UFL/COEL96/008
COMPARISON OF MEASUREMENTS AND MODELS OF
THE VERTICAL DISTRIBUTION OF SUSPENDED
SEDIMENT UNDER WAVES AND CURRENTS
by
Cheegwan Lee
Thesis
1996
COMPARISON OF MEASUREMENTS AND MODELS OF
THE VERTICAL DISTRIBUTION OF SUSPENDED SEDIMENT
UNDER WAVES AND CURRENTS
By"
CHEEGWAN LEE
A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
UNIVERSITY OF FLORIDA
1996
ACKNOWLEDGMENTS
At first, I would like to give thanks and appreciation to my advisor, Dr. Daniel M.
Hanes, for his persistent support and encouragement whenever I was in need of help. I also
want to express gratitude to the committee members, Dr. Robert G. Dean and Dr. Robert
Thieke, who are also excellent professors. I would like to thank to my fellow students, Eric,
Chris and Mike for helping with my project, especially, Eric, who gave me a lot of advice
for our computer system. I also acknowledge Lee's and Wikramanayak's dissertations,
which were a kind of textbooks for my work.
I am also very grateful to the staff members for their assistance during my study in this
department. Becky always gave me kind consideration and help whenever I asked a favor
of her. I will remember Helen and John's cordial work in archives. I am sorry for the fact that
I cannot mention everyone who has helped me very much during my project and school.
During two years of my life in Gainesville, I can't also forget about my friends in
Gainesville and Korea who have given me a cordial encouragement whenever I needed some
advice.
I give a special thanks to my loving parents and younger brother who gave me the love
and support I needed. Finally, I should say thanks to God for all my success.
TABLE OF CONTENTS
ACKNOWLEDGMENTS ............................................. ii
LIST OF TABLES ............... ..................................... v
LIST OF FIGURES ................................................... vi
KEY TO SYMBOLS ................................................. viii
ABSTRACT .......................................................... xi
CHAPTERS
1 INTRODUCTION .................................................... 1
2 FIELD EXPERIMENT ................................................. 6
2.1 Introduction .................................................. 6
2.2 Site Description and Deployment of System .......................... 7
2.3 Hydrodynamic Condition During the Experiments ..................... 9
2.3.1 Wave Direction and Height..................................... 9
2.3.2 Wave Period and Current ..................................... 11
2.4 Characteristics of Bed Materials. ................................ 13
3 HYDRODYNAMIC MODEL .........................................14
3.1 Introduction ................................................. 14
3.2 Determination of Hydrodynamic Input Parameters .................... 14
3.2.1 Current ................................................... 14
3.2.2 Near Bottom W ave Velocity ................................. 15
3.3 Primary Wave Direction ....................................... 16
3.4 Representation of Irregular Waves ................................ 18
3.5 Hydrodynamic Model ......................................... 20
3.5.1 Eddy Viscosity Model ...................................... 20
3.5.2 Current and Wave Velocity Profile of Model ..................... 21
iii
3.6 Ripple Model ................................................ 24
4 THE SUSPENDED SEDIMENT DISTRIBUTION MODEL ................... 25
4.1 Introduction ..................................................25
4.2 Review of Model ............................................. 25
4.2.1 Governing Equation ........................................ 25
4.2.2 Diffusion Model ........................................... 26
4.2.3 Convection Model ......................................... 28
4.2.4 Combined Model ......................................... 29
4.3 Modified Combined Model ................................... 32
4.3.1 Problem Statement of Previous Model .......................... 32
4.3.2 Modification of Eddy Viscosity Model .......................... 33
4.4 Test of M odel ............................................... 35
5 THE COMPARISON OF THE MEASURED DATA WITH MODEL ............ 41
5.1 Itroduction .................................................. 41
5.2 Comparison of Model Input Parameters ............................ 41
5.3 Estimation of Ripple Geometry and Friction Velocity ................. 44
5.4 Comparison of Timeaveraged Vertical Concentration Profiles .......... 47
5.4.1 Villano Data Files ........................................ 47
5.4.2 Supertank Data Files ....................................... 50
5.4.3 Duck94 Data Files ......................................... 54
5.5 Error Analysis ............................................... 65
6 CONCLUSIONS ..................................................... 72
LIST OF REFERENCES ................................................ 75
APPENDIX ........................................................ 77
BIOGRAPHICAL SKETCH ............................................ 141
LIST OF TABLES
Table Page
2.1 : Sieve analysis................................................................................13
4.1 : Input parameters for model test................................................. ........................36
5.1 : Input parameters of Villano data files...................................................................41
5.2 : Input parameters of Supertank data files................................................................42
5.3 : Input parameters of Duck94 data files.....................................................................43
5.4 : Estimated ripple and friction velocity of Villano data files.....................................45
5.5 : Estimated ripple and friction velocity of Supertank data files.................................45
5.6 : Estimated ripple and friction velocity of Duck94 data files....................................46
5.7 : Error analysis of Villano data files........................................................................65
5.8 : Error analysis of Supertank data files...................................................................66
5.9 : Error analysis of Duck94 data files.....................................................................66
LIST OF FIGURES
Figure Page
2.1 : Instrum ent location............................................................................................. 7
2.2 : Front view of the deployed instruments...........................................................8
2.3 : Waves during Duck94 experiment................................................................... 9
2.4 : Wave direction and height during Duck94 experiment.................................... 10
2.5 : Wave period during Duck94 experiment.............................................................11
2.6 : Direction of magnitude of current Duck94 experiment..................................12
3.1 :Procedure of calculation of near bottom wave velocity..................................... 15
3.2 : Example of calculation of near bottom wave velocity....................................16
3.3 : Definition of primary wave direction....................................................................17
3.4 : Power spectrum of near bottom wave velocity.....................................................19
3.5 : Vertical profile of eddy viscosity model.............................................................21
4.2 : Description of sediment conservation equation.................................................26
5.1 : Vertical profiles of sediment concentration of Vilano experiment
under low wave energy condition...................................................................48
5.2 : Vertical profiles of sediment concentration of Valine experiment
under high wave energy condition................................................. .................49
5.35 :Vertical profiles of sediment concentration of Supertank experiment............153
5.611 :Vertical profiles of sediment concentration of Duck94 experiment
on the rippled bed....................................... ................. .............................5661
vi
5.1214:Vertical profiles of sediment concentration of Duck94 experiment
under sheet flow condition.............................. ...............................................6264
5.15 : Correlation between the relative errors and the input parameters.....................69
5.16 : Correlation between the relative errors and the ripple steepness.......................70
KEY TO SYMBOLS
a Nondimensional fall velocity of sediment particle, wo/kucw
Ab Semiexcursion of water particle
C Concentration of suspended sediment
Ci Concentration at level
d5o Median diameter of sediment particle
f Frequency in Hz
f2.5 Grain roughness friction factor
F Probability distribution function of sediment entrainment
FFT{ } Fast Fourier Transform
g Gravitational acceleration
h Mean water depth
hi Height above bed of EMCM
IFFT{ } Inverse Fast Fouriers Transform
Hmo Hmo Wave height
h2 Height above bed of pressure gage
k Wave number
kb Equivalent Nikuradse roughness
P Instantaneous sediment pickup rate at sea bed
qz Total sediment transport rate per unit area in vertical direction
qd Sediment upward flux by diffusion
qc Sediment upward flux by convection
viii
Rpu ,Rpv Cospectra
s Specific gravity of sediment particle
Su Power spectrum of wave enhanced fluid velocity
in primary wave direction near the sea bed
u,v Fluid velocity(horizontal component)
uc,ve Current velocity(horizontal component)
uw,v, Wave velocity(horizontal component)
u*c Current friction velocity
U*, Wave friction velocity
u*cw Combined wavecurrent friction velocity
ud Deflection of wave velocity in boundary layer(= u,,u )
u_ Near bottom potential velocity
U Current velocity at EMCM
U, FFTof u,
Vp Wave velocity in primary wave direction
vr Representative wave velocity
wo Falling velocity of sediment particle
Ze Level of EMCM
zr Reference level.
a Model parameter(=0.5)
6 Boundary layer thickness scale, ku,*w/co
e Ratio of current friction velocity to wavecurrent velocity uJucw
Es Sediment eddy diffusivity
w Angle between the primary wave direction and the current
K Vonkarman constant(=0.4)
x Ripple length
r1 Ripple height
Ut Eddy viscosity
02.5 Grain roughness shield parameter
p Water density
( Nondimensional vertical coordinate
C0 Nondimensional bottom roughness
W Wave frequency in rad/sec
Wo Meanzero crossing wave frequency
Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science
COMPARISON OF MEASUREMENTS AND MODELS OF
THE VERTICAL DISTRIBUTION OF SUSPENDED SEDIMENT
UNDER WAVES AND CURRENT
By
Cheegwan Lee
August, 1996
Chairperson: Daniel M. Hanes
Major Department: Coastal and Oceanographic Engineering
Measurements and models for the time averaged, vertical distribution of suspended sand due
to waves and currents are compared. The measurements were obtained from field experiments at
Valine Beach, Florida and Duck, North Carolina, and from the Supertank laboratory experiment,
held at Oregon State University. The models consist of a pure diffusion model, a combined
convectiondiffusion model, and a new diffusion model which combines elements of
Wikramanayake and Nielsen. All of the vertical distribution models were applied in conjunction
with a bedform model and a reference concentration model.
Overall, the models and measurements are not in close agreement. Sometimes this is a result
of large errors in predicting the vertical profile; other times the errors result primarily from the
discrepancy in the reference concentration. Overall, the Lee and Hanes model performed best, but
xi
all models tended to underestimate the concentration for the Supertank experiments and also for the
field experiments which had low amplitude and high frequency waves.
xii
CHAPTER 1
INTRODUCTION
Nowadays, coastal zones are very valuable natural resources for many human activities
such as port construction and leisure sports. Also they are very important as a fishery to be
protected from pollution. When undertaking coastal engineering projects, it is necessary to
consider the effect of waves and currents that are always present in the near shore zone.
Waves and currents scour structures and erode the beach by the action of hydrodynamic
forces. So it cannot be overestimated that the efficient development and management of
coastal resources is very important.
