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Nearshore Hydrodynamics and the Behaviour of Groynes on Sandy Beaches

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Nearshore Hydrodynamics and the Behaviour of Groynes on Sandy Beaches NEARSHORE HYDRODYNAMICS AND THE BEHAVIOUR OF GROYNES ON SANDY BEACHES by D.J. Walker, B.E.(Hons.), M.Eng.Sc., M.I.E.Aust. August, 1987 A thesis submitted for the degree of Doctor of Philosophy of the University of London and for the Diploma of Membership of the Imperial College Hydraulics Section, Department of Civil Engineering Imperial College of Science and Technology DEDICATION To my wife, Adrienne, and sons, James, Philip and Robert who all helped, although in different ways. 3 ABSTRACT This thesis describes solutions to the nearshore dynamics in an attempt to understand the behaviour of groynes on sandy beaches. The solution of the dynamics is achieved using three finite difference numerical models. The first solves a transient form of the Mild Slope Equation which allows the inclusion of wave diffraction, reflection and refraction by both bathymetry and currents. The second model solves the depth-averaged Navier-Stokes equations to determine local mean velocities, mean free surface elevation and turbulent eddy viscosity. The third model, using values calculated by the first two models, calculates the sediment transport and provides predictions of bathymetric changes caused by that transport. The numerical models are checked for validity against known analytical solutions and, where possible, against field and laboratory data. In addition to the numerical work a series of 1:36 scale model tests was undertaken to provide data with which to compare the numerical model results. Ten experiments were carried out under fixed wave conditions. The parameters varied included the number, spacing, length and height of the groynes. The author was also involved in the collection of full scale data from sites in Norfolk and Lincolnshire, and responsible for its subsequent analysis. The data collected provides further corroboration of the numerical and physical models. The thesis concludes with a number of runs of the numerical models and the prediction of likely accretion and erosion patterns caused by typical groyne arrangements. 4 ACKNOWLEDGEMENTS The author wishes to express his thanks to his supervisor, Professor P. Holmes for the encouragement and help provided during the course of research and for the invaluable criticism of the original manuscript. The author has also benefited from working with colleagues in the section, in particular Dr. Kostas Anastasiou and Mr. Dong Ping. The laboratory staff involved in the project must also be thanked, Messrs. Geoff Thomas, H.(Clem) Clements, Stan Finch, John Audsley and Martin Roper who always reacted quickly, even to the most tedious requests, and came up with helpful suggestions and ideas (like,"that's an interesting idea, but wouldn't it be better to ..."). Thanks also to Mr. Greg Guthrie of CEEMAID Ltd. for all the work in generating the full scale data sets. During the period at Imperial College the author has also had fruitful discussions and correspondance with Profs. J. Fredsoe (Technical University of Denmark), B. O'Connor (Univeristy of Liverpool) and