TABLE OF CONTENTS -- Acknowledgments -- Preface -- Prologue: Cavitation -- On the theory and modeling of real cavity flows Marshall Tulin -- 1. Introduction -- 2. FLOW FIELDS -- 3. VORTICITY -- 4. CAVITY CONFIGURATIONS AS CONSTRAINED BY VORTICITY -- 5. VISCOUS SEPARATION VS. CAVITATION -- 6. THE SUBCRITICAL REGIME -- 7. THE SUPERCRITICAL REGIME -- References -- Chapter 1 : Nonlinear Waves: Theoretical Considerations -- Localization of dispersive waves in weakly random media C. C. Mei, Jorgen H. Pihl, Mathew Hancock & Yile Li -- 1. Introduction -- 2. Nearly sinusoidal waves -- 2.1. The envelope equation -- 2.2. Narrow-banded water waves over intermediate depth -- 2.2.1. Localization of steady Stokes waves -- 2.2.2. Nonlinear instability of side-band disturbances -- 3. Transient long waves in a shallow sea -- 3.1. The Kd V- Burgers integvo-differential equation -- 3.1.1. The evolution equation -- 3.1.2. Sample numerical results -- 4. Concluding remarks -- Acknowledgements -- References -- Water wave equations Jin E. Zhang -- 1. Introduction -- 2. Wu's Unified Theory for Modeling Water Waves -- 3. Boussinesq Models -- 4. Integrable Water Wave Equations -- 4.1. The KdV equation -- 4.2. The Boussinesq single-equation -- 4.3. The classical Boussinesq equation -- 4.4. The Camassa-Holm equation -- 5. Two Problems -- References -- Wu's mass postulate and approximate solutions of the fKdV equation S. S. P. Shen, Q. Zheng, S. Gao, Z. Xu & C. T. Ong -- 1. Introduction -- 2. Amplitude of the upstream solitons -- 3. Mass postulate and the depth of the downstream depression -- 4. Geometry of the waves on the x-t plane -- 5. Solitons in the atmosphere over the Hainan island -- Acknowledgments -- References -- Explicit analytic solutions of KdV equation given by the homotopy analysis method Chen Chen, Chun Wang & Shijun Liao -- 1. Introduction.

2. Solution of periodic wave -- 3. Solution of solitary wave -- 4. Validation of the solutions -- 4.1. Cnoidal waves -- 4.2. Solitary waves -- 5. Conclusions -- References -- Rigorous computation of Nekrasov's integral equation for water waves Sunao Murashige & Shin 'ichi Oishi -- 1. Introduction -- 2. The singular integral of trigonometric polynomials -- 3. The method of verification -- 3.1. The truncated pard of (20) -- 3.2. The finite dimensional part of (20) -- 4. Results -- 5. Conclusions -- Acknowledgments -- References -- Numerical modeling of nonlinear surface waves and its validation W. Choi, C. P. Kent & C. J. Schillinger -- 1. Introduction -- 2. Mathematical Formulation -- 2.1. Asymptotic expansion -- 2.2. Nonlinear evolution equations -- 2.3. Pseudo-spectral method -- 3. Validation of Models for One-dimensional Waves -- 3.1. Exact evolution equations -- 3.2. Numerical method for exact evolution equations -- 3.3. Progressive waves -- 3.4. Benjamin- Feir instability -- 4. Numerical Solutions for Two-dimensional Waves -- 4.1. Nonlinear resonant wave-wave interactions -- 4.2. Nonlinear evolution of random wave fields -- 5. Discussion -- References -- Three dimensional wave for water waves on finite depth: The Davey-Stewartson system K. W. Chow, D. H. Zhang & C. K. Poon -- 1. Introduction -- 2. Formulation -- Appendix -- Acknowledgement -- References -- Rip currents due to wave-current interaction Jie Yu & A. Brad Murray -- 1. Introduction -- 2. Formulation -- 3. Basic state: the 0th order solutions -- 4. Linear instability: the 1st order solution -- 4.1. Solution procedure -- 5. Results and discussion -- 5.1. Eflects of incident wave height -- 5.2. Effects of bottom friction -- 6. Concluding remarks -- Acknowledgments -- References -- Higher order Boussinesq equations for water waves on uneven bottom Hua Liu & Benlong Wang -- 1. Introduction.

