Citation |

- 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
- Creator:
- Lee, Cheegwan, 1967-
University of Florida -- Coastal and Oceanographic Engineering Dept - Place of Publication:
- Gainesville Fla
- Publisher:
- Coastal & Oceanographic Engineering Dept., University of Florida
- Publication Date:
- 1996
- Language:
- English
- Physical Description:
- xii, 141 leaves : ill. ; 28 cm.
## Subjects- Subjects / Keywords:
- 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:
- 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- Source Institution:
- University of Florida
- Holding Location:
- University of Florida
- Rights Management:
- All applicable rights reserved by the source institution and holding location.
- Resource Identifier:
- 35915545 ( OCLC )
## UFDC Membership |

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. Hlanes, 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 ACKNOW LEDGMENTS ................................................ ii LIST OF TABLES ....................................................... v LIST OF FIGURES ..................................................... vi KEY TO SYM BOLS .................................................. viii A B STRA CT ........................................................... xi CHAPTERS I INTRODUCTION ...................................................... 1 2 FIELD EXPERIM ENT .................................................. 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 W ave Direction and Height ..................................... 9 2.3.2 W ave Period and Current ..................................... 11 2.4 Characteristics of Bed M aterials ................................... 13 3 HYDRODYNAMIC MODEL ................................. ......... 14 3.1 Introduction .................................................. 14 3.2 Determination of Hydrodynamic Input Parameters .................... 14 3.2. 1 C urrent ................................................... 14 3.2.2 Near Bottom W ave Velocity .................................. 15 3.3 Primary W ave Direction ........................................ 16 3.4 Representation of Irregular W aves ................................. 18 3.5 Hydrodynamic M odel .......................................... 20 3.5.1 Eddy Viscosity M odel ....................................... 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 Model ............................................. 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 Instrument 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 ......... 51-53 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/ku,c Ab Semi-excursion of water particle C Concentration of suspended sediment Ci Concentration at level I 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 h, 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 q 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 SUU Power spectrum of wave enhanced fluid velocity in primary wave direction near the sea bed u,v Fluid velocity(horizontal component) uc,v Current velocity(horizontal component) UVw Wave velocity(horizontal component) u.C Current friction velocity uw 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) 8 Boundary layer thickness scale, ku*cw/co E Ratio of current friction velocity to wave-current velocity uJu*cw Es Sediment eddy diffusivity kcw Angle between the primary wave direction and the current K Von-karman constant(=0.4) x Ripple length T1 Ripple height 11t Eddy viscosity 02.5 Grain roughness shield parameter p Water density Non-dimensional vertical coordinate C0 Non-dimensional bottom roughness WWave 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 hydrodynamiic 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 crossshore 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 [ 19 81] 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 reseachers 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) SI I I I 2 1 - 20 21 22 23 24 25 August 26 27 28 29 2 - .i .," 2- October Figure 2.3 Waves during Duck94 experiment. 