R. Sternberg (University of Washington) and Drs. C. Fleming (Sir William Halcrow and Partners), J. Nicholson (Univeristy of Liverpool) and P. Nielsen (Public Works Dept., Sydney). The library staff in the Civil Engineering Department, Mrs. Kay Crooks and Miss Jessica Underhill are also thanked for their help as is Kirsten Djorup at the Technical University of Denmark who responded quickly to a couple of urgent requests. Finally the author would like to acknowledge the funding support of the Science and Engineering Research Council. 5 CONTENTS Pag' ABSTRACT 3 ACKNOWLEDGEMENTS 4 LIST OF TABLES 9 LIST OF FIGURES 10 LIST OF PLATES 13 LIST OF SYMBOLS 14 GLOSSARY OF TERMS 18 CHAPTER 1 - INTRODUCTION 19 CHAPTER 2 - LITERATURE REVIEW 21 2.1 Introduction 21 2.2 Groyne Behaviour and Design 22 2.3 Physical Models 23 2.3.1 Scaling Laws 23 2.3.2 Physical Model Tests 24 2.4 Numerical Models 29 CHAPTER 3 - PHYSICAL MODEL TESTS 32 3.1 Introduction 32 3.2 Basin Configuration 32 3.3 Measurement Techniques 37 3.4 Test Results 41 3.4.1 Introduction 41 3.4.2 Test No.l 42 3.4.3 Test No.2 42 3.4.4 Test No.3 42 3.4.5 Test No.4 42 3.4.6 Test No.5 47 3.4.7 Test No.6 47 3.4.8 Test No.7 47 3.4.9 Test No.8 50 3.4.10 Test No.9 50 3.4.11 Test No.10 50 3.5 Discussion of Results 50 6 Pago CHAPTER 4 - FULL SCALE MEASUREMENTS 56 4.1 Introduction 56 4.2 Site and Instruments 56 4.3 Data Recording Programme 65 4.4 Data Analysis 65 4.4.1 Introduction 65 4.4.2 Tidal Elevation and Mean Flows 65 4.4.3 Mean Flow Patterns 70 4.4.4 Surface Wave Energy Spectra 74 4.4.5 Wave Oscillatory Motion 74 4.5 Float Track Experiment 74 4.6 Beach Surveys 82 4.7 Discussion of Results 87 CHAPTER 5 - THE WAVE MODEL 88 5.1 Introduction 88 5.2 Literature Review 88 5.2.1 Introduction 88 5.2.2 Early Works 89 5.2.3 Mild Slope Equation 90 5.2.4 Assumptions and Approaches 92 5.2.5 Wave Breaking 93 5.3 Hyperbolic Approximation 93 5.3.1 Introduction 93 5.3.2 Theory 94 5.4 Finite Difference Equations 97 5.4.1 Introduction 97 5.4.2 Finite Difference Scheme 99 5.4.3 Initial Conditions 100 5.4.4 Driving Boundaries 102 5.4.5 Reflective and Transmissive Boundaries 104 5.4.6 Stability 105 5.4.7 Wave Height and Directions 105 5.4.8 Wave Breaking 106 5.4.9 Radiation Stresses 106 5.5 Model Verification 107 5.5.1 Introduction 107 5.5.2 Pure Refraction by Bathymetry 108 7 Page 5.5.3 Pure Diffraction around a Semi-Infinite Breakwater 108 5.5.4 Pure Diffraction through a Harbour Entrance 108 5.5.5 Pure Refraction by a Shear Current 108 5.5.6 Combined Refraction-Diffraction by a Submerged Shoal 119 5.5.7 Modelling of Arbitrary Configurations 131 CHAPTER 6 - THE CURRENT MODEL 133 6.1 Introduction 133 6.2 Literature Review 133 6.2.1 Introduction 133 6.2.2 Numerical Models 134 6.2.3 Circulating Flows 138 6.2.4 Turbulence Models 139 6.3 Current Model Equations 142 6.3.1 Depth-Averaged Navier-Stokes Equations 142 6.3.2 Radiation Stresses 143 6.3.3 Bottom Friction 143 6.3.4 Turbulence 143 6.4 Finite Difference Approximation 146 6.4.1 Introduction 146 6.4.2 ADI Scheme 147 6.4.3 Navier-Stokes Equations 147 6.4.4 Solution Technique 155 6.4.5 Turbulence Equations 157 6.4.6 Boundary Conditions 161 6.4.6.1 Navier-Stokes Equations 161 6.4.6.2 Turbulence Equations 161 6.5 Model Verification 162 6.5.1 Introduction 162 6.5.2 Comparison