
w2 1x4096 Vertical velocity from ADV1 in m/s, positive upward
Vertical velocity from ADV2 in m/s, positive upward


One example of the processed data is also shown in Fig. 3-12, where the time

series of the velocity components as well as the mean concentration profiles are shown in

the left panels. The bedform profiles, time series of the concentration profiles, and the

directional spectrum are shown in the right panels.

The rotating scanning sonar (RSS) also videotaped the two dimensional features

of the seabeds. These two-dimensional images by RSS are helpful for the decision of the

type of the bedform near the frame while the MTA only provides the one-dimensional

bedform profiles.

In Fig. 3-13, two types of bedforms are compared, in which the RSS images at

two different dates are shown in plan view with the image radius of 5 m. The dark areas

in the figures represent ripple troughs because they are shadowed by the ripple crests

(light areas). Each image in Fig. 3-13 is averaged by 16 consecutive frames in order to

reduce the effects of noise. In the upper panel, the ripples are small in size and there are

no uniform directions of the ripples, showing a type of three-dimensional ripples. In the

lower panel, two large ripples with approximate distance of 1 m between the two adjacent

ripple crests are found near the MTA location. The directions of the large ripples are also

parallel to each other and perpendicular to the MTA, showing a type of two-dimensional

ripples.














SANDYDUCK97, date : 9/27/97 start time :16:34:52, elapsed day: 269.6909, File: c9rg0001

1MHz(-),2MHz(--),SMHz(-.),comblned(+),ste(o) a- offshore Bedforms onshore-
70 averaged 40rble d ist from bot.(m): 073555


10' 10' 10' 50 100 150
concentration (gl) & size (mm) Horizontal distance (cm)
ABS: 1 MHz


0 500 1000 1500 2000
100


50


0 500 1000 1500 2000
50




50
0 500 1000 1500 2000
10




-20
0 500 1000 1500 2000


200


0 500 1000 1500 2000
ABS: 2 MHZ

I *


It IHL &L i I A '
0 500 1000 1500 2000
ABS:5 MHz


I ,

0 i1000
0 500 1o00


St


01

A r.l


1

2000


20


0 500 1000 1500 2000
time (s)


0.6
Of
0 o
o.:
C 0' -
55 tc


Direction (degrees)


Frequency ()
Frequency Oro)


Fig. 3-12: One example of the processed data, mean concentration profiles, time series of
velocities and concentration profiles, directional spectrum, and bedform profiles.


I


'"


'"


0


...........i
: \2:-; :i:"-!:::i












U
M -
MS90


Fig. 3- 13: Two-dimensional images of seabeds measured by RSS.














CHAPTER 4
DATA ANALYSIS


Hydrodynamic Conditions

For the present study, two data sets with comparable hydrodynamic conditions are

chosen. For each case the seabed had LWR (Hanes et al, 2001), however the ABS

location was at relatively different locations on the ripple profile. The time averaged

bedforms and the locations of ADV and ABS measurements are shown in Fig.4-1. The

two different bedform conditions are denoted by Case (A) and Case (B). In Case (A),

'PI' is the location of ADV that is located near the ripple crest (slightly deviated from

crest to onshore side) and 21.8 cm above bed (cab), and 'P2' in Case (B) is the location of

ADV that is positioned at the offshore slope of the ripple crest and 23.2 cab. The time of

the measurements are 11 pm on Oct. 25, 1997 for Case (A), and 5 pm on Sep. 27, 1997

for Case (B). Each bedform profile in Fig. 4-1 is determined from the time average of a

30 min run. In Case (A), the seabed is covered by a LWR with about 0.9m length and

0.06m height. Case (B) has a similar ripple with length of 1.1m and height of 0.05m.

Since they are averaged in time, the seabed profiles in both Case (A) and (B) have

smooth bottom surfaces, showing no small-scale ripples. However, individual bed

profiles are more irregular in shape and have smaller size ripples superimposed on the

large bed profile.











Case (A)
0.3
*
Pi,
ADV location
E 0.2
0
ABS location
0.1 <- offshore onshore->



0
0 0.5 1 1.5 2

Case (B)
0.3
*
P2,
ADV location
E 0.2
0
( ABS location
0.1 <- offshore onshore ->



0 0.5 1 1.5 2
cross-shore distance, m



Fig. 4-1: Time averaged bedform with measurement locations.



The wave heights (Hm0) are similar both in Case (A), 1.09 m, and Case (B), 1.12

m. Both the wave spectrums (Fig. 4-2) show bi-modal shapes, with the two peaks at the

same frequencies, 0.13 Hz and 0.22 Hz. The local water depths are 4.1 m and 4.6 m for

Case (A) and (B) respectively, and the measurements were taken outside the surf zone in

both cases. The wave directions are 92.30 in Case (A) and 87.70 in Case (B), where 900

means normal to the coastline. One of the important assumptions in the present study is

that the ripples observed in Case (A) and Case (B) are uniform in the alongshore









direction. The observation that the wave directions are normal to the coastline supports

this assumption.


0 0.1 0.2 0.3 0.4 0.5
Frequency (Hz)

Fig. 4-2: comparison of the surface elevation spectrum, thicker line: Case (A), thinner
line: Case (B).