90 4 180 0 27 Figure 2.4 Wave direction and height in polar coordinate system * :August 20th August 28th o :Septemnber 1 st 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 o f 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. 1 5 1 1 1 1 1 0 IDi Cl) 20 21 22 23 24 25 26 27 28 2 August U 1 2 3 4 5 6 7 8 9 10 September 15 10 .... .... 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 * *.* -- 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 [Ii I I I I i II I I I I I 2 3 4 5 6 7 8 9 11 September IIII I I1 10 11 12 13 October 14 15 16 17 Figure 2.6 The direction and magnitude of current during Duck94 experiment ~1 -I 20 I I I I I I I A / ii itiiiij I I I 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. U c(Ze) =u(ze~t) -uw(Z,,) vc(z e) =v(ze t) -Vw(Z J)(31 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 Frequenc domain uw(ze ,t) Uw(ze,) FFT U (0,6)= U(zes,). cosh(kz,) IFFT u,(0,t) -< U0,) U .---- EMCM ze Z=o0 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 0 (DP -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 vw, respectively. By a transformation of coordinate, the components of wave velocities in primary direction are ] [ cosOP sinO Uw vr = -sin0p cos, v up I = p (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. I BA RP () 6 =tan- 7k P ()k(W) R(P ) (3.3) B Rpu() and RP,(O) are co-spectra which are obtained from the pressure and u, v data. kP and kv are also defined as following ones. Yk(o) y0cosh(kh2) wcosh(khl) cosh(kh) cosh(kh) (3.4) h, 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 frequncy 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 6) f S u(6))w2d6) f J S .,( 6 ) d w ( 3 .5 ) where Su (w) is the power spectrum of the near bottom wave velocity. Wave energy spectrum x 104 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 - 0.5 0 . I 20 The representative magnitude of wave velocity at bottom in primary direction, vr are defined by N Vr= Nn=1 p,n 2 (3.6) upn 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*,Cw z z _s a6 Ut = ku*wa8 a s z a/e (3.7) ku*cz ab/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*c / U*cw 6 =ku*cw/ 21 where w 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.uz =ku.0., oc 6 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. 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=ab/e. The solutions are us 9 E Iln[ S] k go ,q< a u = E uc[-- -1 +ln[-] k a o uc[ln[ ]+1 +e[ln[-] -1]] k a/ leo ,a < 9 < a/e ,a/e < q where g is the non-dimensional vertical distance denoted by z g=- The governing equation of wave velocity in turbulent boundary layer is a(Uw-U) [v a(U at o z -u (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 UwU =Re(ude it ) lujI (3.12) Substitution of (3.12) into (3.11) gives a new governing equation. d dud -[V- ]-iOUd=0 (3.13) dz dz The boundary conditions for (3.13) are ud= -1 at z=z0 u d-- O at z-_oo (3.14) By substituting (3.5) into equation (3.13), The solution can be obtained as following results. Cl(ker2 q+ikei2v) +C2(ber2 v +ibei2i/ ) o <:a d= C3exp( )+C4exp(- -) g CF(aq E (3.15) Cs(ker2 q +ikei2 ) +C6(ber2 +ibei2 ) a E E E C E 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(ker2o +ikei2o) +C2(ber2o /+ibei2qo) = -1 C6=0 Cl(ker'2 / +ikei 2 / )+C2(ber 2Vi- +ibei 2v/-) = C3 /e V -C4 le -V C-(ker2 +ikei2/-)+C2(ber2 +ibei2/-) = C3e V"+C4e -C3e V'/-+C4e S=C,(ker2 i+ikei2 a) E E C3 Ve 07E +C4 V/e "VE =C5(ker2 +ikei /2 F) (3.16) E 6 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 (0.0 18AbrZ -0.5 S= 0.0007AbZ -1.23 1 (0.15Z -0.009 x 0.0105Z -0.65 ,0.00016 where Tj and X are a ripple height and length, respectively, and Abr is vcO0. Nondimensional parameter 0' is defined by Z S S. is defined by S, 4d (s-1)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 (q.) or diffusive (qd) or usually a combination of these two modes. The governing equation (4.1) can be rewritten ac ac aq d aqC at -z az az (4.2) Figure 4.1 gives a description of each flux. wo(c+-a) qd+ -ddz a + qcdz az az -caz Jt t ac/at 4t t WoC q d 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 0 az az (4.3) The sediment flux by diffusion is given by ac qd = -Esazd s (4.4) By substituting equation (4.4) into equation (4.3), we can get ac w ac a ac) t az 8z a8z (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 sdz (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 followin S--__ c for z < a8 dz kucwz (4.7a) dc Wo X6 -- c for a&z < dz ku ,wa8 E (4.7b) dc WO a8 dc c for < z dz kucz E (4.7c) (4.7c) 27 The above equation is a first order ordinary differential equation. The solutions are the following ones respectively. Cq C5=[ ], r-q"I (4.8a) Cr qr C(q) a -a =[-] e Cc q -- (4.8b) Cr qre E a c(q) a -a eE a. c- [-] C -4 (4.8c) Cr 4re a E 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) wC (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. ac 8c 8PF -Wo-+at 0oz z (4.10) Time-averaging and integrating the above equation leads to the final convective equation under equilibrium conditions. woc(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 kbAb (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 qu(z,t) = -E _c + P(t--L)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 + Es--S F(z)=0 dz where the boundary condition is - dc c=O,-=0,F(z)=O ,when zdz S=O ,F(z)=F(z) ,when z=zr wc p_ Wor F(z) d + wo- crwo F(z) dz F(zc) 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 CrWo F(z) dz kucw ku Z F(Zr) dz ku c,, ku,,cz F(zr) , za6 (4.18a) dc W CrWo F(z) a __+ c a dz ku,,wa6 ku ,cwa8 F(zr) E dc Wo cWo F(z) a8 +-c- -- The solutions of above differential equations are c~z2 Z =() z -a[a za-1F(z)dz+cl]l C- P a z a c(z) -e ab [ e F(z)dz+c2] r a S a z a c(Z)z [ zE F(z)dz+c3] Cr a6 C (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=a/E, the integration constants can be found. cl =Zra (4.20a) c2=(-S )-'[a f za-1 F(z) dZ+Zra] e f F(zd) (4.20b) Zr e a E a 6c3 =(a-) [ e 7ZF(z)dz] +c2 ab8 f 8 (4.20c) 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=0.5,Z1 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. p- a8a6 E = p a bt < z < --C = E (4.22) p+q - p = V(2zZ12) +(ku,,c a)2+2(2oz12)(ku cab)cos"w q = kuc(--) 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. 2 kb = 811+502.5d50 1 f2.55p2 02.5 2 2 (s-1)gd5o f2.5 = 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. Z - zva 8-1c F(z) dz+cl] C(Z) =z fz F(z) dz+c (4.23a) Z c(z)=e -v[ e vZcyV F(z) dz+c2] (4.23b) S F(Zr) a8r -w. z w._.