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A Numerical Study of Wave-Breaking Turbulence Beneath A NUMERICAL STUDY OF WAVE-BREAKING TURBULENCE BENEATH SOLITARY WAVES USING LARGE EDDY SIMULATION by Jacob James Sangermano A thesis submitted to the Faculty of the University of Delaware in partial fulfillment of the requirements for the degree of Master of Civil Engineering Spring 2013 © 2013 Jacob James Sangermano All Rights Reserved A NUMERICAL STUDY OF WAVE-BREAKING TURBULENCE BENEATH SOLITARY WAVES USING LARGE EDDY SIMULATION by Jacob James Sangermano Approved: __________________________________________________________ Tian-Jian Hsu, Ph.D. Professor in charge of thesis on behalf of the Advisory Committee Approved: __________________________________________________________ Harry W. Shenton III, Ph.D. Chair of the Department of Civil and Environmental Engineering Approved: __________________________________________________________ Babatunde A. Ogunnaike, Ph.D. Interim Dean of the College of Engineering Approved: __________________________________________________________ James G. Richards, Ph.D. Vice Provost for Graduate and Professional Education ACKNOWLEDGMENTS This thesis is the product of the work and input of a talented group of people, without whom I am sure much of this would not have been possible. I first need to thank my adviser, Dr. Tom Hsu, for his guidance and wisdom. Our weekly conversations about this project largely resulted in this manuscript, and it would be impossible to overstate how much I have learned from him. My work also included significant input from two other members of our group, Zhen (Charlie) Cheng and Zheyu (Nancy) Zhou. Their immense knowledge of numerical modeling and patience in working with me as I learned the basics is beyond impressive, and many of the tools I utilized were a result of their efforts. I also would like to acknowledge Dr. Kirby, Dr. Kobayashi, and Dr. Puleo, for the knowledge they imparted to me during the time I spent at the Center for Applied Coastal Research. Special thanks are due to Dr. Francis Ting of South Dakota State University for generously allowing us access to the data from his pioneering laboratory tests on breaking waves. His efforts were largely the inspiration and benchmark for this work. I want to thank my family, my parents Jim and Mona, and my brother and sister, Matt and Emily, who have always been in my corner since I dreamed of being a professional basketball player. Without you all I would not be the person I am today. Finally, I would like to dedicate this thesis to my wife, Marlee, for the unfathomable devotion and love she has supported me with throughout this often arduous process. Every day she inspires me to try harder, and when I think I have failed, she and our cat, Dhina, are always there to prove me wrong. iii TABLE OF CONTENTS LIST OF TABLES ........................................................................................................ vi LIST OF FIGURES ...................................................................................................... vii ABSTRACT .................................................................................................................. xi Chapter 1 INTRODUCTION .............................................................................................. 1 1.1 Introduction to Turbulence Generated by Breaking Waves ...................... 1 1.2 Breaking Induced Turbulence Effects ....................................................... 5 1.3 Numerical Modeling of Breaking Waves .................................................. 9 2 NUMERICAL MODEL OVERVIEW ............................................................. 14 2.1 Governing Equations ............................................................................... 15 2.2 Large Eddy Simulation Subgrid-scale Closure ....................................... 17 2.3 Boundary Conditions and Interface Tracking Method ............................ 18 2.4 Numerical Schemes ................................................................................. 23 3 VALIDATION OF OPENFOAM NUMERICAL MODEL ............................ 24 3.1 Solitary Wave Propagation over a Constant Depth Tank ........................ 25 3.2 Non-breaking Solitary Wave Run-up on a Steep Plane Beach ............... 29 3.3 Solitary Wave Breaking over a 1/20 Slope Beach .................................. 33 3.4 Solitary Wave Breaking over a 1/50 Sloping Beach ............................... 38 4 VISUALIZATION AND QUANTIFICATION OF THE TURBULENT FLOW FIELD .................................................................................................. 64 4.1 Point Sensor Detection of Turbulent Coherent Structures ...................... 64 4.2 Oblique Descending Eddy Flow Field Signatures ................................... 