• TABLE OF CONTENTS
HIDE
 Cover
 Title Page
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Key to symbols
 Abstract
 1. Introduction
 2. Field experiment
 3. Hydrodynamic model
 4. The suspended sediment distribution...
 5. The comparison of measured data...
 6. Conclusions
 List of References
 Appendix






Group Title: UFLCOEL-96008
Title: Comparison of measurements and models of the vertical distribution of suspended sediment under waves and currents
CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00084990/00001
 Material Information
Title: Comparison of measurements and models of the vertical distribution of suspended sediment under waves and currents
Series Title: UFLCOEL-96008
Physical Description: xii, 141 leaves : ill. ; 28 cm.
Language: English
Creator: Lee, Cheegwan, 1967-
University of Florida -- Coastal and Oceanographic Engineering Dept
Publisher: Coastal & Oceanographic Engineering Dept., University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1996
 Subjects
Subject: Suspended sediments -- Mathematical models   ( lcsh )
Sediment transport -- Mathematical models   ( lcsh )
Ocean waves -- Mathematical models   ( lcsh )
Ocean waves -- Simulation methods   ( lcsh )
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF   ( lcsh )
Coastal and Oceanographic Engineering thesis, M.S   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (M.S.)--University of Florida, 1996.
Bibliography: Includes bibliographical references (leaves 75-76).
Statement of Responsibility: by Cheegwan Lee.
 Record Information
Bibliographic ID: UF00084990
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 35915545

Table of Contents
    Cover
        Cover
    Title Page
        Page i
    Acknowledgement
        Page ii
    Table of Contents
        Page iii
        Page iv
    List of Tables
        Page v
    List of Figures
        Page vi
        Page vii
    Key to symbols
        Page viii
        Page ix
        Page x
    Abstract
        Page xi
        Page xii
    1. Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
    2. Field experiment
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
    3. Hydrodynamic model
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
    4. The suspended sediment distribution model
        Page 24a
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
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        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
    5. The comparison of measured data with models
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
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        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
    6. Conclusions
        Page 72
        Page 73
        Page 74
    List of References
        Page 75
        Page 76
    Appendix
        Page 77
        Page 78
        Page 79
        Page 80
        Page 81
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Full Text



UFL/COEL-96/008


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 Time-averaged 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

5.3-5 :Vertical profiles of sediment concentration of Supertank experiment............1-53

5.6-11 :Vertical profiles of sediment concentration of Duck94 experiment
on the rippled bed....................................... ................. .............................56-61

vi








5.12-14:Vertical profiles of sediment concentration of Duck94 experiment
under sheet flow condition.............................. ...............................................62-64

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 Semi-excursion 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 Co-spectra

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 wave-current 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 wave-current velocity uJucw

Es Sediment eddy diffusivity








w Angle between the primary wave direction and the current

K Von-karman constant(=0.4)

x Ripple length

r1 Ripple height

Ut Eddy viscosity

02.5 Grain roughness shield parameter

p Water density

( Non-dimensional vertical coordinate

C0 Non-dimensional bottom roughness

W Wave frequency in rad/sec

Wo Mean-zero 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

convection-diffusion 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 cross-shore 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 cross-shore

sediment transport mechanism is still not understood as well as the long shore one. One of

the approaches to predict the cross-shore 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 near-bottom 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 wave-current condition uses the time-invariant 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

time-averaged 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 time-invariant 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 time-invariant 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 176-acre 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 cross-shore

distance from the beach. Because the instrument was deployed outside of the breaking

zone, most of the waves were under non-breaking 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 23-31 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 non-breaking 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 time-invariant eddy viscosity

model are also introduced briefly.



3.2 Determination of hydrodynamic input parameters for model

3.2.1 Current

Fluid velocity in x-y direction is measured by EMCM. The current velocity can be

calculated by time-averaging 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 cross-shore(+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

cross-shore(+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 co-spectra 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 non-narrow band

or double-peak spectrum. In this paper, the mean zero-crossing 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

Time-invariant 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 non-dimensional 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"w-u-) 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 z--oo (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 V-C4ie -V

Cl(ker2- +ikei2/-a)+C2(ber2/ +ibei2-a) = 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


Z-c
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, Time-averaging 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 a-uz < -
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,
S4-1 [--] 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 non-negative 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)




Time-averaging 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 semi-excursion