-- 0 ku 6 kU.c Wo F(z) dz+c c(z)=(p+kusc(Z--)) c[ f(p+ku c(z-- )) C dz+ E _6 p +kum(z i a') F(z) (4.23c) E w Where v=- o P By applying and matching at the boundaries, we can get the integration constants which result into cl =z vas (4.24a) a8 c2=e V()-vaz vas-1 F) dz+cl] (4.25b) f F(Zr) c3=p ku.ce [ fevZ c-v dz+c2] (4.25c) 8 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 4.1 a -d, TESTO9, TEST11, TEST13 and TEST 15 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(do =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 In meters for model test. File W up U d5o File 6) Up U d50 rad/s cm/s cm/s mm rad/s cm/s cm/s mm TESTO 1.0 30 10 0.1 TEST09 1.0 30 10 0.2 TEST02 1.0 60 10 0.1 TESTIO 1.0 60 10 0.2 TEST03 1.0 30 40 0.1 TEST 11 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 TESTO2 concentration(g/1) concentration(g/A) TESTO3 TESTO4 1+ 1 + 1 + + !+ + 1 + \. + 100 concentration(g/I) concentration(g/) Figure 4.2 Test of models 30 E -0 0) 20 E 0 01 ol10 c 10 .5 TEST05 TESTO6 concentration(g/) concentration(g/) TESTO7 TESTO8 10- 100 10 100 concentration(g/I) concentration(g/I) Figure 4.3 Test of models E V ")20 E 0 co ,= o0 TESTO9 TEST10 30 30 020 D20 E E + 20 0 + 010. 010 + c) *+ c \ + olO1- ol1 + (U + E 1+ E 1+ 0 AI 01I 10o 100 10- 100 concentration(g/1) concentration(g/1) TEST11 TEST12 P 110 30 ,30 , 0P 1~+ "+ + + i+ -a 20 + 120 1020 1 E E + 0 i+ 0 + 0+ 01 + o. + + A + C + * i + 0 1 0 105 100 105 100 concentration(g/) concentration(g/1) Figure 4.4 Test of models TEST13 TEST14 concentration(g/) concentration(g/l) TEST15 E 0 20 E 0 ' 00 CO S 10 5 concentration(g/I) TEST16 + 1+ :+ + + .+ 1 100 concentration(g/I) Figure 4.5 Test of models 020 M , E 0 o010 "C P ge 401 missing from M M 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 5.1 Model 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 )C, :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 ex eriment 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 Run8lM 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 kw 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 Il/,X uC Uw 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 rj/X uC U*cw Cr cm cm/sec cm/sec mg/1 Runl8B 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 I q/X uC uYev 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 E 2 20 a) C Mc cci 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 10.2 10 1 sediment concentration(g/I) a0508m50 An." sediment concentration(g/I) a0508m52 An .0 E 2 20 01) ._ 104 10.2 10 10 10" 10-2 100 102 sediment concentration(g/I) sediment concentration(g/I) Figure 5.2 Vertical profiles of sediment concentration of Vilano data files under high wave energy condition - :measured + :LH95 model o:modified -+- :diffusion E 220 C An 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 catagorized 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 tle 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 E E EE ++ c + c + .o. 0 0 C 8+ 5 5 0 5 10 10 10 105 10 10 concentration(mg/) concentration(mg/1) RUN54 RUN81 20 20 o * Cd + 0 0 -5 0 5 -105 0 10 10 5 105 10 10 concentration(mg/1) concentration(mg/1) Figure 5.3 Vertical sediment concentration profiles of'Supertank data files under monochromatic wave condition. :measured + :LH95 model :modified -+-:diffusion 0 0 . - :maueE L9 oe :mdfid -+Odifon RUN18 RUN47 20 20 E + 0)0 E E '4- 4010 010 C C V *.+ -5 0 5 -5 0 5 10 10 10 10 10 10 concentration(mg/) concentration(mg/1) RUN52 RUN55 20 20 + .o. .o. -1-: S10 + o10 + o E 0) 0 E .+ E+ 10 10 1 1 10s 4- A4 concentration(mg/I) concentration(mg/1) Figure 5.4 Vertical sediment concentration profiles of Supertank data files under broad band random wave condition. - :measured + : LH95 model S:modified -+- : diffusion 1" 10 10 10 10 10 concentration(mg/1) concentration(mg/) Figure 5.4 Vertical sediment concentration profiles of Supertank data files under broad band random wave condition. - :measured + LH95 model . :modified -+- diffusion RUN26 RUN59 20 20 o E + *. ++ 0 E 0 10- 10 0 0 - 0 5 5 0 5 C r "o + . + 10 10 10 10 10 10 concentration(mg/1) concentration(mg/) RUN73 RUN74 2- :0 mse +L 20 0. i + f 010 o10 + 4C + 0 C 5 5 0 0 1 0 10 10. 