Sediment transport processes in the coastal zone are very complicated and difficult to
predict. To predict sediment transport, we have to obtain an estimation of fluid velocity as
well as the concentration of sediment. A reasonable estimation model of them can be made
by experiments in laboratories and field measurements as well as by theoretical studies.
There are two kinds of sediment transport processes : long shore and crossshore sediment
transport. Generally the long shore process has been well studied in comparison with cross
shore counterpart by Inman and Bagnold[1963], and Dean[1989]. But the crossshore
sediment transport mechanism is still not understood as well as the long shore one. One of
the approaches to predict the crossshore process is to describe the fluid and sediment motion
2
at the local point in detail. This approach studies the initiation of sediment motion, eddy
viscosity model, ripple geometry and vertical sediment concentration profiles, with the
hydrodynamic input conditions. If we know the fluid velocity and concentration profile, we
can calculate the amount of sediment transport at each grid point. Therefore the beach profile
which results from the erosion or accretion of sediment at various locations can be predicted.
In deep water, the nearbottom velocity of waves is negligible. However, in the coastal
zone, the near bottom velocity will increase and it gives a thin boundary layer and shear
velocity sufficient to initiate the motion of sediment. The boundary layer model developed
by Grant and Madsen[1979] under the wavecurrent condition uses the timeinvariant eddy
viscosity model which is less sensitive to wave frequency. But the eddy viscosity is also
strongly dependent on the wave frequency that influences the concentration profiles.
Nielsen[1992] used a different eddy viscosity model more sensitive to frequency to get the
timeaveraged concentration profile using the combined model.
Bed roughness affecting the velocity field in boundary layers is also dependent on bed
geometry. Nielsen[1981] developed the empirical model for ripple height and length using
the field data. Wikramanayake[1993] also suggested the ripple model in terms of a skin
friction shield parameter.
Sediment transport has two kinds of different modes : bed load and suspended load
transport. Bed load transport is defined as a part of the total load which is supported by
intergranular forces. Suspended load transport is defined as taking place in the main body
3
of the flow where intergranular forces are negligible and the sediments are carried in
suspension by turbulence. It is very difficult to differentiate the suspension load from bed
load. But the measurement techniques using the acoustic concentration profiler give some
solutions.
To model the vertical distribution of suspended sediment concentration, first the
reference concentration should be predicted and the vertical profile of concentration should
also be determined.
In general, the sediment suspension mechanism can be divided into two processes. One
is an orderly convective process and the other is a diffusive process, but most approach
combined these two. If the mixing length is sufficiently large compared to the overall scale
of the sediment distribution, the process is convective. Conversely, if the mixing length is
small compared to the overall scale, the process may be described as diffusive. Vertical
sediment distribution is the result of a balance between sediment settling velocity and
upward flux by turbulence. Recently Wikramanayake[1993] suggested a diffusion model
using the timeinvariant eddy viscosity model. Also Nielsen[1992] developed a convection
and combined models using his eddy viscosity model. Lee and Hanes[1995] hereafter
refereed to as LH95, combined Wikramanayake's diffusion model and Nielsen's convection
model and compared the model results with field data. In his dissertation Lee indicated that
the diffusion model is better than the convection model in sheet flow, but the reverse is true
for the rippled beds. Overall the combined model is best to predict the vertical distribution
4
of sediment. However, Wikramanayake's eddy viscosity model in the pure diffusion and the
LH95 model are not sensitively responsive to the wave frequency.
In this thesis, the modified eddy viscosity model which is a combination of
Wikramanayake's and Nielsen's one is used in developing the combined model. This new
model is applied to Vilano, Duck94 near shore field experiment data and Supertank data.
Also Both pure diffusion and LH95 model are applied to the same field and the laboratory
data to compare their relative errors. This application will be focused on Duck94
experiment.
In Chapter 2, the description of the site, the deployment of the measurement system and
the hydrodynamic conditions in Duck94 Near shore Experiment will be presented briefly.
This chapter is focused on the difference in hydrodynamic conditions for these three
experiments.
Chapter 3 presents the method to calculate the hydrodynamic input parameters which
consist of the near bottom wave velocity in primary wave direction and the representative
wave frequency. The timeinvariant eddy viscosity model and velocity profile in turbulent
boundary layer are described in this chapter.
Chapter 4 gives the theoretical backgrounds of the suspension model. The diffusion, the
convection and the combined models are introduced. Also based on modified eddy viscosity
model, the solution of modified combined model is derived from the governing equation.
5
Chapter 5 presents the comparison of measurements with model results in vertical
sediment concentration profiles. A special emphasis is on the difference in the concentration
profiles depending on the hydrodynamic conditions. Also the relative errors of all models
applied to the different data set are calculated and compared.
In Chapter 6, conclusions and evaluations are given to help in developing a more accurate
and universal model in the future.
CHAPTER 2
FIELD EXPERIMENT
2.1 Introduction
In this chapter, site descriptions and hydrodynamic conditions during experiments are
briefly suggested to assist a comprehension of potential readers, even though they are
well depicted by Lee's[1994] and Marusin's[1995] thesis, but the explanations are
concentrated on Duck94 field experiments as a representative. You can find a more
detailed description in Lee[1994]'s thesis for the Vilano experiment, Thosteson[1995]'s
one for Supertank and Marusin[1995]'s for Duck94.
During the nearshore experiments known as Duck94 in August October in 1994, the
sediment concentration and the hydrodynamic parameters were measured at Duck, NC.
This project was jointly supported by the US Army Corps of Engineers, the Office of
Naval Research, and United States Geological Survey. The Purpose of Duck94 is to
increase our basic understanding of sediment transport in the coastal zone through an
field measurements and numerical modeling.
The instruments consisting of Three Frequency Acoustic Concentration Profiler, the
pressure gauge and the electromagnetic current meter were deployed to get the
hydrodynamic data.
2.2 Site Description and Deployment of System
The Field Research Facility(FRF), located at the Duck, NC provides the researchers
with the capability to conduct diverse surf zone and nearshore field experiments. The
FRF has continuously collected meteorological and oceanographic data. This facility has
a 176acre tract and office and field operation buildings. The location and design of the
facility was specially chosen to permit studying the hurricanes and intense storms that
affect the area. The measurement system was mounted on the outside of offshore bar at
345 meters of longshore distance North of the FRF pier and 190 meters of crossshore
distance from the beach. Because the instrument was deployed outside of the breaking
zone, most of the waves were under nonbreaking condition.
Figure 2.1 Instrument location
Instruments FRF Pier
345 m
190 m
Instruments
The instrument array consists of a Three Frequency Acoustic Profiler, a data logger, a
current meter and an electromagnetic current meter. They were mounted on a vertical
pole, which was attached to the horizontal frame. Figure. 2.2 provides a observation of
this instruments.
The data logger controls the TFACP and other instruments and transmits the data with
a burst duration to the shore station. Typically the burst duration is 2331 min and data
sampling frequency is 2 sec.
The system measured the hydrodynamic conditions (current, waves, tide), the sediment
concentration and the bed level change. Through spectral analysis, we can obtain the
hydrodynamic information at a certain depth and the signals measured by TFACP
transducer can be converted to the concentration. This process is well explained by LEE
[1994] and Marusin [1995].
Figure 2.2 Front view of the deployed instruments
2.3 Hydrodynamic Conditions During The Experiment
2.3.1 Wave Direction and Height
The information of waves, current were obtained from the pressure gauge and EMCM.
These data are analyzed by spectral analysis to get a Hmo wave height. Figure 2.3 presents
the Hmo wave height and Figure 2.4 shows the wave directions and heights in polar
coordinate system during Duck94 field experiments.
Wave Height(Hmo)
2
S
,o"
1 "
n 
20 21 22 23 24 25
August
26 27 28 29
2
4
2 .. .., ** ,.*.,,,
* *".* *"
1 2 3 4 5 6 7 8 9 1C
September
n _________ l  l  l 
October
Figure 2.3 Waves during Duck94 experiment.
904
120 60
180 0
+ 0
+X
210 \ + \ /330
240 300
270
Figure 2.4 Wave direction and height in polar coordinate system
: August 20th August 28th
o : September 1st September 9th
+ : October 9th 15th
Figures 2.3 indicates two storms which occurred on September 3rd September 5th
and on October 12th October 16th. But most of waves were under nonbreaking wave
condition except on October 3rd 4th.
Figure 2.4 shows the relationship between the wave direction and the height, suggesting
that wave directions are usually distributed between 210 deg 270 deg clockwise from
the north. The orientation of shoreline is 20 deg in anticlockwise from North.
2.3.2 Wave Periods and Currents
Both wave period and magnitude of current influence significantly the vertical profiles
of suspended sediment concentration. The influence of wave period is more dominant in
wave boundary layer than the one of current, but the reverse is true in outer layer of the
wave boundary. In Vilano field experiments conducted by Lee, the range of wave periods
which is roughly from 4 sec to 6 sec, but in Duck94 experiments, the wave periods have
larger number than those in Vilano data set as you can see in Figure 2.5. It may be due to
a long waves generated by storms.
151 I I I I I I
0
01
0
0 I I I I I
20 21 22 23 24 25 26 27 28 2E
August

U
1 2 3 4 5 6 7 8 9 10
September
1 0 " o '* " ,
15
10 ..... *
5 I I I I I I
5
9 10 11 12 13 14 15 16
October
Figure 2.5 The wave period during Duck 94 experiment
Figure 2.6 shows the directions and magnitudes of currents, which indicate the strong
current during the period of two storms. If we consider the range of wave direction
*.*==.
'5. l~
=
12
between 210 deg and 280 deg as the figure 2.4 suggests, the angles between currents and
waves are usually larger than 90 deg, which means obtuse angles. This is also different
with Vilano data set which have similar wave and current direction.
4
21 22 23 24 25
August
26 27 28
[i I Il I i
1 1IIIIII/m/mIN /
2 3 4 5 6 7 8 9 11
September
I. 1\
I' ^ I I
10 11 12 13
October
14 15 16 17
Figure 2.6 The direction and magnitude of current
during Duck94 experiment
"1
I
20
Isl I, I I I
2.4 Characteristics of Bed Materials
The fall velocity of sediment determined by size is one of the most important factors
which influence the sediment suspension. Sediments in field experiment such as Duck94
and Vilano are sampled by divers and characterized by sieve analysis. Some portion of
bed materials like shell are neglected for analysis because they have a minor effect on
vertical sediment distribution. The result of analyses are suggested in Table 2.1. This
data comes from Lee's[1994], Marusin's[1995] thesis and the report of Supertank
experiment.