One interesting feature of the hydrodynamic conditions is that offshore mean

flows are observed in both cases, and the magnitudes of the mean flows are also

comparable in both cases. The magnitudes of the mean flow in offshore direction are 8.3

cm/sec for Case (A) and 6.1 cm/sec for Case (B).

As shown in Table 4-1, in which the comparisons of the hydrodynamics between

the two cases are listed. The statistical values of the hydrodynamic conditions are not

clearly different between the cases. For example, the root mean squared value of the

velocity is not different much between two cases in all the velocity components, u, v, and









w. This means that the total wave energy is comparable in Case (A) and (B). Also, the

RMS values are much higher in the cross-shore direction than in the longshore direction,

so the assumption of the uniformity on the longshore direction is valid. The skewnesses

of velocity are also similar and have low values in the horizontal velocity components, so

linear wave theory can describe the wave conditions of the two chosen cases. Also, the

accelerations are similar between the two cases.


Table 4-1: Comparison of the hydrodynamic conditions between Case (A) and (B).

Case (A) Case (B)
HmO (m) 1.09 1.12
Tpeak (sec) High freq. 4.6 4.6
Low freq. 8.0 8.0
Tdir (degree, 900 offshore) High freq. 41.5 60.0
Low freq. 92.3 87.7
Mean velocity (m/s) U (+ onshore) -0.083 -0.061
V (+ downcoast) 0.092 0.056
W (+ upward) -0.015 -0.004
RMS of velocity U (demeaned) 0.262 0.260
V (demeaned) 0.166 0.140
W (demeaned) 0.026 0.023
Skewness of velocity U 0.100 0.005
V -0.113 -0.078
W -0.307 -0.555
Mean acceleration (m/s2) U 0.000 0.000
V 0.000 0.000
W 0.000 0.000
RMS of acceleration U (demeaned) 0.263 0.274
V (demeaned) 0.216 0.171
W (demeaned) 0.034 0.029
Skewness of acceleration U 0.039 -0.049
V 0.026 0.039
W 0.280 0.543










As a result, the hydrodynamic conditions in both cases are comparable so we

presume that the main difference between the two cases is the relative locations of the

sediment concentration measurements over the ripples.


Mean Concentration Profiles

Fig 4-3 shows the time-averaged sediment concentration profiles of 35 min

duration. Out of three frequency transducers of ABS, the concentrations measured by

2.17 MHz transducer are analyzed for the present study. As already mentioned, the

vertical resolution is 0.74 cm and the lowest elevation of the reliable concentration

measurement is 1.17 cm above bottom.


20

18

E 16

S14 -

S12-
o
m 10




c)
> 6
u


10-3 10-2 10' 100
concentration g/l

Fig. 4-3: Vertical profiles of the time-averaged suspended sediment concentration;
square: Case (A), circle: Case (B).









In Fig. 4-3, the mean concentration decrease rapidly in both of the profiles at low

elevations, and the decreasing rate is reduced as elevation increases. Above 10 cab, the

variation of SSC are negligible, which indicates that the vertical mixing or the horizontal

movement of the SSC mainly occur near the bottom. The magnitude of the concentration

is higher in Case (B) particularly at low elevations, and the cause for this is not clearly

known from the understanding of the hydrodynamic conditions that are hardly

distinguished between the two cases. One possible explanation is the location of the

concentration measurements. If the sediment suspension occurs in the lee of the ripple

crest due to the turbulent vortex, high concentration is expected at this position such as

Case (B). As the suspended sediment moves, it is diffused and diluted, resulting in lower

concentration at some distance, such as ripple crest (Case (A)). This result is coincident

with the measurement by Vincent el al.(1999). They found that high concentrations are

distributed above ripple crest and lower concentrations are found above ripple crest.


Ensemble Average Technique for Suspension Events

Previous experiments (Brenninkmeyer, 1976; Thornton and Morris, 1978; Hanes,

1988; Hanes, 1991) have found that in the nearshore environment the suspension of sand

is intermittent, and tends to occur more often during relatively larger waves and during

wave groups.

For this reason, we select the waves that are coincident with high concentrations,

because the ensemble average of all the waves would smear out the distribution patterns.

SSC events are selected if the peak concentration is greater than the mean plus the

standard deviation of the whole time series of the sediment concentration. The each

concentration event is identified with one wave, determined from zero-downcrossings of









the velocities. By doing this, 102 waves were selected out of a total of 344 waves for

Case (A). For Case (B), 109 waves were taken out of 367 waves. Examples of the

selected waves are shown in the upper panel in Fig. 4-4 with a thicker line for case (B). In

the lower panel the corresponding peak concentrations are shown with circles.


c, 0.!
E

o
-0.
> -0.!


0 50 100 150
time, sec


Fig. 4-4: Time series of the horizontal velocities in the cross-sectional direction (upper
panel) and the corresponding sediment concentrations at z = 1.02 cab (lower panel). The
displayed time series are the first 200 seconds data for case (B). The selected waves
according the "concentration events" are also shown with the thicker line (upper panel).
The circles in the lower panel indicate the peak concentrations that exceed the mean +
standard deviation of the concentration (dashed line).




