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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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models of turbulence, PhD dissertation, Technical Univ. of Denmark.
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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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