with Longuet-Higgins Profile 162 6.5.3 Comparison with Physical Model Results 162 6.5.4 Comparison with Full Scale Data 173 CHAPTER 7 - THE SEDIMENT MODEL 177 7.1 Introduction 177 7.2 Modes of Transport 177 7.3 Literature Review 178 7.3.1 Introduction 178 Pago 7.3.2 Longshore Sediment Transport 179 7.3.3 Cross Shore Sediment Transport 184 7.3.4 Experimental Studies 190 7.3.5 Vertical Velocity Profile 197 7.3.6 Bathymetric Evolution Models 197 7.4 Sediment Model Equations 200 7.4.1 Introduction 200 7.4.2 Longshore Transport 201 7.4.3 Cross Shore Transport 203 7.4.4 Vertical Velocity Profile 204 7.4.5 Bed Evolution Model 208 7.5 Finite Difference Equations 209 7.5.1 Introduction 209 7.5.2 Longshore Transport 209 7.5.3 Cross Shore Transport 211 7.5.4 Vertical Velocity Profile 214 7.5.5 Bed Evolution Model 218 7.6 Model Verification 218 7.6.1 Introduction 218 7.6.2 CERC Bulk Formula 219 7.6.3 Cross Shore Distribution of Transport 219 7.6.4 Comparison with Vertical Concentration Data 224 7.6.5 Onshore-Offshore Transport Mechanism 229 CHAPTER 8 - BATHYMETRIC MODEL RESULTS 231 8.1 Introduction 231 8.2 Numerical Prediction Results 232 8.2.1 Single Groyne, Surface Piercing 232 8.2.2 Single Groyne, Partially Submerged 238 8.2.3 2 Groynes, Surface Piercing, S/L=1.0 238 8.2.4 2 Groynes, Surface Piercing, S/L=2.0 244 8.3 Discussion of Results 244 CHAPTER 9 - SUMMARY, DISCUSSION AND CONCLUSIONS 253 9.1 Summary 253 9.2 Conclusions 254 9.3 Recommendations 257 REFERENCES 259 9 LIST OF TABLES Page 3.1 Physical Model Wave Parameters 43 3.2 Physical Model Test Details 43 6.1 k-e Model Empirical Constants 145 7.1 North Shore Wave Data 221 1 0 LIST OF FIGURES Page 2.1 Physical Model Results of Hulsgergen et al 26 2.2 Model Results of Price et al 30 3.1 Wave Basin Layout 33 3.2 Wave Heights in Wave Basin 38 3.3 Physical Model Results - Test 1 39 3.4 Signal from Current Velocity Probe 40 3.5 Physical Model Results - Test 2 44 3.6 Physical Model Results - Test 3 45 3.7 Physical Model Results - Test 4 46 3.8 Physical Model Results - Test 5 48 3.9 Physical Model Results - Test 6 49 3.10 Physical Model Results - Test 7 51 3.11 Physical Model Results - Test 8 52 3.12 Physical Model Results - Test 9 53 3.13 Physical Model Results - Test 10 54 4.1 Sea Palling - Location Plan 57 4.2 Sea Palling - Site Plan 58 4.3 Beach Cross Section - Open Beach 59 4.4 Beach Cross Section - Groyne Bay 60 4.5 Beach Sand Sieve Test Results 61 4.6 Beach "Pod" 63 4.7 Typical Data from Beach Pod 64 4.8 Mean Water Depth at Pod 3 66 4.9 Mean Water Depth at Pod B 67 4.10 Mean Velocity at Pod 3 68 4.11 Mean Velocity at Pod B 69 4.12 Wave Height Record for Experiment Duration 71 4.13 Mean Flow Patterns - Records 43-49 72 4.14 Wave Energy Spectra from Pod and Waverider Buoy 75 4.15 Bivariate Plot from Current Meter 76 4.16 Plot of Water Particle Displacement 77 4.17 Float used in Float Track Experiment 79 4.18 Float Track Records - May 1984 80 4.19 Float Track Records - October 1984 81 4.20 Total Beach Volume 83 4.21 Selected Beach Cross Sections - Section 1 84 4.22 Selected Beach Cross Sections - Section 2 85 4.23 Selected Beach Cross Sections - Section 3 86 5.1 SolutionGrid Layout for Wave Model 98 11 Page 5.2 Numerical Grid for Wave Model 101 5.3
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