74 4.3 Turbulent Coherent Structure Visualization Using the λ2 Criterion ........ 79 4.4 Co-evolution of Vorticity and Turbulent Kinetic Energy ....................... 84 4.5 Turbulent Coherent Structure Bed Impingement and Resulting Bed Stress ..................................................................................................... 105 5 DISCUSSION ................................................................................................. 123 iv 6 CONCLUSIONS AND FUTURE WORK ..................................................... 130 REFERENCES ........................................................................................................... 134 Appendix LETTER OF PERMISSION FOR USE OF TING, [2006] DATA ............... 138 v LIST OF TABLES Table 3.1: Dissipation statistics for H = 0.5 m, h = 1.0 m case........................................27 Table 3.2: Dissipation statistics for H = 0.2 m, h = 1.0 m case........................................28 vi LIST OF FIGURES Figure 2.1: Generic schematic of numerical wave tank domain. ............................ 20 Figure 3.1: Schematic image of simulated Zelt, [1991] wave tank.. ....................... 30 Figure 3.2: Non-dimensionalized free surface elevation comparison over non- dimensionalized time 8.426 m from inlet.. ........................................... 31 Figure 3.3: Non-dimensionalized run-up profiles at instantaneous non- dimensionalized times. ......................................................................... 32 Figure 3.4: Schematic image of simulated Synolakis, [1987] wave tank. .............. 34 Figure 3.5: Non-dimensionalized run-up profile comparison for non- dimensional times (t’ = t(gd)1/2) 10, 15, 20, 25, 30, and 50. ................ 37 Figure 3.6: Schematic image of simulated Ting, [2006] wave tank. ...................... 40 Figure 3.7: Wave height time series data recorded (from top to bottom, left to right) at cross-tank locations. ............................................................... 41 Figure 3.8: Comparison of wave height decay using different specified wave conditions. ............................................................................................ 44 Figure 3.9: Average streamwise velocity where x = 7.375 m (water depth, h = 0.1525 m), taken at different vertical locations above the bed. ............ 47 Figure 3.10: Average vertical velocity where x = 7.375 m (water depth, h = 0.1525 m), taken at different vertical locations above the bed. ............ 49 Figure 3.11a: Root mean squared turbulent kinetic energy and streamwise, spanwise, and vertical turbulent velocity fluctuations at elevations above bed z = 110 and x = 7.375 (h = 0.1525 m). ................................ 51 Figure 3.11b: Same as Figure 3.11a, except z = 100 mm. .......................................... 52 Figure 3.11c: Same as Figure 3.11b, except z = 70 mm. ............................................ 53 Figure 3.11d: Same as Figure 3.11c, except z = 50 mm. ............................................ 54 vii Figure 3.11e: Same as Figure 3.11d, except z = 30 mm. ............................................ 55 Figure 3.12: Energy spectrum in spatial domain. ..................................................... 57 Figure 4.1: Model-data comparison of instantaneous turbulent velocity fluctuations time series at 70 mm above bed. ....................................... 65 Figure 4.2a: Coherent turbulent velocity fluctuations 130 mm above the bed, y = 0.00375m in numerical domain. ........................................................... 68 Figure 4.2b: Coherent turbulent velocity fluctuations 110 mm above the bed, y = 0.00375m in numerical domain. ........................................................... 69 Figure 4.2c: Coherent turbulent velocity fluctuations 100 mm above the bed, y = 0.075m in numerical domain. ............................................................... 70 Figure 4.2d: Coherent turbulent velocity fluctuations 50 mm above the bed, y = 0.015m in numerical domain. ............................................................... 71 Figure 4.2e: Coherent turbulent velocity fluctuations 30 mm above the bed, y = 0.0225m in numerical domain. ............................................................. 72 Figure 4.2f: Coherent turbulent velocity fluctuations 10 mm above the bed, y = 0.255m in numerical domain ................................................................ 73 Figure 4.3: Contour plots of vertical velocity fluctuations (w’), instantaneous turbulent kinetic energy (k), and the z-normal component of vorticity at z = 70 mm above the bed ................................................... 75 Figure 4.4: Contour plots of vertical velocity fluctuations (w’), turbulent kinetic energy (k), and the z-normal component of vorticity
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