Suspended Sediment Distributions over Large Wave Ripples

The selected waves and concentration events are then ensemble averaged by wave

phase. In Fig. 4-5 the ensemble average of the vertically integrated concentration as well










as the ensemble average of horizontal velocity are shown in the upper panel. The vertical

structure of the ensemble average of the SSC is shown in the lower panel of Fig. 4-5. The

integrated concentration in the upper panel is the result of the integration of the vertical

distribution of concentrations in the lower panel and it is drawn because the overall

pattern of the suspended sediment concentrations can be easily compared with the

horizontal velocity. In Fig. 4-5, the velocity shown is the cross-shore component, and

velocities have positive values when the flows are in the onshore direction.


Case (A)


0.2

E 0.15
0
> 0.05

0.05


Vitr


Case (B)


0.2

0.15

0.1

0.05


0 7/2 x 3x/2 2x
ot


0 x/2 7 3x/2 27
ot


Fig. 4-5: Ensemble averaged data of the horizontal velocities, vertically integrated
suspended sediment concentration (upper panel) and the vertical distribution of the
suspended sediment concentrations.









The averaged velocity profiles in Fig. 4-5 have similar patterns in both Case (A)

and Case (B). Both of them show an asymmetry with higher maximum velocity in the

offshore direction than in the onshore direction due to the offshore currents. It should be

noted that the asymmetries are not due to the mean currents of the whole time series, but

rather are due to the mean of the time periods selected for ensemble averaging. The

overall mean flows are in the range of 6-8 cm/sec for Case (A) and (B). The averaged

wave period of the waves selected for ensemble averaging is 6.5 sec for Case (A) and 6.0

sec in Case (B), compared with the overall average wave period of 6.0 for Case (A) and

5.6 sec for Case (B).

Though the ensemble averaged velocities show similar patterns for both cases, the

distributions of the SSC are very different. In Case (A) the concentration peak occurs

after the offshore to onshore flow reversal and then the SSC decreases over the rest of the

wave period. In Case (B) the peak of the concentration occurs near the time of offshore to

onshore flow reversal. The difference in the timing of the peak concentration related to

flow reversal can be understood by considering the SSC measurement location relative to

the ripple crest location. As already mentioned, the ABS was located about 10 cm

shoreward of the ripple crest for Case (A), and about 30 cm seaward of the ripple crest

for Case (B). So, if the sediment is entrained from the lee of the ripple crest at the time of

flow reversal by the action of the turbulent eddies, the sediment cloud will be

subsequently advected over the ripple by the flow. In Case (B) the highest concentrations

are measured near the time of offshore to onshore flow reversal (Fig. 4-5). This is

expected because the concentration measurements are located on the offshore slope of the

bedform, where the sediment cloud is expected to form near the time of flow reversal. In









contrast, the ABS for Case (A) is located on the shoreward side of the ripple crest. If the

sediment cloud is formed on the offshore slope of the ripple at the time of offshore to

onshore flow reversal, this cloud will be carried by the onshore flows and will be detected

by the ABS at a later time as seen in Fig. 4-5. An interesting feature in the sediment

concentration distribution in Fig. 4-5 is that only one concentration peak is found over

one wave period in both Case (A) and (B). If flow reversals cause the formation of a

sediment cloud, then there should be two clouds formed during each full wave cycle. One

explanation for this is the asymmetry in the velocities. Because the magnitude of the

maximum offshore velocity is higher than the maximum onshore velocity, the offshore to

onshore transition results in stronger bottom shear stresses and greater turbulence

intensities.

In summary, the observations are consistent with the hypothesis that sediment is

entrained on the offshore slope of the ripple, and that the cloud of suspended sediment

begins to move upward and onshore at the time of the offshore-to-onshore velocity

reversal. However, these data only provide a limited description for the suspension

process. In order to provide a more detailed description of the turbulence and sediment

dynamics, numerical model is utilized in the next section.














CHAPTER 5
NUMERICAL INVESTIGATIONS


Non-Dimensional Parameters

Because all the equations are non-dimensional, the inputs to the model need to be

parameterized with non-dimensional values, such as Reynolds number, Froude number,

and angular frequency. Those parameters can be estimated from the dimensional values,

such as depth of domain (D), wave period (T), and maximum velocity (U0) outside the

boundary layer. In this study, D is chosen to be 1 m though the measured water depth is

about 4 m. The reason for the choice of 1 m instead of the measured depth is that, for

given domain width 2.39 m, a large value of D does not give the grid resolution dense

enough near the bed unless a large number of vertical grid points are used, which increase

the computational time. The wave period and the maximum velocity are determined

based on the field measurements. For example, the wave period is found to be 6.5 sec and

U0 is 0.39m/s for Case (A). For Case (B), the wave period is 6.0 sec and U0 is 0.40 m/s.

The median grain diameter is 0.16 mm. From these values, the non-dimensional

parameters are found as

2rD
Non-dim. wave frequency = D/a = J =2.48 (Case (A)), 2.62 (Case (B))
UoT


Reynolds number = UoD = 3.9* 10 (Case (A)), 4.0* 105 (Case (B))
V


Froude number = U 0.1245 (Case (A)), 0.1277 (Case (B))
gD









The bed roughness (KN ) is often chosen to be 2.5 times larger the median grain

diameter. However, the choice of this value tends to underestimate the output

concentrations when compared with the measurements. In the present study, the

roughness is chosen to be 3 times larger than usual in order for the maximum

concentration to be agreed with the measurement at the lowest elevation (1.17 cab) for

Case (A). The non-dimensional roughness, KN / D, is then set to be 1.18*10-3. In order to

get a stable solution, at least 4 wave periods are needed and one wave cycle is divided


into 240 time steps, which gives the non-dimensional time step, At = rad.
240


Generation of Wave and Current Conditions

Dune2d requires the specification of the pressure gradient in order to generate the

input hydrodynamic forcing. The same pressure gradients are applied at all grid points in

the domain, consistent with the shallow water approximation, and the fact that the

domain scale is small compared to the surface gravity wave length. The input pressure

gradients corresponding to the ensemble averaged flows in Fig. 4-5 are created by

combining the pressure gradients due to a sine wave and the pressure gradients due to

mean current.