4.2.4 Combined model

Lee and Hanes[1995] suggested the combined convection-diffusion 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 a-F(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 time-invariant eddy

viscosity model is not very sensitive to the wave frequency. The other problem is that the

time-invariant eddy viscosity model used the maximum shear velocity as a function of eddy

viscosity. According to the experiments of Bosman[1982] and Ribberink & Al-Salem[1989],

time-averaged 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: semi-excursion 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 (s-1)gd5o
2.5 = exp[5.213(2.5d50/Ab)0194-5.977] (6.26)



By substituting (6.25) into (6.19) and solving the 1st-order 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 vas-1 dz+cl] (4.25b)
f F(r)
Zr



a8
ku- -E F(z)
c3=p ce [ f e v-v 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 10-5 100
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 +
10-5 10 10-5 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 time-averaged 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


10-4 10-2 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 10-2 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 time-invariant 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
10-5 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 .
0-5 10 105 10-5 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-




0-5 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 3rd-September 5th and October 12th-

October 16th.

In Figure 5.6-5.11, 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(0.5-0.8 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 5.12-5.14, 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 non-breaking 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. 3-4 Oct. 12-16). In Marusin's thesis[1995],

TFACP transducers(0.97MHz and 2.35MHz) show consistent results under non-breaking

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 10-4 102 10
Concentration(g/) Concentration(g/I)
6 da22092 8/21/17:33:7 9 da23095 8/21/18:21:40


10-4 10.2 10o 102 10-4 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


10-2 100
Concentration(g/I)
45 da25131 8/24/9:47:37


10-2 100
Concentration(g/l)
46 da25132 8/24/10:3:48




A+-


10-4 10.2 100 102 10-4 102 100
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


10-2 100
Concentration(g/l)


104 10-2 100 102
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


10-2 100
Concentration(g/)
81 ds06084 9/6/17:0:0
1


10-4 10-2 10 102 10-4 102 100
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| --n-therippled- b2ed-- t-T ---
S+ +
S:i+ +
+ +
+ +




+ +


0 0





10-4 10,2 0 10 2 i-4 10-2 100 102
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


10-2 100
Concentration(g/)
76 do14076 10/14/21:0:0



+


10-2 100
Concentration(g/)


10-2 100
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


10-2 100
Concentration(g/I)
91 do15091 10/15/13:0:0



.


10-2 100
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

+
!+
+ +
+ +
+
+
+


10-4 10.2 100 10 10-4 10-2 100
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. 3rd-4th, Oct. 12th-16th) 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 time-averaged 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 time-invariant 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 convection-diffusion 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(0.5-0.6 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 time-variant 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. 233-262.

Dean, R. G., 1989. Measuring longshore transport with traps, in Nearshore Sediment
Transport, Plenum Press, New York, NY., pp. 313-336.

Grant, W. D. & Madsen, O.S., 1979. Combined wave and current interaction with rough
bottom, J. Geophys. Res., Vol. 84, No. C4, pp. 1797-1808.

Horikawa, K., 1991. Coastal engineering, University of Tokyo Press, Tokyo, pp. 274-290.

Inman, D. L., and Bagnold, R. A., 1963. Littoral processes, in The Sea: Ideas and
Observations, Vol 3, Interscience, New York, NY, pp. 529-533.

Kaczmarek, L. M. & Ostrowski, R., 1992. Modeling of wave-current boundary layer in the
coastal zone, Coastal Engineering 1992, Vol 9, pp. 350-363.

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. DRP-91-1, 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 time-averaged suspended sediment concentration
under waves, Coastal Engineering, Vol 8, pp.51-72.

Nielsen, P., 1992. Combined convection-diffusion modeling of sediment entrainment,
Coastal Engineering, Vol 9, pp 3202-3215.

75








76


Nielsen, P., 1992. Coastal bottom boundary layer and sediment transport, Advanced series
on ocean engineering, Vol 4, River edge, NJ, pp.233-262.

Nishi, R., 1992. Grain-size distribution of suspended sediments, Coastal Engineering, pp.
2293-2306.

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.


10-2 100
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+
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S\+
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: +
..+










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



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E10





on


: +

+
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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
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Q)
r"

0

a,
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r-

2










20 da23106 8/22/11:26:42


10-2 100 102 10-4 10-2 100
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


10-2 10 102 10-4 102 100
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+
+
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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




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