Table 2.1 Sieve Analysis
Vilano Supertank Duck94
Diameter Proportion Diameter Proportion Diameter Proportion
0.077mm 9.22 % 0.088mm 0.10% 0.088mm 10.0%
0.115mm 12.19% 0.105mm 0.87% 0.105mm 14.1%
0.137mm 36.45% 0.125mm 2.14% 0.125mm 29.4%
0.163mm 28.21% 0.149mm 7.70% 0.149mm 26.6%
0.193mm 9.78% 0.177mm 32.06% 0.177mm 12.4%
0.230mm 2.08% 0.210mm 42.77% 0.210mm 2.8%
0.275mm 0.72% 0.250mm 13.85% 0.250mm 2.7%
0.413mm 1.35% 0.297mm 0.51% 0.297mm 2.0%
Median 0.144mm Median 0.22mm Median 0.148mm
CHAPTER 3
HYDRODYNAMIC MODEL
3.1 Introduction
In field experiments, measured current and waves are irregular, in other words, the
measured waves are the sum of numerous sinusoidal waves with different frequencies. Also
the magnitude and direction of waves changes with time. Therefore, these measured data
should be processed to be used as input parameters for model.
In this chapter, the method of calculating the model input parameters from the irregular
.wave and current data is given. Wikramanayake[1993]'s timeinvariant eddy viscosity
model are also introduced briefly.
3.2 Determination of hydrodynamic input parameters for model
3.2.1 Current
Fluid velocity in xy direction is measured by EMCM. The current velocity can be
calculated by timeaveraging of the measured EMCM data. A vector sum of these two
components is the magnitude of current and the direction of current can be found since the
current meter is fixed to a specific angle relative to North.
Uc(Ze) =u(ze,t) Uw(ze,t)
vc(ze) =v(zet) vw(zet)
15
The elevation of EMCM from bed can be determined by the instantaneous elevation of
TFACP above the bed since the distance of EMCM relative to TFACP are not changed.
3.2.2 Near bottom wave velocity
The measurement of wave velocity at EMCM can be transformed to the near bottom wave
velocity by linear wave theory. However, the waves observed in the field are irregular, so the
random waves should be decomposed into sinusoidal components with different frequencies
by a Fourier transform. After the decomposing process by FFT method, irregular waves in
time domain are converted to the sinusoidal components in frequency domain.
Time domain Frequency domain
uw(ze ,t)  Uw(ze,,O)
FFT
U, (0,t )= U,(ze (),
IFFT
u,(O,t) I(F U,(O, )
. EMCM
Ye
Z=o
Figure 3.1 The procedure of calculation of near bottom wave velocity
Wave Particle Velocity at EMCM
Near bottom velocity in crosshore direction
E
0
50 0
o
(D
50
0
50
0
0
50
0
Figure3.2 The example of calculation of near bottom wave
velocity from wave velocity at EMCM.
And then each sinusoidal component at bottom is calculated by linear wave theory. Finally,
the information in frequency domain is converted into the near bottom wave velocity in
time domain by IFFT method.
3.3 Primary wave direction
100 200 300 400 500 600 700 800 900 1000
time(sec)
17
Since the direction of irregular waves is variable with time, the primary wave direction
is found by an analysis of directional spectrum from pressure and wave velocity data. Figure
3.3 shows the definition of primary wave direction.
Shore
Primary
wave
direction
EMCM
Orientation
+x
Figure 3.3 Definition of the primary wave direction
during Duck94 experiment
If the crossshore(+y) and the long shore(+x) components of the wave velocity in orientation
of EMCM are denoted by uw and v,, respectively. By a transformation of coordinate, the
components of wave velocities in primary direction are
S[ cosO p sine
v I sine0 cosep
(3.2)
18
A directional wave spectrum is essentially a representation of the wave number, if the
crossshore(+y) and long shore spectrum of water surface waves follow the dispersion
relationship of linear wave theory. The primary wave direction relative to the orientation of
EMCM, 0p is found by following formulae.
B BA R (6)
6 =tan'l() A 7 )k()
R (0) (3.3)
Rpu(o) and Rp,(o) are cospectra which are obtained from the pressure and u, v data, k, and
k, are also defined as following ones.
Y0cosh(kh2) wcosh(kh,)
k (0= k()= (3 .4)
Scosh(kh) cosh(kh) (3
hi height above the bed of EMCM
h2 height above the bed of pressure gage
Yo specific weight of seawater
3.4 Representation of irregular waves
The ocean waves are irregular waves with contributions from many frequency components.
Therefore, the irregular waves should be represented by a single wave with representative
wave velocity and frequency. Figure 3.4 shows a power spectrum of wave velocity. The
elementary method of choosing the representative frequency of random waves is to select it
19
as the peak period in power spectrum. But this method is not suitable for nonnarrow band
or doublepeak spectrum. In this paper, the mean zerocrossing wave frequency is used as
the following
Sf Su,()o)2do)
f JS.())do (3.5)
where Su1 (o) is the power spectrum of the near bottom wave velocity.
Wave energy spectrum
x 10
2r;
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
frequency f
Figure 3.4 Power spectrum of near bottom wave velocity
1.5 1
0.5
0
. I
20
The representative magnitude of wave velocity at bottom in primary direction, v, are defined
by
vr= __ u 2
= Nn=1 p,n (3.6)
up, is near bottom wave velocity in primary wave direction. The assumption comes from the
normal distributions of wave velocity and the Rayleigh distributions of amplitude. Even
though the assumption is only true in deep water, it is reasonable in offshore side of sand
bar.
3.5 Hydrodynamic model
3.5.1 Eddy viscosity model
Timeinvariant eddy viscosity model was suggested by Wikramanayake [1989]. This
model is given by following one.
ku*,C z z a6
t = ku*,wa6 a5 s z < ac/e (3.7)
ku*,z abl/e z
k=0.4 :von Karman's constant
a=0.5 : model parameter
u*cw :combined maximum shear velocity
u,* :current shear velocity
e = U* / u*cw
6 = ku*cw,/
21
where o is the wave frequency and e is the ratio of current relative to wave. This eddy
viscosity profile is shown in Figure 3.5. There are three regions which consist of the bottom
layer, the intermediate layer and the upper layer. The magnitude of eddy viscosity in the
bottom layer is proportional to the combined shear velocity. It is constant in the intermediate
layer but proportional to current shear velocity in the upper layer.
z
ut = ku.ez
a 6/e   * 
U, = ku.,,z
V.
eddy viscosity
Figure 3.5 Vertical profile of eddy viscosity
3.5.2 Current and wave velocity profile of model
To solve the current problem, the eddy viscosity model of equation (3.7) should be
substituted into the following governing equation.
du
duc 2
Vt= =U(
dz c (3.8)
22
This differential equations can be solved by using the boundary conditions at the z=zo, z=ab
and z=a6/e. The solutions are
u ]
e ln[ ]
k go
,q< a
S= u[ 1 +ln[ ]]
k a o
c[ln[ ]+1+e[ln[] 1]]
k ale Eo
,a < 9 < a/e
,ale <
where g is the nondimensional vertical distance denoted by
Zo
The governing equation of wave velocity in turbulent boundary layer is
The governing equation of wave velocity in turbulent boundary layer is
a(u"wu) a a
[at (u,u,
8t 8z 8z
(3.9)
(3.10)
(3.11)
where uw and u. are the wave velocity in boundary layer and the near bottom potential wave
velocity respectively. The solution of PDE (3.11) can be obtained as following one
w =Re(ude it )
luj (3.12)
Substitution of (3.12) into (3.11) gives a new governing equation.
d dud
[v, ]i(OUd=0 (3.13)
dz dz
The boundary conditions for (3.13) are
ud= 1 at z=zo
Sd O at zoo (3.14)
By substituting (3.5) into equation (3.13), The solution can be obtained as following results.
Cl(ker2 +ikei2v) +C2(ber2 /q +ibei2i/ ) qSo
ud 3exp( )+C4exp( ) (3
p ) E ~ (3.15)
Cs(ker2 q+ikei2 ) +C(ber2 +ibei2 ) a
By applying the boundary equation (3.15) and matching the values of ud and dud/dz at q=a
and q=a/E, we can get the 6 complex coefficient.
Cl(ker2 +ikei2o) +C2(ber2o r+ibei2~I) = 1
C6=0
Cl(ker '2~/ +ikei 2/) +C2(ber /2 +ibei 2v/) = C3Fie VC4ie V
Cl(ker2 +ikei2/a)+C2(ber2/ +ibei2a) = C3e \ +C4e /
C3e vN +C4e /E=C,(ker2ii +ikei2 a)
E E
C3 Ve 07E +C4 nV/e "VE =C5(ker2r +ikei /2 F) (3.16)
E E
3.6 Ripple model
The estimation of ripple geometry based on shield parameter was suggested by
Wikramanayake[1993]. The shield parameter is proportional to the ratio between the surface
shear stress and the submerged weight of sand. The stronger the surface shear stress is, the
lower the ripple height is. His formulae based on field data are
( 0.01 8AbrZ 0.5
0 .0007AbZ 1.23
TI 0.15Z 0.009
X [ 0.0105Z 0.65
,0.00016
,0.012
,0.0016
,0.016
where rl and A are a ripple height and length, respectively, and Abr is v/~o. Nondimensional
parameter 0' is defined by
Zc
S,
S, is defined by
d 4v(s1)gd
4v
with v being the kinematic viscosity of sea water and s is being the specific gravity of sand.
CHAPTER 4
THE SUSPENDED SEDIMENT DISTRIBUTION MODEL
4.1 Introduction
The vertical concentration profile of suspended particles is determined by the balance
between upward sediment flux and downward falling velocity. The upward flux can be
explained by mixing scale. Distribution process of suspended sediment can be well described
as an orderly convective processes and as a disorderly diffusive processes or as a combined
one. Of course, hydrodynamic conditions decide which model is predominant.
In this chapter, a pure diffusion model and a combined model are suggested. And also the
combined model is modified by using a new eddy viscosity model which is a combination
of Wikramanayake's and Nielsen's eddy viscosity model.