In Fig. 5-1, the output horizontal velocities at the top of the domain are compared

with the ensemble averaged velocities from Fig. 4-5. The combination of the pressure

gradients of the sine wave and mean currents gives good agreement with data in terms of

the velocity magnitude, although there are some discrepancies on the time of flow

reversal for Case (A). As a result, the use of a linear sine wave to create the ensemble

averaged velocity data can be accepted with no serious disagreements.










Case (a)
a 0.5
E
o 0.25 0
"0 t0o o
W00 0
o o<.-------y o---o--
3 0

0
5 -0.25 oo
OO
c -0.25O

c -0.5

Case (b)
0.5

.-..---------..------,


0
> 0
5 -0.25
0 a
-c -0.5
0 7t/2 x 37/2 27
cot


Fig. 5-1: Horizontal velocity comparison over one wave period, o : data at P1 (Case (A))
and P2 (Case (B)) solid : Dune2d calculations at P (Case (A) and P2 (Case (B), to :
time of offshore to onshore flow reversal of Dune2d calculations.




Effects of Small-Scale Ripples

As mentioned earlier, it has been observed that SWR exist on the top of the LWR

(Hanes et al, 2001). The size of SWR is from 5 10 cm in length and 0.3 1.0 cm in

height. If SWR are superimposed, the bottom roughness is increased and the flows

become more turbulent near the bottom due to more irregular shape of seabed. In Fig. 5-2

the flow fields calculated using Dune2d are shown for Case (A) for LWR in the upper

panel (which we will refer to as the smooth bed) and superimposed SWR and LWR

(rough bed) in the lower panel.







61


The LWR has a length of 90 cm and a height of 6 cm, the SWR has a length of 7

cm and a height of 0.5 cm. The flow field in Fig. 5-2 is a "snap-shot" just before the


offshore to onshore flow reversal (t-to-n/20), when the turbulent eddy is expected to be

generated in the lee of the ripple crest.



smooth bed, t = to t/20


E

o 0.1
,=
a,
rg
JU


rough bottom, t= to 7r/20
I I I "

r yet, fttt

4*r
4. 4- 4'i4- (4t' tI' .^e 4
'' < 4' 4- 4' 4'4 (



4^ -:: .* '^/ j4 ^ ll <--- t ^ ^
Iji CCC~ttCCf


0.5
<- offshore


1 1.5
cross-shore distance, m


2
onshore ->


Fig. 5-2: Comparison of velocity fields between the smooth and rough bottom at flow
reversal, Case (A). The flows are shown with arrows and drawn at every third grid points.










In Fig. 5-2, the turbulent eddies are evident on the offshore side of the ripple crest

over both smooth and rough bed. However, the size of the turbulent eddy is small and

confined closer to bed over the smooth bed. In the rough bed simulation the size of

turbulent eddy is larger and higher, extending up to 10 cm above the bed. So, the flow

becomes more turbulent due to increased bottom roughness if the SWR are superimposed

upon LWR.

The flow variations due to the addition of SWR can also be found from the

vertical profiles of the horizontal velocities. In Fig. 5-3, the vertical profiles of the

horizontal velocities are compared over smooth and rough beds at different times. The

velocity profiles are calculated from Dune2d at the horizontal position P1 for Case (A).



t=to to+x)/4 to+x/2 to+3/4x to+x


o-1 .
10

E
E 0-I I
0 1I

\ I I I
I I I I I
S/ 1 i 1




10 \
0 0.2 0.4 0 0.5 1 0 0.5 1 0 0.5 -0.2 0 0.2
mrn/s m/s m/s m/s m/s

Fig. 5-3: Calculated vertical profiles of horizontal velocity at position P1, Case (A), solid:
rough bottom, dashed : smooth bottom.



The difference between the smooth bed and the rough bed velocity profiles are

strongest near the bottom. The rough bed profile has a phase lead inside the boundary







63


layer, relative to the smooth bed profiles. The vertical gradient is stronger and extends to

higher elevation for the rough bed case. This means that the vertical mixing is stronger if

the seabed is rougher due to the SWR. The differences in the profiles decrease with


elevation and no differences are found above 10 cab because the flows outside the

boundary layer are not affected by the bottom roughness.