10 1010 10 10 concentration(mg/I) concentration(mgA) 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 12thOctober 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(O.5-0.8 rad/sec) and low wave energy (vr <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( vr<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(O.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 2 0 2 --4 .20 10 10 10 104 10 10 Concentration(g/) Concentration(g/I) 6 da22092 8/21/17:33: 7 9 da23095 8/21/18:21:40 -4 -2 0 2 "-4 -2 0 10- 102 10 10 10 10.2 10 Concentration(g/) Concentration(g/I) 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 - 2 0 2 --4 -2 0 10 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 * .20I 10-4 10 100 10 104 10-2 100 1 Concentration(g/) Concentration(g/I) Figure 5.7 Vertical sediment concentration profiles of Duck94 data files on the rippled bed - :measured + :LH95 model S: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 S 10-2 100 Concentration(g/I) 46 da25132 8/24/10: 3:48 A+ 104 102 100 102 104 102 100 Concentration(g/I) Concentration(g/) 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: 0 102 100 Concentration(g/1) 27 ds05028 9/2/13: 0: 0 10-2 100 Concentration(g/I) 104 102 100 10 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 20 I E V C) E 10 0 4 C 102 100 Concentration(g/I) 79 ds06082 9/6/15: 0: 0 1 76 ds06079 9/6/12: 0: 0 10-2 100 Concentration(g/I) 81 ds06084 9/6/17: 0: 0 1 10-4 10-2 10 102 10-4 10.2 100 Concentration(g/I) Concentration(g/I) Figure 5.10 Vertical sediment concentration profiles of Duck94 data files on the rippled bed - :measured + :LH95 model . :modified -+- :diffusion 1+ 27 do12027 10/12/0:0:0 28 do12028 10/12/2:0:0 ...20 l 20 :+ E + * 0 + + D 2+ fl+ + +. 10 1+ E10 + 2 ..0 :+ + + 3 o :+ + * + + + 0 + + + + 00 . 10-4, 2 100 2 104 102 100 102 Concentration(g/I) Concentration(g/) 29 do12029 10/12/4:0:0 30 do12030 10/12/6:0:0 120 I20 -31 + E 101+ E + : + + + + + + + 1- + E1 + + 0 + + + + ++ 2 +0 S 10-4 10 100 10 10-4 10-2 100 10 Concentration(g/1) Concentration(g/) Figure 5.11 Vertical sediment concentration profiles of Duck94 data files on the rippled bed - :measured + :LH95 model . :modified -+- :diffusion 74 do14074 10/14/19: 0: 0 10-2 100 Concentration(g/) 76 do14076 10/14/21: 0: 0 + 1+ 1+ 1+ \+ i+ i+ 10-2 100 Concentration(g/) 102 100 Concentration(g/1) 77 do14077 10/14/22: 0: 0 - -4 -2 0 10 10 10 Concentration(g/I) 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 S 102 100 Concentration(g/) 92 do15092 10/15/14: 0: 0 .,I ! + -4 -2 0 2 -4 -2 0 10 10 10 10 10 10 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 S:modified -+- :diffusion 90 do15090 10/15/12: 0: 0 48 ds05049 9/3/11: 0: 0 10 100 Concentration(g/I) 50 ds05051 9/3/13:0:0 10. 100 Concentration(g/I) 51 ds05052 9/3/14: 0: 0 I+ !+ + + + + + + + 10-4 102 100 102 10-4 10-2 100 Concentration(g/A) Concentration(g/1) Figure 5.14 Vertical sediment concentration profiles of Duck94 data files under sheet flow condition - :measured + :LH95 model S: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. (5.1 a) n (logCi) a(logCi*) 2' 0.5 i= i az measured aZ model A2= 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 A1 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 Runl8 B 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 Run81 M 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 ds05O5O 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 ds05O52 