4.2 Review of model
4.2.1 The governing equation
A change of the local sediment concentration is equal to a divergence of sediment flux
field. If we assume the horizontally uniform sediment concentration field i.e c=c(z,t) and the
correspondingly uniform sediment velocity field. The governing equation is then suggested
by
ac dqz
at dz (4.1)
25
where q, denotes the total sediment transport rate per unit area in vertical direction. This
vertical sediment flux consists of a downward flux ( w0c ) due to the settling of particles,
and an upward flux which is convective (qc) or diffusive ( qd) or usually a combination of
these two modes. The governing equation (4.1) can be rewritten
ac ac aqd aqc
at w z az az (4.2)
Figure 4.1 gives a description of each flux.
wo(C+) qd+ dz q + dz
dz dz c z
ac/at
S t t
woc qd qc
Figure 4.1 Description of sediment conservation
in terms of vertical flux components
4.2.2 Diffusion model
Diffusion process takes place from higher toward lower concentration. So the upward flux
is proportional to the gradient of concentration and sediment diffusivity E,. For the pure
diffusion process, the mass conservation equation becomes
ac ac aqd
w 
at a z az (4.3)
The sediment flux by diffusion is given by
ac
qd = s
zd (4.4)
By substituting equation (4.4) into equation (4.3), we can get
ac ac a ac)
w + (e )
t a 9z 9z z (4.5)
If we only consider a steady concentration state which is balanced between the upward
and.downward flux of sediment, Timeaveraging and integrating of the equation (4.5 ) leads
to the more simplified form.
dc
woc + Es = 0
dz (4.6)
It is assumed that the magnitude of sediment diffusivity is equal to the one of eddy
viscosity suggested by Wikramanayake[ 1993]. By substituting the eddy viscosity of equation
(3.7) into the equation (4.6), three equations are obtained as following
de WO 4a
c for z < a
dz kucwz (4.7a)
dc Wo a6
S c for auz < 
dz ku ,wa6 (4.7b)
dc WO a8
 c for _< z
dz kucz E
(4.7c)
27
The above equation is a first order ordinary differential equation. The solutions are the
following ones respectively.
C)=[ i' rQ<"a (4.8a)
Cr r
c() a a
[ ] e a (4.8b)
Cr qre E
a
c(q) a a eE a,
S41 [] 4 (4.8c)
cr 4e a E (4.8c)
4.2.3 Convection model
The processes which the mixing length scale is of the same magnitude as the sediment
distribution cannot only be described by diffusion processes. Nielson[1992] developed the
simple convective model in which a concept of probability distribution function of
entrainment distance was introduced. In his model, the convective sediment flux is expressed
by
qc(z,t) = p(t z)F(z)
w
C (4.9)
The pickup function p(t) is a nonnegative function indicating the instantaneous pickup
28
rate at the bed. The convective distribution function F(z) is a probability function
determining the rate of the entrained sand which is transported beyond the level z, that is P{
ze > z } = F(z).
By substituting equation (4.9) and qd=0 into (4.2), we can derive the following
conservation equation.
9c 9c 9PF
9t o z z+ (4.10)
Timeaveraging and integrating the above equation leads to the final convective equation
under equilibrium conditions.
wc(z) = PF(z) (4.11)
The following probability distribution function of entrainment is developed by
Nielsen[1992]. It's based on laboratory experiment.
F(z)= [ 1+ Z ]2
0.09 kbA (4.12)
kb: the equivalent Nikuradse roughness
Ab: the horizontal semiexcursion
4.2.4 Combined model
Lee and Hanes[1995] suggested the combined convectiondiffusion model using
29
Wikramanayake[1993] eddy diffusivity model and Nielsen [1992]'s pure convective model.
The upward sediment transport term which is the sum of the diffusive and convective flux
is
q(z,t) = E c + P(t)F(z) (4.13)
a z w
If equation (4.13) is substituted into (4.2) and we average and integrate the resulting
conservation equation, The governing equation of combined model is
(4.14)
w c + E PF(z)=0O
dz
where the boundary condition is
 dc
c=0,=0,F(z)=O ,when z
dz
Es=O ,F(z)=F(z) ,when z=z,
we
p or
F(z)
dc w+ c wo F(z)
dz + C F(z
dZ Es Es F(zr)
Therefore
(4.15)
(4.16)
(4.17)
By substituting equation (4.16) into (4.14), we can get first order ordinary differential
equation.
By applying the eddy diffusivity model of equation (3.7), the equation (6.19) is divided into
three parts.
dc Wo CrW F(z)
+z k
dz ku cwe kucz F(zr)
, za6
(4.18a)
dc W CrW F(z) ab
+_c a6_z
dz ku ,wa6 kucwa F(zr) E
dc Wo crwo F(z) a6
+c 'z
dz ku,Z kuz F(z) E
The solutions of above differential equations are
Z
c() z a[afz aF(z)dz+cl]
C
a z a
c(z= e a [ e a F(z)dz+c2]
r a6
(z a z 
c(=z '[ z F(z)dz+c3]
r a6
E
(4.18b)
(4.18c)
(4.19a)
(4.19b)
(4.19c)
By applying the boundary condition at z=zr, and matching the concentrations at the z=a6 and
z=a6/E, the integration constants can be found.
cl =zra
(4.20a)
a a F(z)
c2=( )[a a ) dz+z a]
e f F(zr) (4.20b)
Zr
_a E a
c3=(ee) a [ f F(z)dz] +c2
a8 ab J (4.20c)
a5
4.3 Modified combined model
4.3.1 Problem statement of previous combined model
Generally, the magnitude of sediment diffusivity at a specific level is proportional to the
intensity of wave and current shear velocity. Also it depends significantly on wave frequency.
In Lee's combined model, as suggested in previous section, the timeinvariant eddy
viscosity model is not very sensitive to the wave frequency. The other problem is that the
timeinvariant eddy viscosity model used the maximum shear velocity as a function of eddy
viscosity. According to the experiments of Bosman[1982] and Ribberink & AlSalem[1989],
timeaveraged concentration over rippled beds in an oscillating water tunnel is proportionally
increased with frequency. This change of concentration profile indicates the different
distribution of sediment diffusivity by diffusion model framework. However it's not proper
explanation because the sediment diffusivity are closely related to the eddy viscosity under
similar hydrodynamic condition of experiments. Here a modified eddy viscosity model
32
which is an combination of Nielsen's and Wikramanayake's one to predict the concentration
profiles is tried.
4.3.2 Modification of eddy viscosity model.
Nielsen used the eddy viscosity in wave boundary layer as following one in view of
experiment.
Ut=0.50z1 2 =0.004wrAb Es=4Ut (4.21)
r : Nikuradse equivalent roughness
Ab: semiexcursion of water particle
There is an increase in turbulence fluctuation due to the addition of current in wave
boundary layer. So we can add the sediment diffusivity by current to the above sediment
diffusivity by wave in scale of wave boundary layer under wave and current. This addition
should be a sum of vectors. An assumption of no turbulent fluctuation at bottom and linearly
increasing eddy viscosity with current shear velocity in outer region of boundary layer is
reasonable. Therefore sediment diffusivity can be assumed as follows.
PZ ,z
a a6
E = p ,a6
e (4.22)
a6
p+q ,
E
p = (2w12)2 +(kusc a)2+2(2oz12)(kucab6)cosc
q = kuc(z)
E
where z, is 0.0081rAb.
This sediment diffusivity model has a similar profile and same boundary layers with
previous model but the absolute value of eddy viscosity is different. Originally, the
equivalent Nikuradse roughness (r) is calculated by the following formula that Nielsen[1992]
suggested using a measured bed geometry.
r2
kb = 8+502.5d50
1 f2.55p2
02.5 2
2 (s1)gd5o
2.5 = exp[5.213(2.5d50/Ab)01945.977] (6.26)
By substituting (6.25) into (6.19) and solving the 1storder ODE, the solutions and
integration constants are obtained in three layers.
vc(8) =z e va ) dz+cl]
F(z)z (4.23a)
Z
c(z)=e vZ[ fe c F(z) dz+c2] (4.23b)
f, F(Zr)
a8r
 0 ku0,cu a6 ,c W F(Z) dz +c
c(z)=(p+ku.c(Z)) c[f(p+ku c(Z )) C d
E p +ku,(z ) F(z) (4.23c)
as p+kuc(z
w
Where v=
P
By applying and matching at the boundaries, we can get the integration constants which
result into
clz =z (4.24a)
c2 =e V(as)v fz vas1 dz+cl] (4.25b)
f F(r)
Zr
a8
ku E F(z)
c3=p ce [ f e vv dz+c2] (4.25c)
a8 F(zr)
4.4 The test of model
The diffusion, Lee's combined, the modified model was tested with the change of the
listed input parameters. To compare the changing patterns of model results and evaluate the
effect of each parameters on models, the definitely different flow conditions are chosen as
shown in Table 4.1. Also, three models have the same reference concentration and the same
bed form.
In figure 4. a d, TEST09, TEST11, TEST13 and TEST15 show that the modified model
gives almost the same predictions with Lee's combined model under low wave velocity
35
(up=30cm/sec) and the sediment size(dso =0.2 mm). But under high wave velocity and the
sediment size(d5o=0.1 mm), the modified model underpredicts the suspended sediment
concentration compared to Lee's combined model. This fact indicates that the magnitude of
estimated eddy viscosity in modified model is smaller than one in Lee's combined model.
But we have to consider that the bed roughness in Nielsen's eddy viscosity model, eq. (4.21),
was not estimated by using a measured ripple geometry but a calculated one. Under both
strong current(U=60 cm/sec) and fine sediment(d50 =0.1 mm) condition, the pure diffusion
model gives very similar results with Lee's combined model because diffusion processes are
more dominant than convection processes.
Table 4.1 Input parameters for model test.