TKE (m2/s2), t=to-7/20, smooth bed


E
0
. 0.1


0.05


0.5 1


TKE (m2/s2), t=to-n/20, rough bottom


0.5 1 1.5 2
cross-shore distance, m


Fig. 5-4: Turbulent Kinetic Energy comparison over smooth and rough bottom, t = to -
rT/20, Case (A).


x10-
14

12

10


4

2


E
C
0
S0.1


x 04
14

12

10


S6

4

2


'3~K~
~**$kra~ia~Ur









The effects of the SWR also can be investigated from the field of the Turbulent

Kinetic Energy (TKE) calculated from Eq. (7). Fig. 5-4 shows the distribution of the TKE

over smooth and rough bed at the same time as Fig. 5-2 for Case (A). The TKE is higher

near the bed then decreases with elevation. The TKE is also higher on the offshore side of

the ripple crest. This is consistent with the formation of a vortex eddy. For the rough bed,

the TKE is higher than that of the smooth bed and extends up to higher elevations, which

means that the turbulence is enhanced by the existence of the SWR.


Temporal and Spatial Variations of the Flow, Turbulence, and Concentration

One of the difficulties in the investigation of sediment suspension over rippled

seabeds is the fact that the uniformity in the horizontal direction cannot be guaranteed

because of the irregular shape of the bottom. The temporal and spatial variations of the

bottom shear stresses are not easily predictable due to the complexity of the flow and

turbulence over the ripples. So, it can be expected that sediment suspension above ripples

will occur in a quite different manner from the suspension over flat bed.

In order to understand the behavior of the suspended sediment above ripples, it

will be helpful to review sediment suspension above a flat bed. It is generally assumed

that the reference concentration that serves as bottom boundary condition for suspended

sediment is directly related to the local shear stresses. The reference concentration

increases as the shear stress increases, which is approximately proportional to the

velocity squared. An example of the suspended sediment concentration distribution over

a flat bed predicted by Dune2d is shown in Fig. 5-5. The concentration and TKE are large

at the same phase as the peak velocity magnitude near the bed, showing two peaks over

one wave period.


1












(a) SSC over flat bed


0.05-


0.04-

E
- 0.03 -


> 0.02 -
(Uj


(b) TKE over flat bed


.,


0.01 -

0o --




0.05-


0.04-

E
- 0.03 -
.2
O

> 0.02-


0.01 "


0
0


Fig. 5-5: Temporal and spatial variation of SSC and TKE over flat bed.




In this example the pressure gradient used as the input forcing is the same as the

input for Case (A), showing asymmetry in the magnitude of maximum velocity in

onshore and offshore flow. The magnitude of the concentration and TKE also shows the

asymmetry between onshore and offshore phase, which indicates that the sediment

concentration and TKE are directly influenced by the velocity magnitude. Once sediment


I I
t/2 7E
cot









is entrained from the bed, it is diffused upward in a smooth manner showing phase

differences in the vertical direction.


(a) t = t


(b) t = t


1 2


(c) t = t3


1 2
cross-shore distance, m


0.2

0.15;,
$4
0.1 4

0.05

0
0


0.2
-

0.15

0.1

0.05

0
0


1 2
(d) t = t


1 2
cross-shore distance, m


Fig. 5-6: Time variation of velocity field, Case (A). ti: time of maximum offshore
velocity, t2: time of offshore-onshore flow reversal, t3: time of maximum onshore
velocity, t4: time of onshore-offshore flow reversal. The arrow scale in (b) and (d) is
magnified twice for a better view.



Over rippled seabeds the temporal and spatial variation of the flow are affected by

the turbulent vortices that may be generated in the lee of ripple crests. Also, the mixing of

SSC will be influenced by the vortices. Fig. 5-6 shows the flow at four different times for


0.15

0.1

0.05









Case (A) over the rough bed. At tl the offshore flow has its maximum magnitude and t2 is

the time of offshore to onshore flow reversal. The snap shot of the flow at the time of t2 is

same as the rough bed case shown in Fig. 5-2. At t3, the onshore flow has its maximum

velocity and t4 is the time of onshore to offshore flow reversal.

A turbulent eddy is formed on the offshore side of the ripple crest at time t2 (panel

b). Since the time t2 is just before the offshore to onshore flow reversal, the flow outside

the boundary layer is weakly directed offshore, but there are strong flows directed

onshore near the bed due to the velocity phase lead inside the boundary layer. The strong

vertical gradient of the horizontal velocity results in the vortex generation at this time.

However, no vortices are formed at the time of onshore to offshore flow reversal, t4. One

explanation for this is the asymmetry in the magnitude of the horizontal velocity. Because

the maximum offshore horizontal velocity is larger than the maximum onshore velocity

outside boundary layer (P1), the maximum velocity magnitude as well as the vertical

gradient is also larger inside the bottom boundary layer at the time of offshore to onshore

flow reversal (t2). As shown in Fig. 5-3, the horizontal velocity profiles are compared at

the time of offshore to onshore flow reversal (to) and at the time of onshore to offshore

flow reversal (to + i). The magnitude of the onshore velocities at to is about 30 cm/s near

the bottom while the magnitude of the offshore velocity at to + it is about 20 cm/s. The

corresponding vertical gradient of the horizontal velocity is also higher at time, to. So, the

less velocity magnitude and the smaller vertical gradient result in the absence of the

vortices at time t4. At the time of maximum onshore and offshore velocities (tl and t3), the

flows are parallel to the bottom topography, showing no vortices or perturbations. At

these wave phases, the vertical gradients of the flows are small.









The flow fields of Case (B) are also compared at the same time steps (tt, t2, t3, and

t4) in Fig. 5-7, in which the velocity distributions are similar to Case (A). The vertical

gradients are higher at t2 than t4, and the flows are parallel to the bottom at strong wave

phases, tl and t3.