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 do15091 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 0 C i 1 0 0 >) 0 0.5 2ol C1J c 0 0 L 0 b 0.1 CO 0) 4- + + + ++ -++ + ) 20 40 E nearbottomrn wave velocity 0 50 100 150 200 angle between wave and current Figure 5.15 Correlation between the relative error of concentrati and the input parameters for diffusion model. August data files in DUCK94. S1.5 0 1 C L. o 1 0 0.5 ) U) c 1.5 0 C: C 0 L 0 0.5 ca O) ._> + + 4 + + + +- + +++ IlI IIII + + S+ + + + + + + + ++ + + ++ III 1 I 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. 1.8 1.6E 0 1.4 w 1.2 0 a o t S0.8 0 > 0.6 0).8 CO LO0.6 0.4 0.2 1.5 CL 0 0 L 0 ? 0.5 (D -. 0.5 1 frequency 1 CL '0 0.8 a 0.8 0 0 0.6 UD "E 0 0.2 0 +++ ++ ++ ++ + + ++ + 20 40 near bottom wave velocity 0 0 0 > 0.5 .-. 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. +. + + F + +++ ++ 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(O.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, 0. 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 wavecurrent 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 9 . . 10-2 100 Concentration(g/) 5 da22091 8/21/17:16:56 I 4 da22090 8/21/17: 0:45 102 100 Concentration(g/I) 6 da22092 8/21/17:33:7 I -4 -2 0 2 "-4 -2 0 2 10 10-2 10 10 104 10 10 10 Concentration(g/) Concentration(g/I) L0 E (D E 0 0 a .c - cn a 0 : + * + : + : + : + + \ + : + :.+ 7 da22093 8/21/17:49:18 10 100 102 Concentration(g/) 9 da23095 8/21/18:21:40 I , + : + -+ : + * + -+ + + + :+ * + + *, + *. + *+ -2 0 10 100 Concentration(g/1) 8 da22094 8/21/18:5:29 S 102 100 10 Concentration(g/I) 10 da23096 8/21/18:37:51 - -4 -2 0 2 10 10 10 10 Concentration(g/) -20 E .c E10 0 0 4w .0) *0 UJ 11 da23097 8/21/18:54:2 102 100 Concentration(g/I) 120 E E0 0 0 S0 C , 0 12 da23098 8/21/19:10:13 " + : + \ + : + + :+ : + + \* + :. + **+ '* + ** + + 10-2 100 Concentration(g/I) 13 da23099 8/21/19:26:24 14 da23100 8/21/19:42:35 n f / I 10 10.2 100 102 04 102 100 Concentration(g/) Concentration(g/I) -20 E .C E 1 0 .4 0A c, on : + + :4 + , + : + * + **+ . + *\\+ .\+ 15 da23101 8/22/10: 5:47 16 da23102 8/22/10:21:58 10 10 10 10 102 10 Concentration(g/I) 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 10 10 10 10 10 10 10 10 Concentration(g/A) Concentration(g/A) E .C *0 ElO 0 c a, 0 C 4 C,, 20 da23106 8/22/11:26:42 102 100 10 104 10-2 100 Concentration(g/) Concentration(g/) 21 da23107 8/22/11:42:53 22 da23108 8/22/11:59:4 10.4 102 10 102 104 10.2 10 Concentration(g/) Concentration(g/I) 19 da23105 8/22/11:10:31 23 da23109 8/22/12:15:15 10 10 2* 20 10-2 10 102 10-4 10 10 Concentration(g/) Concentration(g/) 25 da23111 8/22/13: 7:24 26 da23112 8/22/13:23:35 10 102 10 10 104 102 10 Concentration(g/) Concentration(g/l) 24 da23110 8/22/12:31:26 27 da24113 8/22/15:30:25 28 da24114 8/22/16:2:12 4 102 100 102 102 100 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 2 104 102 10 10 104 10 10 10 Concentration(g/) Concentration(g/) E o V "0 EIO 0 L, 4 0 C 4-^ 31 da24117 8/23/11:2:14 32 da24118 8/23/11:18:4 + + S + + V V + C *+ C + 0 '+ 0 + - s-+ .- *+ * *+ 2 10E 104 + 0 0 + C e + + +- + -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 on. I oA, .. 1 10 10 10 1 Concentration(g/1) --4 -2 0 2 10-4 10 10 10 Concentration(g/A) -0 E 0 0 4 Elo 0 2 U/) ,,1 0 ft 5+ :+ *+ 5+ :+ :+ + .+ 36 da25122 8/23/12:21:24 102 100 102 Concentration(g/1) 102 100 Concentration(g/I) 37 da25123 8/23/12:37:14 38 da25124 8/23/12:53: 4 -20 I%20 I E : E : 8t!+ o .+ v + v + 0 + 0+ 0 + D + C C 0 EIO 0 0 a CD 4. 4-4 2 -40 10 10 10 10 10 102 10 Concentration(g/) Concentration(g/I) 35 da25121 8/23/12: 5:34 |