File I up U d5o File o) Up U dso
rad/s cm/s cm/s mm rad/s cm/s cm/s mm
TEST01 1.0 30 10 0.1 TEST09 1.0 30 10 0.2
TEST02 1.0 60 10 0.1 TEST10 1.0 60 10 0.2
TEST03 1.0 30 40 0.1 TEST11 1.0 30 40 0.2
TEST04 1.0 60 40 0.1 TEST12 1.0 60 40 0.2
TEST05 0.5 30 10 0.1 TEST13 0.5 30 10 0.2
TEST06 0.5 60 10 0.1 TEST14 0.5 60 10 0.2
TEST07 0.5 30 40 0.1 TEST15 0.5 30 40 0.2
TEST08 0.5 60 40 0.1 TEST16 0.5 60 40 0.2
TEST01
TEST02
concentration(g/1) concentration(g/)
TEST03 TEST04
1+
+
!+
+
c 1+
100
concentration(g/l)
concentration(g/l)
Figure 4.2 Test of models
30
E
0
0) 20
9
S10
c
I
olO
S10.5
TEST05
TEST06
concentration(g/I) concentration(g4)
TEST07 TEST08
105 100 105 100
concentration(g/I) concentration(g/I)
Figure 4.3 Test of models
E
V
Q)20
E
2
0
o
C
.4
ci
*0
TEST09 TEST10
30  30
E E
020 D 20
( +
O10,5 100 100 C 0
E + E \+
concentration(g/1) concentration(g/1)
TEST11 TEST12
30 30 C.
S20 *20 +
E E +
o0 1+ 0 +
105 10 105 10
+.. +
4 I \c +
01 010 +
O *.o+ l +
O ..+ + +
3+
20 0
10.5 100 10.5 100
concentration(g/I) concentration(g/l)
Figure 4.4 Test of models
TEST13
TEST14
concentration(g/) concentration(gl)
TEST15
E
20
E
0
'
Co
105
concentration(g/I)
TEST16
+
1+
: +
+
+
+
,+
100
concentration(g/l)
Figure 4.5 Test of models
E
20
020
n
E
0
o10
r
Page
40
missing
from
original
CHAPTER 5
COMPARISON OF MEASURED DATA WITH MODELS
5.1 Introduction
In previous chapters, three prediction models were introduced. In this chapter, the field
data of Vilano, Supertank and Duck94 experiments are compared to the models. According
to flow conditions and the field environment, the best fit model is found to differ. Also
several input parameters and estimated ripple height and length are presented.
5.2 Comparison of model input parameters
The field data selected from Vilano, Supertank and Duck94 experiments are compared.
The data sampling rate are 2Hz, 4Hz and 2Hz for Vilano, Supertank and Duck94 data
respectively. The parameters for Vilano comes from Lee's dissertation [1994].
Table 5.1Model input parameters of Vilano data files
Data Frequency vr U kw Depth Height of
File rad/sec cm/sec cm/sec degree cm EMCM
a020880 1.640 29.5 12.6 56.5 363.6 140.7
a020894 1.340 28.4 19.9 63.2 275.9 141.1
a020895 1.400 26.3 20.2 64.0 272.4 141.1
a020896 1.400 28.2 18.3 61.4 267.6 141.0
a050846 1.420 57.2 43.2 59.7 393.9 141.6
a050848 1.320 61.2 52.4 48.3 381.5 141.5
a050850 1.320 69.6 61.7 58.9 371.5 141.7
a050852 1.400 66.6 63.6 65.7 361.3 141.7
vr : The representative near bottom wave velocity
in primary wave direction
U : The current velocity
,W : The angle between current and wave direction
The method to calculate the above parameters has been suggested by Chapter 3 in this
thesis and Chapter 6 in Lee's dissertation in detail.
Table 5.2 Model input parameters of Supertank experiment data files.
Data File Frequency vr U Depth Height of
rad/sec cm/sec cm/sec degree cm EMCM
Runl8B 2.11 32.34 3.04 0 193.5 33
Run26 N 1.49 43.52 0.11 0 214.8 33
Run43 M 2.09 79.17 7.50 0 222.6 33
Run45 M 0.78 23.89 0.37 0 200.5 33
Run47 B 1.06 26.93 0.40 0 198.0 33
Run52 B 1.11 46.73 0.08 0 192.2 33
Run54 M 2.03 14.36 0.35 0 199.9 33
Run55 B 2.08 18.16 0.38 0 196.9 33
Run59 N 2.01 36.57 0.42 0 194.8 33
Run73 N 0.90 33.22 0.47 0 190.2 33
Run74 N 0.92 26.80 0.58 0 176.5 33
Run81M 0.93 50.92 0.51 0 195.8 33
M: Monochromatic
N :Narrow band random
B :Broad band random
Ten data files set of a table of 83 Supertank experiment data are selected to consider
diverse wave conditions. The current velocity is very weak and can be negligent and the
height of EMCM from the bottom is assumed as 33cm even though the bed changes slightly
over the course of a single run and also between runs.
Table 5.3 Model input parameters of Duck94 experiment data files
Data Frequency vr U cw Depth Height of
files rad/sec cm/sec cm/sec Degree Cm EMCM
da22092 0.56 28.5 17.1 51.7 512.2 192.5
da22091 0.54 30.9 18.9 53.2 502.3 192.5
da22092 0.56 28.5 17.1 51.7 512.2 192.5
da23095 0.53 30.5 13.9 45.6 529.3 192.5
da24115 0.77 24.8 50.8 86.4 457.0 193.9
da24119 0.56 31.7 43.0 169.6 522.6 199.1
da25122 0.59 28.4 41.1 174.5 490.4 196.9
da25124 0.55 28.3 42.9 169.0 473.0 196.9
da25129 0.54 38.6 24.5 173.6 566.7 193.9
da25130 0.52 41.7 26.4 173.5 560.0 193.9
da25131 0.52 35.5 26.2 167.7 554.5 193.9
da25132 0.50 39.6 27.1 165.0 547.9 193.9
ds05026 1.26 24.9 21.1 163.2 440.5 199.1
ds05027 1.22 27.0 20.9 169.4 459.9 198.4
ds05028 1.21 27.8 21.3 153.3 490.8 197.6
ds05029 1.22 39.3 22.1 131.3 515.0 197.6
ds05049 1.10 65.4 37.3 120.7 450.6 201.3
ds05050 1.08 66.9 32.4 136.8 459.6 202.1
ds05051 1.07 60.5 37.1 134.7 484.8 202.1
ds05052 1.03 68.4 40.2 125.0 519.9 203.6
Table 5.3 continued
ds06078 0.73 41.5 32.1 176.0 429.3 199.9
ds06079 0.76 43.1 29.1 165.7 388.6 199.9
ds06082 0.75 38.6 27.3 146.1 394.4 200.6
ds06084 0.71 35.4 27.5 138.1 497.8 200.6
do12027 1.55 26.3 39.1 173.5 600.2 213.2
do12028 1.58 24.1 40.3 166.5 594.3 212.5
do12029 1.61 25.1 39.3 174.5 530.9 211.7
do12030 1.53 29.1 39.6 167.6 470.1 211.7
do14074 0.92 89.0 69.6 105.7 475.1 199.1
do14075 0.92 92.7 76.1 124.8 442.8 196.9
do14076 0.95 91.2 62.3 122.8 419.9 196.2
do14077 0.93 87.3 80.1 113.9 417.6 196.9
do15089 0.86 94.6 60.8 148.5 435.9 186.5
do15090 0.85 101.3 70.3 155.1 458.5 185.8
do15091 0.86 100.1 65.1 153.7 487.3 185.0
do15092 0.85 95.9 57.6 156.0 519.5 183.6
da : Duck 94 August data file.
ds : Duck 94 September data file.
do : Duck 94 October data file.
5.3 Estimation of ripple geometry and friction velocity
Wikramanayake[1993] suggested his ripple model based on field data as we reviewed the
formulae in Chapter 3. In this section, ripple geometry and friction velocity calculated from
Wikramanayake's model are presented. Also these ripple data are used to calculate the
equivalent Nikuradse roughness for the combined and the modified models. This formula are
also given in Chapter 4.
Table 5.4 Estimated Ripple and Friction Velocity(Vilano Data Files)
File Name r Il/X u* U*cw Cr
cm cm/sec cm/sec g/1
a020880 0.171 0.046 0.84 3.99 1.722
a020894 0.229 0.049 1.17 4.00 1.169
a020895 0.231 0.052 1.17 3.82 1.032
a020896 0.217 0.049 1.08 3.96 1.176
a050846 0.000 0.000 2.30 5.35 1.211
a050848 0.000 0.000 2.73 5.87 1.490
a050850 0.000 0.000 3.15 6.45 2.139
a050852 0.000 0.000 3.16 6.21 2.013
Table 5.5 Estimated Ripple and Friction Velocity(Supertank Data Files)
File Name rl rj/X uC u*,w Cr
cm cm/sec cm/sec mg/l
Run 18 0.437 0.076 0.45 5.48 3051
Run26 N 0.505 0.061 0.09 6.57 5430
Run43 M 0.000 0.000 0.93 7.43 2747
Run45 M 2.080 0.112 0.17 4.93 613
Run47 B 1.262 0.098 0.15 5.17 676
Run52 B 0.692 0.059 0.09 6.97 5933
Run54 M 0.719 0.134 0.08 3.24 144
Run55 B 0.653 0.117 0.09 3.83 651
Run59 N 0.410 0.068 0.13 5.85 3953
Run73 N 1.320 0.084 0.21 5.90 905
Run74 N 1.526 0.100 0.20 5.20 556
Run81 M 0.795 0.056 0.26 7.40 8373
Table 5.6 Estimated Ripple and Friction Velocity(Duck94 Data Files)
File Name 1r rU/Uu u v u Cr
cm cm/sec cm/sec g/1
da22090 0.771 0.057 1.31 4.44 0.449
da22091 0.779 0.055 1.37 4.62 0.470
da22092 0.788 0.057 1.25 4.44 0.398
da23095 0.809 0.058 1.24 4.38 0.410
da24115 0.594 0.063 2.73 4.14 0.646
da24119 0.692 0.052 2.69 5.46 2.487
da25122 0.734 0.057 2.54 5.14 1.749
da25124 0.797 0.058 2.64 5.20 1.671
da25129 0.649 0.045 1.79 5.52 0.925
da25130 0.627 0.043 1.93 5.82 1.333
da25131 0.720 0.049 1.87 5.33 0.789
da25132 0.692 0.045 1.96 5.68 1.040
ds05026 0.313 0.058 1.23 3.97 1.014
ds05027 0.301 0.055 1.26 4.17 1.173
ds05028 0.297 0.533 1.30 4.23 1.222
ds05029 0.218 0.040 1.40 5.07 2.515
ds05049 0.000 0.000 1.99 5.58 1.531
ds05050 0.000 0.000 1.81 5.71 1.550
ds05051 0.000 0.000 1.98 5.35 1.313
ds05052 0.000 0.000 2.18 5.82 1.664
ds06078 0.401 0.041 2.01 5.74 4.642
5.4 Comparison of timeaveraged vertical concentration profile
5.4.1 Vilano data files
Originally, Lee applied the pure convection, the pure diffusion and the combined model
using both median and multiple grain sizes to Vilano data files. But in this thesis, only results
using multiple grain sizes are shown in figures. In addition, the modified model was
applied to the same data files. The same reference concentration model which had been
developed by Madsen[1991] was used to predict the suspended sediment concentration.