(a) t = ti


(b) t = t


0.2


E 0.15
'-
I 0.1
I)0
' 0.05


1 2


0.2

0.15

0.1

0.05

0


(c) t = t3


1 2
cross-shore distance, m


0.2

0.15

0.1

0.05

0
0


1 2


(d) t = t4


1 2
cross-shore distance, m


Fig. 5-7: Time variation of velocity field, Case (B). ti: time of maximum offshore
velocity, t2: time of offshore-onshore flow reversal, t3: time of maximum onshore
velocity, t4: time of onshore-offshore flow reversal. The arrow scale in (b) and (d) is
magnified twice for a better view.


0.15

0.1

0.05









The temporal and spatial variation of the TKE and suspended sediment

concentration is shown in Fig. 5-8 and 5-9.


Case (A)
0.2
E

0.1

0
0 1 2
E 0.2

0
10.1

0
0 1 2
0.2.
E0-2 .--.........--
E0.1

o
0)0
0 1 2
E 0.2

0.1

0
0 1 2
cross-shore distance, m


0.2


t=t1 0.1

0
0
0.2

t=t 0.1

0-
0
0.2


t=t 0.1
0-
0
0.2

t=t4 0.1

0
0


Case (B)


1 2






1 2






1 2






1 2
cross-shore distance, m


Fig. 5-8: Temporal and spatial variations of the distributions of the Turbulent Kinetic
Energy, tl,t2,t3, and t4 are same in Fig. 5-6 and 5-7.



The left four panels in Fig. 5-8 are the TKE variations for Case (A) and the right

four panels are for Case (B). The time t1,t2,t3, and t4 are identical to the times in Fig. 5-6

and 5-7. At the offshore to flow reversal (t2), high values of TKE are distributed near the

bottom, and the highest TKE is concentrated on the offshore side of ripple crest, which is








consistent with the location of the vortex. So, these high TKE are generated due to the

vortex. At the time of strong onshore velocity, t3, high TKE is observed near the ripple

crest. This is because the high KTE generated by the vortex at t2 is advected horizontally

with the onshore flow. At the time of onshore to offshore flow reversal (t4), this high

TKE is advected farther in the onshore direction. Also, less TKE is distributed along the

ripples at t4 than t2 because of the wave asymmetry.


Case (A)


Case (B)


0 1 2





0 1 2


0 1 2




N ."

C


0)


1 2
cross-shore distance, m


0.2

t=t1 0.1

0
0.2

t=t2 0.1

0
0.2

t=t3 0.1

0
(
0.2

t=t4 0.1

0
(


1 2


3 1 2





3 1 2
cross-shore distance, m


Fig. 5-9: Temporal and spatial variations of the distributions of the suspended sediment
concentrations, ti,t2,t3, and t4 are same in Fig. 5-6 and 5-7.


(


E 0.2

0
E



0
o


0,
I0.1


u
0.2

0.1

0
0.2

0.1

0


L~Jh---


~ ~3~--~


t


t~/~g`l


I


I I


-


0


0
-_


0









The variation of the suspended sediment concentrations is similar to TKE

variations as shown in Fig. 5-9. A cloud of sediment is observed at the offshore slope of

the ripple crest at time, t2. This sediment cloud indicates that the sediments are suspended

from the bottom due to the vortex. This entrained sediment cloud is advected horizontally

with the flow to a position near ripple crest at t3 and further at t4. The cloud is enlarged

and diluted due to the diffusion processes.

At the time of maximum offshore flow (ti) high concentrations are also found

along the bed. This is due to the formulation in Dune2d that uses the reference

concentration boundary condition. The concentration near the bed is high at large

velocities just as in the case of a flat bed (Fig. 5-5). Dune2d is formulated to describe the

entrainment from the bed at strong bed shear stresses, and the subsequent mixing by

turbulent diffusion. The entrainment of the sediments due to the turbulent vortex at the

time of flow reversal can also be described in this context. The strong near bed velocities

due to the phase lead inside the bottom boundary layer entrain the sediment from the bed

into the turbulent vortex at the time of flow reversal. Then the sediment is advected with

the flow until sediment settles down to the bed due to gravity. So in Dune2d the

sediment suspension is basically described by the diffusion process due to the vertical

gradients of the sediment concentration.


Comparison of Model Predictions of SSC with Data.

The numerical calculations from Dune2d can be compared with the

measurements. The comparison of the horizontal velocities at the positions, P1 and P2

were already shown in Fig. 5-1, and showed reasonable agreements with data.









The ensemble averages of TKE measurements are compared with Dune2d

predictions in Fig. 5-10. The separation of the turbulence components from velocity

measurements are performed according to the method suggested by Trowbridge

(Trowbridge, 1998), which gave the "best-fit" results with the field measurements out of

the three different methods of turbulence estimation (Mouraenko, 2001). In Fig. 5-10,

The TKE of measurements (circles) and model predictions (solid line) are compared over

one wave period at the position P1 (Case (A)) and P2 (Case (B). Both of the

measurements and model predictions seem unrelated with velocity patterns shown in Fig.