ds06079 0.376 0.039 1.81 5.75 5.083
ds06082 0.421 0.043 1.69 5.33 1.437
ds06084 0.488 0.047 1.79 5.09 1.117
do12027 0.226 0.054 2.11 4.51 1.758
do12028 0.237 0.054 2.11 4.51 1.545
do12029 0.225 0.056 2.06 4.39 1.672
do12030 0.212 0.050 2.07 4.69 2.016
do14074 0.000 0.000 3.47 7.16 2.887
do14075 0.000 0.000 3.78 7.87 3.404
do14076 0.000 0.000 3.20 7.51 2.936
do14077 0.000 0.000 3.81 7.39 3.093
do15089 0.000 0.000 3.29 7.94 3.238
do15090 0.000 0.000 3.78 8.63 3.649
do15091 0.000 0.000 3.59 8.45 3.693
do15092 0.000 0.000 3.27 8.04 3.233
48
In Figure 5.1, the model results are compared with the measured data under low wave
energy conditions which implies the existence of ripples. Under low wave energy condition,
even though the model results is not close to the field data, LH95 model gives the best fit
with field data and the modified model presents similar results because the convective
process is much more dominant than diffusion process. The prediction by pure diffusion
model is the least accurate.
a0208m80
a0208m94
sediment concentration(g/1)
a0208m95
sediment concentration(g/I)
sediment concentration(g/I)
a0208m96
sediment concentration(g/I)
Figure 5.1 Vertical profiles of sediment concentration of Vilano data files
under low wave energy condition.
:measured + :LH95 model
o :modified + :diffusion
do
E
2 20
a)
0
C
O
cI
(0i
:3
49
In Figure 5.2, the field observations are under high wave energy condition which implies
sheet flow. The figure shows that LH95 model gives very accurate agreement with field
data and the pure diffusion model is also very good in prediction. But the modified model
has the less accurate results than other models. This implies that the eddy diffusivity in the
modified model could be underestimated when the model is applied to Vilano data set.
a0508m46
a0508m48
104 102 10 1
sediment concentration(g/l)
a0508m50
An, 
sediment concentration(g/l)
a0508m52
An
"o
.Q
0)
E
20
o)
ca
t)
.v
104 10.2 10 10 104 102 10 102
sediment concentration(g/I) sediment concentration(g/l)
Figure 5.2 Vertical profiles of sediment concentration of Vilano data files
under high wave energy condition
:measured + :LH95 model
o:modified + :diffusion
Q)
*C
E
220
C
'
5.4.2 Supertank data files
Originally, these suspension models were developed for field conditions. So we may
expect them not to be accurate in prediction of suspended sediment concentration in
laboratory experiment. Moreover, the diffusion model based on timeinvariant eddy
viscosity model developed by Wikramanayake[1993] is not suitable for the flow conditions
having a very weak current relative to wave. Because this eddy viscosity model strongly
depends on the intensity of the current, the magnitude of the eddy viscosity out of the wave
boundary layer could be underestimated with weak currents. Unfortunately, the magnitudes
of currents in Supertank experiment were very weak.
The data files in experiment are categorized by three wave conditions which are
monochromatic, broad band random and narrow band random in terms of wave energy
spectrum. Figure 5.2a, 5.2b and 5.2c shows the comparison of the predicted concentration
with the measurements under monochromatic, broad band random and narrow band random
wave conditions respectively.
Overall, the prediction of models is not accurate but LH95 model and the modified one
are much better in model results than the pure diffusion one. Also we can see that models
give the best fit under narrow band random wave condition similar to real field conditions.
However, the model results are far away from the measurements.
RUN43 RUN45
20 20
+
c + +c
\+
20 + 20
E E
o 0
+d + Cd
E C
0 0
105 10 105 105 10 105
concentration(mg/I) concentration(mg/I)
RUN54 RUN81
20 20C
u ma E c+i
+ +
:10 . o10u
El0 40
o : eo fo
0 0 .
05 10 105 105 10 105
concentration(mg/I) concentration(mg/I)
Figure 5.3 Vertical sediment concentration profiles of Supertank data files
under monochromatic wave condition.
:measured + :LH95 model
:modified + :diffusion
RUN18 RUN47
20 20
E E +
0
10) 10 1 10 10 10
o a ,
+ \+
c E
Cj C
10 100 10s 10 10 105
concentration(mg/I) concentration(mg/1)
RUN52 RUN55
20 20 +
under broad band random wave condition.
E E
:measured + +
S:modified + : diffusion
c +
+ z
10 V10.
0 *cn 0)
:easured + LH95 model
:modified + diffusion
RUN26 RUN59
S\ +
20 20
E E
. + +
03 \+ 0 ) 0
0 n
010 10 101 10
C C \
: u+ +
105 100 105 105 100 105
concentration(mg/I) concentration(mg/)
RUN73 RUN74
20 20
E1 E \
o10 \; o10 \'
+4
05 10 105 0 10 10
concentration(mg/l) concentration(mg0)
Figure 5.5 Vertical sediment concentration profiles of Supertank data files
under narrow band random wave condition.
measured + :LH95 model
:modified + :diffusion
5.4.3 Duck data files
36 field data files are selected for comparison. Because of the acoustic scattering of the
sea bed, accurate measurements are only obtained above 3cm above the seabed. The flow
conditions are quite different from those of the Vilano experiment. Overall, the wave
frequency is smaller than one in Vilano, in the other hand, the angle between wave and
current is larger than one in the Vilano field experiment. These different flow conditions
contribute to the different distribution of suspended sediment concentration. Note there were
two strong North eastern storms on September 3rdSeptember 5th and October 12th
October 16th.
In Figure 5.65.11, 36 sets of field measurements under low wave energy conditions are
compared with model results. Model results are plotted for height above 3cm above sea bed
because of measurement limit. All models used the multiple fall velocity classes, the same
reference concentration formulae and the same ripple prediction model. Overall, the
diffusion model give a best fit in prediction of the vertical distribution of suspended
sediment concentration. The modified model doesn't give good agreement with measured
data, except Figure 5.6 and Figure 5.7 with the low wave frequency(0.50.8 rad/sec) and low
wave energy (v, <30 cm/sec). The result may be due to the underestimation of sediment
diffusivity by Nielsen's model. On the other hand, the LH95 model tends to overestimate
the concentration under low wave energy condition because of less suspension of particles
by low frequency and smaller fall velocity classes of sediments in comparison of those of
Vilano's experiment. But, in Figure 5.11, the results of three models are far away from the
measured concentration. It should be noted that the flow conditions for these data files are
under high frequency( >1.5 rad/sec) and low wave energy( v,<30 cm/sec).
When the wave frequency becomes higher, more particles are suspended by the increase of
fluid acceleration. Moreover, low wave energy condition underestimate the reference
concentration of models. Therefore, the models don't properly respond to this flow condition.
It resulted into the underestimation of concentration. Figure 5.1 shows similar case.
In Figure 5.125.14, 3 sets of measured concentration under high wave energy condition
which means the sheet flow are compared with model results. Overall, LH95 model gave
the best agreement with measurements with nonbreaking waves.
Exceptionally, Figure 5.14 shows the worst underestimation of all models in comparison
with field data. These data files have similar flow conditions with the Vilano data set except
the angle between wave and current, but the results are totally different. It might be due to
breaking waves during the storm period(Sep. 34 Oct. 1216). In Marusin's thesis[1995],
TFACP transducers(0.97MHz and 2.35MHz) show consistent results under nonbreaking
waves, but the difference between them becomes extremely large in the storm situation when
breaking and broken waves are observed.
5 da22091 8/21/17:16:56
102 10 10 104 102 10
Concentration(g/) Concentration(g/I)
6 da22092 8/21/17:33:7 9 da23095 8/21/18:21:40
104 10.2 10o 102 104 10.2 10o
Concentration(g/) Concentration(g/l)
Figure 5.6 Vertical sediment concentration profiles of Duck94 data files
on the rippled bed
:measured + LH95 model
S:modified + :diffusion
4 da22090 8/21/17: 0:45
29 da24115 8/22/16:33:59
102 10 10 104 10 10
Concentration(g/I) Concentration(g/I)
36 da25122 8/23/12:21:24 38 da25124 8/23/12:53:4
011!i1 'I201 1 
104 102 10 10 10 10 12 10 1
Concentration(g/I) Concentration(g/I)
Figure 5.7 Vertical sediment concentration profiles of Duck94 data files
on the rippled bed
:measured + :LH95 model
:modified + :diffusion
33 da24119 8/23/11:33:54
43 da25129 8/24/9:15:15
102 100
Concentration(g/I)
45 da25131 8/24/9:47:37
102 100
Concentration(g/l)
46 da25132 8/24/10:3:48
A+
104 10.2 100 102 104 102 100
Concentration(g/l) Concentration(g/l)
Figure 5.8 Vertical sediment concentration profiles of Duck94 data files
on the rippled bed
:measured + :LH95 model
S:modified + :diffusion
44 da25130 8/24/ 9:31:26
25 ds05026 9/2/11:0: 0
102 10
Concentration(g/1)
27 ds05028 9/2/13: 0: 0
102 100
Concentration(g/l)
104 102 100 102
Concentration(g/I)
Figure 5.9 Vertical sediment concentration profiles of Duck94 data files
on the rippled bed
:measured + :LH95 model
S:modified + :diffusion
26 ds05027 912/12: 0: 0
75 ds06078 9/6/11:0:0
nn I
0
)
a
E 10
0
.4
C
Q
102 100
Concentration(g/l)
79 ds06082 9/6/15: 0: 0
1
76 ds06079 9/6/12: 0: 0
102 100
Concentration(g/)
81 ds06084 9/6/17:0:0
1
104 102 10 102 104 102 100
Concentration(g/I) Concentration(g/I)
Figure 5.10 Vertical sediment concentration profiles of Duck94 data files
on the rippled bed
:measured + :LH95 model
S:modified + :diffusion
+
+
.