8 because they are separated from the waves. Since P1 and P2 are slightly higher than 20

cab, the TKE pattern do not seem to be affected by the ripples either.



x10-4 Case (A) x 10-4 Case (B)
7 7

o0 o




4 4-o
0 E
i3 3

2 2

1 1


0 p/2 p 3p/2 2p 0 p/2 p 3p/2 2p
wt wt

Fig. 5-10: Comparison of TKE between data and model predictions at P1 and P2, solid:
model predictions, circles: measured data









Fig. 5-10 shows that the magnitude of the TKE is underestimated by Dune2d

under the condition of the reasonable agreements in horizontal velocities. The TKE

magnitude of measurements are 2 3 times larger than that of model predictions. This

underestimation reveals that the Dune2d is not appropriate to produce the active

turbulence fields in the real seas. One possible explanation for this is the use of rigid lid

at the top of the computational domain. The use of rigid lid confines the flows generated

by Dune2d to be rather U-tube type flows than the flows by the real waves under surface

elevation variation. This condition may restrict the turbulence produced by Dune2d less

active than real seas.

The comparison of the vertical distribution of SSC shows that the magnitude is

even more severely underestimated by Dune2d while it shows some agreements in the

timing of the peak concentration. The data and numerical calculations at P1 are compared

in Fig. 5-11 for Case (A). In panel (a), the ensemble averaged SSC shows that a

concentration peak is found near the time of 37t/2 and this peak lasts for more than half of

the wave cycle. This peak of concentration is not consistent with sediment suspension

above a flat bed because its peaks are not at the time of the peak velocity. The SSC peak

can be explained if the sediment cloud is advected horizontally toward and through the

measurement location. In panel (b), the calculated SSC also has one peak near the time of

37n/2. In Fig. 5-9, it is observed that the sediment cloud suspended at time t2 moves

through the ABS location near the time of 37r/2 (t3). So the concentration peak in Fig. 5-

1 Ib is the sediment cloud that is transported from the offshore side of the ripple crest,

after it was suspended at the time of offshore to onshore flow reversal. Since the time of

the concentration peak between the field measurements and model predictions are in








74


agreement, it can be interpreted that the distribution of the SSC shown in Fig. 5-11 results


from the advection of the sediment cloud that was suspended by turbulent vortex.


(a) data, Case (A)


-0.5


-1





-2


-2.5


(b) model, Case (A)


-0.5

0
M *-1


-1.5


-2


-2.5
...... ~~ ~ s ..;; .-,.


Fig. 5-11: comparison of the vertical distribution of the suspended sediment
concentration between data and model results at P2. Case (A)




Figure 5-12 shows the time variation of the measured and predicted SSC for Case


(B). The concentration measurements are located on the offshore slope of the ripple crest.


0.1 -

0.09 -
0.08 -

E 0.07
. 0.06
H 0.05-
S0.04 -

0.03-

0.02


0.1-

0.09- U
0.08 -

E 0.07-
S0.06-
, 0.05-
S0.04-
0.03-
0.02-
L_^r


~~ Lr

I'


---- -- 1~~-1-;- RNWAO."~ll


~ .1 ~~_Y~IS~Y


|


o
cn
S
~=6)











High sediment concentrations occur near the time of offshore to onshore flow reversal in


both the measurements and the model predictions.


(a) data, Case (B)

^. ^Sv'^-jSS ~ a!'.''.r


0.1 -
0.09-
0.08 -,

E 0.07 -'
o 0.06 -
> 0.05 -
(a 0.04 -
0.03
0.02


-1.5


-2


----2.5


(b) model, Case (B)


0.09-
0.08-

E 0.07-
o 0.06-
> 0.05-
a3 0.04-
0.03-
0.02-


U1


S -2


--2.5


ot


Fig. 5-12: comparison of the vertical distribution of the suspended sediment
concentration between data and model results at P2. Case (B)


However, the time of the peak concentrations are slightly different. The peak


measured concentration occurs at approximately 57t/4 but the peak model prediction


----plll~Y~II_~.


.










occurs at approximately 3rn/4. The use of the reference concentration in Dune2d can

explain this discrepancy. Since the turbulent vortex is formed and starts to entrain

sediment from the bed at the time of flow reversal, a sediment cloud is formed at (or

slightly after) the flow reversal. However, Dune2d predicts high reference concentrations

coincident with high velocities.





0.2

0.18-

0.16

0.14

E 0.12 -
C
U, .1

0.08

0.06
-- Data, Case (A)
0.04 -e- Model, Case (A)
-- Data, Case (B)
0.02 -- Model, Case (B)

10-10 105 100 10
concentration, g/l

Fig. 5-13: Comparison of SSC profiles between measurements and model predictions; the
profiles are determined from the maximum values at each elevation.



As mentioned earlier with the TKE comparison, the underestimation by Dune2d is

even severe in case of SSC. There is a significant discrepancy between the magnitude of

the observed SSC and model predictions at high elevations. For example, the sediment

cloud shown in Fig. 5-1 lb is suspended only up to 5 cab and exists only for short time;









the measured SSC in Fig. 5-1 la extends higher than 10 cab, and last for longer time. Fig.