S+
27 do12027 10/12/0:0:0 28 do12028 10/12/2:0:0
,20 i ,20
3 + E +
+ +
\+ 5 "+
+ +
I104 E 10
20 !. 0 +
a 1 + +
Concentration(g/I) Concentration(g/l)
,20 ntherippled b2ed tT 
S+ +
S:i+ +
+ +
+ +
+ +
0 0
104 10,2 0 10 2 i4 102 100 102
Concentration(g/l) Concentration(g/l)
Figure 5.11 Vertical sediment concentration profiles of Duck94 data files
on the rippled bed
measured + :LH95 model
:modified + :diffusion
*:modified + :diffusion
74 do14074 10/14/19:0: 0
102 100
Concentration(g/)
76 do14076 10/14/21:0:0
+
102 100
Concentration(g/)
102 100
Concentration(g/i)
77 do14077 10/14/22:0:0
i+
i+
104 102 10
Concentration(g/l)
Figure 5.12 Vertical sediment concentration profiles of Duck94 data files
under sheet flow condition
:measured + :LH95 model
:modified + :diffusion
75 do14075 10/14/20: 0: 0
89 do15089 10/15/11:0:0
102 100
Concentration(g/I)
91 do15091 10/15/13:0:0
.
102 100
Concentration(g/l)
92 do15092 10/15/14:0:0
i+
]+
4 2 0 2 4 2 0
10 10 10 10 104 102 10
Concentration(g/I) Concentration(g/1)
Figure 5.13 Vertical sediment concentration profiles of Duck94 data files
under sheet flow condition
:measured + :LH95 model
:modified + :diffusion
90 do15090 10/15/12: 0: 0
48 ds05049 9/3/11:0: 0
102 100
Concentration(g/)
50 ds05051 9/3/13:0:0
10 100
Concentration(g/I)
51 ds05052 9/3/14:0:0
+
!+
+ +
+ +
+
+
+
104 10.2 100 10 104 102 100
Concentration(g/) Concentration(g/1)
Figure 5.14 Vertical sediment concentration profiles of Duck94 data files
under sheet flow condition
:measured + :LH95 model
modified + :diffusion
49 ds05050 9/3/12: 0: 0
5.4 Error analysis
To evaluate the models, the relative errors of the predicted concentration value and the
slope of vertical sediment distribution curve are calculated by below formula respectively.
(5.1a)
S (logC) (logC*) 2 0.5
2 i1 az measured a model
n a(logCi) 2
i=1 aZ measured
(5.1b)
Where n is the total number of segments of distance from bed, z, Ci and C*, are the measured
and predicted concentration values, respectively. Equation (5.1b) is only to compare the
slope of the profile in model results with one of measurements. The calculated errors are
listed on Table 5.7.
Table 5.7 Error analysis of Vilano data files
diffusion LH95 modified
Al A2 Al A2 Al A2
a020880 0.964 0.806 0.827 0.390 0.921 0.161
a020894 0.956 0.343 0.835 0.271 0.943 0.242
a020895 0.961 0.357 0.833 0.236 0.932 0.178
a020896 0.965 0.405 0.860 0.303 0.948 0.267
a050846 0.613 0.307 0.200 0.326 0.815 0.317
a050848 0.466 0.375 0.203 0.413 0.728 0.470
a050850 0.384 0.258 0.241 0.283 0.644 0.321
a050852 0.551 0.258 0.142 0.275 0.715 0.266
Table 5.8 Error analysis of Supertank data files
diffusion LH95 modified
Al A2 Al A2 Al A2
Run 18B 0.968 7.222 0.861 4.181 0.936 2.834
Run26 N 0.868 6.024 2.247 4.986 0.692 3.732
Run43 M 0.956 2.233 0.903 1.850 0.984 1.390
Run45 M 0.933 4.172 0.785 3.177 0.793 3.318
Run47 B 0.939 6.407 0.775 4.627 0.858 4.397
Run52 B 1.953 5.450 5.836 5.028 0.811 4.988
Run54 M 1.000 22.02 0.988 5.792 0.987 4.818
Run55 B 0.999 17.02 0.945 5.567 0.947 4.282
Run59 N 0.909 5.072 0.719 3.112 0.884 1.753
Run73 N 0.824 7.148 0.650 5.936 0.764 6.501
Run74 N 0.940 4.772 0.724 3.349 0.842 3.454
Run81M 0.730 2.299 2.818 2.169 0.605 3.110
Table5.9 Error analysis of Duck94 data files.
diffusion combined modified
Al A2 Al A2 Al A2
da22090 0.353 0.524 1.546 0.495 0.365 0.233
da22091 0.591 0.542 2.347 0.512 0.151 0.254
da22092 0.301 0.478 1.134 0.444 0.473 0.233
da23095 0.370 0.527 1.634 0.495 0.427 0.252
da24115 0.726 0.665 0.408 0.642 0.565 0.614
da24119 0.157 0.547 0.905 0.525 0.119 0.347
da25122 0.448 0.519 0.170 0.502 0.462 0.352
da25124 0.428 0.540 0.239 0.521 0.381 0.374
da25129 0.265 0.605 1.446 0.631 0.473 1.075
da25130 0.224 0.564 1.337 0.573 0.448 0.929
da25131 0.212 0.566 0.599 0.568 0.551 0.778
da25132 0.126 0.458 0.220 0.540 0.501 1.353
ds05026 0.711 0.417 0.421 0.431 0.879 0.443
ds05027 0.362 1.024 1.063 1.125 0.697 1.069
ds05028 0.342 0.695 0.672 0.765 0.752 0.724
ds05029 0.319 1.050 0.739 1.144 0.843 1.403
ds05049 0.897 0.280 0.834 0.275 0.972 0.228
ds05050 0.893 0.405 0.828 0.465 0.978 1.021
ds05051 0.930 0.291 0.887 0.283 0.980 0.176
ds05052 0.893 0.271 0.828 0.263 0.966 0.301
ds06078 1.794 0.533 3.920 0.536 0.342 0.660
ds06079 2.037 0.560 4.302 0.564 0.337 0.685
ds06082 0.120 0.504 0.745 0.509 0.704 0.607
ds06084 0.207 0.548 0.771 0.531 0.603 0.286
do12027 0.891 0.318 0.811 0.384 0.934 0.373
do12028 0.895 0.341 0.815 0.385 0.927 0.367
do12029 0.904 0.376 0.832 0.458 0.939 0.450
do12030 0.904 0.351 0.838 0.432 0.951 0.437
do14074 0.425 0.483 0.109 0.477 0.605 0.360
do14075 0.424 0.502 0.138 0.510 0.603 0.570
do14076 0.596 0.528 0.373 0.533 0.779 0.580
do14077 0.566 0.468 0.323 0.461 0.674 0.334
do15089 0.600 0.534 0.360 0.530 0.785 0.410
do15090 0.490 0.552 0.227 0.554 0.668 0.639
dol5091 0.318 0.639 0.155 0.657 0.592 0.949
do15092 0.489 0.821 0.246 0.870 0.729 1.586
By above error analysis, LH95 model gives the least relative error in the concentration
data under high wave energy conditions for all three experiments. But, the error in slope of
profile of modified model is least in Vilano and Supertank data set and the diffusion model
is best in Duck94 data set.
Figure 5.15 show the correlation between the relative error of the diffusion model and the
input parameters on August. All of three models give a distinct correlation between the
representative wave velocity and the relative errors. In Figure 5.15, the model errors are
decreased with the increasing of the representative near bottom wave velocity on August
because the models give a better prediction under high wave energy in normal wave
condition. But, the reverse is true on September because of some breaking wave condition
during storm( Sep. 3rd4th, Oct. 12th16th) as explained in Figure 5.14. Figure 5.16 shows
the correlation between the relative errors and the ripple steepness. The errors are
proportional to the ripple steepness. When the ripple becomes steeper, the convection
process becomes more important In Figure 5.17, there is no distinct relationship between
model input parameters and A2.
+
+
+
4 +
+ +
0.5 1
frequency
current
c 1.5
4
0
C 1
0
S0.5
>
U0
C 1.
c
o
0
0
U
0
0.
o
C O
0)
4
+
+
+
+++
i n.+
W++4 +
S 20 40 E
nearbottom wave velocity
0 50 100 150 200
angle between wave and current
Figure 5.15 Correlation between the relative error of concentrate and the input
parameters for diffusion model.
August data files in DUCK94.
c 1.5
0
1
L
o 1
0
0
0.5
0
f 0
C 1.5
: .
c 1
C
o
L
0
0.5
0)
+
++
4 + +
+ +
+^
1
++ + +, + ++
+
} 
[
+
++ ++
++
++
0.02 0.04 0.06 0.08 0.1 0.12
ripple steepness
0.14 0.16 0.18
Figure 5.16 Correlation between the relative error of concentration
and the ripple steepness for diffusion model.
August data files in Duck94.
1.E
1.E
I
S1.4
C
w 1.2
0
a
0
0
o
t 1
e 0.8
0.6
.r
S0.6
0.4
0.2
1.5
0
o
0
L
0
? 0.5
.
U)
0.5 1
frequency
1
a
o 0.8
4
0
0 0.6
S0
0.4
)
0.2
0
+++
++
+ ++ + +
++ +
+
20 40
near bottom wave velocity
0
1
0
0
> 0.5
.
L
0 20 40 60 0 50 100 150 200
current angle between wave and current
Figure 5.17 Correlation between the slope of profile
and the input parameters for diffusion model.
August data files in Duck94.
+ + + +
+
++
++
#~T'
I
CHAPTER 6
CONCLUSIONS
The objective of the study in this thesis was to apply the pure diffusion, the LH95
model and the modified model to the field experiment data and to compare the measured
concentration data with the model results.
The timeaveraged vertical sediment distribution is the result of the balance between
the fall velocity of sediment and the upward sediment flux by turbulence. By Lee's
dissertation[1994], under low wave energy condition, the convection processes are
dominant, but under high wave energy condition, the diffusion processes are dominant.
The diffusion processes are very sensitive to fall velocity but the convection processes are
relatively less sensitive to fall velocity of particles
In this study, the model results give such a tendency and agree well with field data but
the diffusion model predicts pretty well the sediment concentration even under low wave
energy condition in Dcuk94 data set. If we review the poor accuracy of the pure diffusion
model applied to Vilano data files under low wave energy condition, the results can be a
little strange. However, it should be noted that the wave frequency is relatively low in
comparison of Vilano data set. With low frequency waves, the sands are less suspended.
In addition, since fall velocity classes of particles used in applying the model to Vilano
data files are measured by experiment and settling velocities in Duck94 data files are
underestimated in comparison of those in Vilano in calculating them by model, the results
are reasonable.
LH95 model using the timeinvariant eddy viscosity model developed by
Wikramanayake gave a very good prediction in diverse flow conditions. But it's also not
sensitive to wave frequency. Actually, a vertical distribution of sediment concentration
are dependent on a falling velocity but also on a wave frequency. To compensate this
weak point, a modified convectiondiffusion model was developed with a sediment
diffusivity model which combined Nielsen' s and Wikramanayake's sediment diffusivity
model. This model gave a very good prediction under the low frequency and low wave
energy condition, but it's not good enough to be compared with LH95 model. However,
we cannot properly evaluate the modified model only with this visible results because the
bed roughness in the modified sediment diffusivity model using the predicted ripple
geometry, might be underestimated in comparison with real bed roughness. Originally, a
measured bed geometry to calculate a bed roughness should be used in this model.
On the other hand, LH95 model predicted well the suspended sediment concentration
under normal wave condition, but it underpredicted the concentration under breaking
wave condition because of different mechanism of sediment suspension. Here are the
summary of conclusions.
1. Overall, LH95 combined model gives the best prediction of vertical distribution of
suspended sediment concentration.
2. Even though the modified model tends to underpredict the suspended sediment
concentration, it is best to predict the concentration under the low wave
frequency(0.50.6 rad/sec) and low wave energy(vr < 30 cm/sec).
3. All of three models underpredict the suspended concentration under the high
frequency( coo > 1.3 rad/sec) and low wave energy. In other word, these model are not
sensitive to wave frequency.
4. All of three models underpredict the concentration under breaking wave condition
because the mechanism of sediment entrainment is different.
There are also some uncertainties in evaluation of the velocity profiles in turbulent
boundary layer to determine a friction velocity. Madsen and Wikramanayke[1991]'s
hydrodynamic model may not be suitable for the rippled bed. The measurement of
velocity profile in field experiment is needed for comparison with model.
Finally, the most important factor in determining the model result, eddy viscosity
model is also needed to be improved. Use of timevariant eddy viscosity model may give
a better prediction of the diffusion or the combined model.
LIST OF REFERENCES
Dean, R. G. & Darlrymple, R. A., 1993. Water wave mechanics for engineers and scientists,
Advanced series on ocean engineering, Vol 4, River edge, NJ, pp. 233262.
Dean, R. G., 1989. Measuring longshore transport with traps, in Nearshore Sediment
Transport, Plenum Press, New York, NY., pp. 313336.
Grant, W. D. & Madsen, O.S., 1979. Combined wave and current interaction with rough
bottom, J. Geophys. Res., Vol. 84, No. C4, pp. 17971808.
Horikawa, K., 1991. Coastal engineering, University of Tokyo Press, Tokyo, pp. 274290.
Inman, D. L., and Bagnold, R. A., 1963. Littoral processes, in The Sea: Ideas and
Observations, Vol 3, Interscience, New York, NY, pp. 529533.
Kaczmarek, L. M. & Ostrowski, R., 1992. Modeling of wavecurrent boundary layer in the
coastal zone, Coastal Engineering 1992, Vol 9, pp. 350363.
Lee, T., 1994. Acoustic measurement and modeling of the vertical distribution of suspended
sediment driven by waves and currents, Ph.D. dissertation, University of Florida, Gainesville.
Lin, L. & Wang, H., 1996. Data analysis techniques, University of Florida, Gainesville,
Unpublished.
Madsen, O. S. & Wikramanayake, P. N., 1991. Simple model for turbulent wave current
bottom boundary layer flow, Contract Rep. DRP911, U.S. Army Corps of Engineers,
Coastal Engineering Research Center, Vicksburg, MS.
Marusin, K. V., 1995. Determination of concentration and size of suspended sediments in
the coastal zone using acoustic backscatter measurements, M.S. thesis, University of Florida,
Gainesville.
Nielsen, P., 1984. Field measurements of timeaveraged suspended sediment concentration
under waves, Coastal Engineering, Vol 8, pp.5172.
Nielsen, P., 1992. Combined convectiondiffusion modeling of sediment entrainment,
Coastal Engineering, Vol 9, pp 32023215.
75
76
Nielsen, P., 1992. Coastal bottom boundary layer and sediment transport, Advanced series
on ocean engineering, Vol 4, River edge, NJ, pp.233262.
Nishi, R., 1992. Grainsize distribution of suspended sediments, Coastal Engineering, pp.
22932306.
Ono, M., 1994. Suspended sediment caused by waves and currents, Coastal Engineering,
pp.2476 2487.
Thostesen, E. D., 1995. Nearbed sediment suspension in the offshore zone of a large scale
wave tank, M. S. Thesis, University of Florida, Gainesville.
Wikramanayake, P. N., 1993. Velocity profiles and suspended sediment transport in wave
current flows, Ph. D. dissertation, Massachusetts Institute of Technology.
APPENDIX
FIGURES OF VERTICAL DISTRIBUTION OF THE SUSPENDED SEDIMENT
CONCENTRATION PROFILES DURING DUCK94 EXPERIMENT
3 da22089 8/21/16:44:34
o3.n .. I.
102 100
Concentration(g/)
5 da22091 8/21/17:16:56
I
4 da22090 8/21/17:0:45
102 100
Concentration(g/l)
6 da22092 8/21/17:33:7
I
4 2 0 2 4 2 0 2
10 10 10 102 10 10 100 10
Concentration(g/l) Concentration(g/I)
.u
E
(D
0a,
n
0
a,
2

0
0
: +
* +
: +
I+
* +
S\+
*\ +
: +
..+
7 da22093 8/21/17:49:18
102 10 102
Concentration(g/I)
9 da23095 8/21/18:21:40
I
+
\ +
+
+
+
+
+
+
+
:+
+
+
*, +
*. +
*+
10"2 10
Concentration(g/1)
8 da22094 8/21/18:5:29
S 102 100 102
Concentration(g/I)
10 da23096 8/21/18:37:51
 4 2 0 2
104 102 10 10
Concentration(g/l)
20
E
.c
E10
0
C,
0
o
Q .
11 da23097 8/21/18:54:2
10.2 100
Concentration(gI)
120
E
E10
*o
4.
C
5,
Q .
12 da23098 8/21/19:10:13
+
t +
\ +
: +
+
+
102 100
Concentration(g/I)
13 da23099 8/21/19:26:24 14 da23100 8/21/19:42:35
rIn i
104 102 100 1 10104 102 100
Concentration(g/) Concentration(g/I)
.20
E
E10
A,
.0
r
E10
on
: +
+
+
+
+
: +
*+
15 da23101 8/22/10:5:47
16 da23102 8/22/10:21:58
102 10 10 14 102 10
Concentration(g/) Concentration(g/I)
17 da23103 8/22/10:38:9 18 da23104 8/22/10:54:20
14 12 0 2 4 '2 0 2
104 10 100 2 10 10 10 10
Concentration(g/l) Concentration(g/l)
E
0
co
..
Q)
r"
0
a,
0
r
2
20 da23106 8/22/11:26:42
102 100 102 104 102 100
Concentration(g/) Concentration(g/)
21 da23107 8/22/11:42:53 22 da23108 8/22/11:59:4
104 10.2 10o 2 2 10*4 10.2 10
Concentration(g/) Concentration(g/l)
19 da23105 8/22/11:10:31
23 da23109 8/22/12:15:15
102 10 102 104 102 100
Concentration(g/I) Concentration(g/)
25 da23111 8/22/13:7:24 26 da23112 8/22/13:23:35
10"4 102 100 102 104 102 100
Concentration(g/) Concentration(gl)
24 da23110 8/22/12:31:26
27 da24113 8/22/15:30:25
28 da24114 8/22/16:2:12
4 102 100 102 04 10 102 10
Concentration(g/) Concentration(g/1)
29 da24115 8/22/16:33:59 30 da24116 8/22/17:5:46
4 2 0 2 4 2 0 2
10 10 10 10 102 1 12 10 10
Concentration(g/) Concentration(g/)
E
o
E 10
..u
0
Lu
4
0
4
31 da24117 8/23/11:2:14
32 da24118 8/23/11:18:4
E E +
3 + +
.0 + 0 +
O 0 *+
0 
Q 4 2 0 2 Q 4 2 0
10 10 10 10 10 10 10
Concentration(g/) Concentration(g/)
33 da24119 8/23/11:33:54 34 da25120 8/23/11:49:44
10 10 10 102 10 10 10
Concentration(gA) Concentration(gA)
33 da24119 8/23/11:33:54 34 da25120 8/23/11:49:44
on,  on,. I
102 100 102
Concentration(g/1)
104 10 100 10
Concentration(g/)
,
E
0
C
0
4
4'
0),
Q '
5+
5+
5+
5+
+
+
+
+
36 da25122 8/23/12:21:24
10.2 100 102
Concentration(g/1)
10'2 100
Concentration(g/l)
37 da25123 8/23/12:37:14 38 da25124 8/23/12:53:4
^20 % 20 
E + E +
+ +
S+ 0 +
0 !+ ( *+
it + o +
E 10 E10
0.\ o
0 0
V D
o 0
4 2 40
10 102 100 10 10 102 100
Concentration(g/I) Concentration(g/I)
35 da25121 8/23/12:5:34