5-13 shows a comparison of the SSC profiles between the measurements and model

predictions. The profiles are determined by taking the maximum concentration value at

each elevation. Because the Dune2d model is adjusted by increasing the bed roughness as

three times as the theoretical value of 2.5 d, the maximum magnitudes of the sediment

concentration near bottom (about 1 cab) are comparable between data and model. But the

maximum magnitude of the model prediction is only 10 % of the measured magnitude 5

cab for Case (A), and even much less for Case (B). In Fig. 5-13, the slope of the

concentration profiles are much less for model predictions, which means that the decrease

rate of SSC is much higher in model predictions than the observations.

As mentioned before, one possible cause for this underestimation can be found

from the surface boundary condition in Dun2d (rigid lid). Since the use of rigid lid leads

to less active flow conditions near the seabeds than real seas, the sediment suspension

and its convection by the flow is not as active as real seas. In addition, as shown in Fig.

17, the less amount of TKE produced by Dune2d results in the underestimation of the

eddy viscosity because the eddy viscosity is calculated by the K co model and it is

proportional to TKE. Since the eddy viscosity is adapted as the eddy diffusivity in the

sediment transport module, the underestimation of the eddy viscosity leads to the

underestimation of eddy viscosity, and this results in the less vertical mixing of the SSC

in the Dune2d predictions.














CHAPTER 6
CONCLUSIONS



Sediment suspension occurs in a more complex way over rippled seabeds, that are

frequently observed in the coastal regions, than over the flat beds because the flow

separation over ripples produces a large scale vortex that can entrain and advect

sediment. The sediment tends to get entrained from the seabed in the form of a sediment

cloud due to turbulent vortices that are generated in the lee of the ripple near the time of

flow reversal. The suspended sediment is advected by the flow until settling back down

to the bed.

Ensemble averages of suspension events show that the SSC at the slope of the

ripple has a peak at the time of flow reversal. Near the ripple crest, in contrast, the peak

concentration occurs some time after flow reversal. These results are consistent with the

hypothesis by Sleath (1982) that the sediment is suspended in the lee of the ripple crest

due to turbulent vortices, and these sediment clouds are advected by the flow. Only one

concentration peak is observed during wave period in both data sets. The likely

explanation for this is the asymmetry in the horizontal velocity. The stronger offshore to

onshore flow reversal causes flow separation and vortex formation but the weaker

onshore to offshore flow reversal does not. It is not known yet if this is a general result.

The field measurements are simulated using the Dune2d boundary layer model.

The observed LWR are re-generated on a numerical domain and wave and current

conditions similar to the ensemble averaged velocities are used as input. The effects of









SWR superimposed on LWR are evaluated using Dune2d. When SWR with 7 cm length

and 0.5 cm height are superimposed on the LWR, the formation of turbulent eddies is

enhanced. Larger and stronger turbulent eddies are found at the lee of the ripple crest if

the SWR are superimposed. Also, the turbulent kinetic energy is increased with the SWR.

Therefore, it can be concluded that the SWR increase the roughness at the seabed, so the

flow near the seabed becomes more turbulent, with larger amounts of suspended

sediment.

The temporal and spatial variations of the flow, the turbulent kinetic energy, and

the SSC are also investigated using Dune2d. The flow patterns indicate that turbulent

vortices are generated at the offshore side of the ripple crest at the time of the flow

reversal. No vortices are generated at the time of the onshore to offshore flow reversal,

which is consistent with the field observations. The turbulent kinetic energy and the SSC

patterns show that high turbulent energy and high concentrations are found near the

location of the turbulent eddies, which indicates that the eddies form sediment clouds.

Moreover, these sediment clouds are advected with the flow after they are generated. So,

the basic hypotheses for sediment suspension and advection over rippled seabeds are

confirmed with the numerical model and with the field observations.

The comparison between model predictions and field observations also indicate

some obvious discrepancies. The magnitudes of the suspended sediment concentrations

are under-estimated by Dune2d at high elevations, even though the magnitudes near the

bed are comparable between the model predictions and the measured SSC through the

adjustment of bed roughness. One explanation for this is that Dune2d employs rigid lid

condition as the surface boundary condition, which produces less active turbulence, and






80

this results in poor sediment suspension and convection processes. The sediment mixing

may also be underestimated due the less eddy diffusivity through the underestimation of

TKE.

It is obvious that a weakness of the present study is to use a numerical model that

employs an inappropriate surface boundary condition. Therefore, there is a need to create

a more realistic wave condition with surface wave elevations.
















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BIOGRAPHICAL SKETCH


Yeon Sihk Chang was bor to Young Whan Chang and Yang Sook Huh in Seoul,

the capital city of Korea, on July 19, 1968. He grew up with two brothers in a happy

family environment. His parent was stem but full of affection in teaching their children.

He graduated with a Bachelor of Science degree in oceanography from the Seoul

National University in February 1991. After he served in the Korean Army for 18

months, he returned to the Seoul National University to continue his study in the master's

program. For the Master of Science degree, he majored in the physical oceanography

with specific interests on the numerical modeling until he graduated in August 1995.

He came to the University of Florida for the Ph.D. program in civil and coastal

engineering in August 1996. For his Ph.D. research, he studied sediment transport in the

near shore areas. He participated in SandyDuck97 and SISTEX99 experiments that

expanded his experience to meet the scientific leaders in the field.

He married Eun Young Choi in November 1997. They have two sons, James,

bor in September 1998, and Charles, born in October 2000.

During their stay in Gainesville they made lots of friends from all over the world,

and they did have the chance to meet God and his love.




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