2. Mathematical Formulation -- 3. Numerical Method -- 4. Numerical Results -- 5. Concluding Remarks -- Acknowledgments -- References -- Waves on a liquid sheet S. P. Lin -- 1. Governing Equations -- 2. Sheet Waves -- 2.1. Linear Sheet Waves -- 2.2. Sinuous mode -- 2.3. Varicose mode -- 2.4. Nonlinear Sheet Waves -- 3. Discussion -- References -- A different view on data from a nonlinear and nonstationary world Norden E. Huang -- 1. Introduction -- 2. The Hilbert-Huang Transform -- 2.1. The Empirical Mode Decomposition Method: The Sifring Process -- 2.2. The Hilbert Spectral Analysis -- 3. Mathematical Problems related to HHT -- 3.1. Adaptive data analysis methodology -- 3.2. Nonlinear system identification -- 3.3. Prediction problem for nonstationary processes, the end effects of EMD -- 3.4. The Spline problem (best spline implement of HHT, convergence and 2-D) -- 3.5. The Optimization Problem (the best IMF selection and uniqueness Mode mixing) -- 3.6. Approximation problem (Hilbert transform and quadrature) -- 3.7. Miscellaneous statistical questions concerning HHT -- 4. Conclusion -- Acknowledgements -- References -- Chapter 2: Nonlinear Waves: Experiments and Computations -- Solitary-wave collisions Joseph Hammack, Diane Henderson, Philippe Guyenne & Ming Yi -- 1. Introduction -- 2. Experimental Program -- 2.1 Wave Channel -- 2.2 Wave-maker -- 2.3 Wave & Depth Measurements -- 2.4 Data Acquisition & Control -- 2.5 Procedures -- 2.6 Wave Generation -- 2.7 Discussion -- 3. Mathematical Models -- 3.1 Euler Model -- 3.2. Kd V Models -- 4. Head-on (counter-propagating) collision -- 5. Following (co-propagating) collision -- 6. Summary -- References -- Computer simulations of overtaking internal solitary waves Brian C. Barr & Daniel T. Valentine -- 1. Introduction -- 2. Computational analysis methodology -- 2.1. Flow-field geometry and initial condition.

2.2. Equations of motion -- 2.3. Computational-solution methods -- 3. Wave Theory -- 3.1. Weakly nonlinear model -- 3.2. Fully nonlinear model -- 4. Results and discussion -- 4.1. Internal solitary waves -- 4.2. Overtaking solitary waves -- 5. Conclusions -- References -- Theoretical and experimental investigation of waves due to a moving dipole in a stratified fluid Shiqiang Dai, Gang Wei, Dong-Qiang Lu & Xiao-Sing Su -- 1. Introduction -- 2. Theoretical Approach -- 2.1. Formulation of Problem -- 2.2. Method of Green's Function -- 2.3. Divergence field on the free surface -- 2.4. Wave elevation at the interface -- 3. Comparison with experimental results -- 4. Conclusions -- 5. Acknowledgment -- 6. References -- Thin film dynamics in a liquid lined circular pipe Roberto Camassa & Long Lee -- 1. Problem formulation and Poiseuille solutions -- 1.1. Comparison with experimental data -- 1.2. Eflective viscosity -- 2. A two-phase gas-liquid model -- 2.1. The evolution equation for a bounded film -- 2.2. Numerical solutions and comparison -- 2.3. Modified effective viscosity -- 2.4. Surface tension parameter -- 3. Discussion and conclusion -- References -- Transverse waves in a channel with rectangular cross section L. M Deng & A. T. Chwang -- 1. Introduction -- 2. Experimental Configuration -- 3. Experimental Results -- 4. Discussion and Conclusions -- Acknowledgments -- References -- Long time evolution of nonlinear wave trains in deep water Hwung-Hweng Hwung & Wen-Son Chiang -- 1. Introduction -- 2. Experiments -- 3. Evolution of non-breaking type -- 4. Evolution of breaking type -- 5. Conclusions -- Acknowledgments -- References -- On the Zhang-Wu run-up model Hongqiang Zhou, Michelle H. Teng & Kelie Feng -- 1. Introduction -- 2. The Zhang-Wu Run-Up Model -- 3. Numerical and Experimental Results -- 4. Discussions and Conclusions -- 5. Acknowledgement.

References -- A numerical study of bore runup a slope Qinghai Zhang & Philip L.-F. Liu -- 1. Introduction -- 2. Governing Equations and Boundary Conditions -- 3. Numerical Setup -- 4. Numerical Results -- 4.1. Bore Collapse -- 4.2. Runup -- 4.3. Rundown -- 4.4. Turbulent Kinetic Energy Evolution during Runup -- 5. Conclusions -- Acknowledgment -- References -- Studies of intense internal gravity waves: Field measurements and numerical modeling Hsien P. Pao & Andrey N. Serebryany -- 1. Introduction -- 2. Study 1: Intense Internal Waves on Shelf -- 2.1. Numerical Modeling -- 3. Study 2: Generation of Intense Internal Waves by Surface Intrusions on a Shelf -- 3.1. Numerical Modeling -- 3.2. Numerical Results -- References -- Nonlinear internal waves in the South China Sea Antony Liu, Yunhe Zhao & Ming-Kuang Hsu -- 1. Introduction -- 2. Recent SAR observations -- 3. Internal Wave Data Analysis -- 4. Nonlinear Internal Wave Evolution on a Shelf -- 5. Numerical Simulation and Comparison -- 6. Summary and Discussion -- Acknowledgement -- References -- A numerical predictive model of tides around Taiwan Hsien- Wen Li & Yung-Ching Wu -- 1. Introduction -- 2. Governing Equations -- 3. Results -- 4. Discussion and Conclusion -- Acknowledgements -- References -- New concepts in image analysis applied to the study of nonlinear wave interactions Steven R. Long -- 1. Introduction -- 2. General Concepts of Image Processing -- 3. New Concepts in Image Analysis -- 3.1. The Laboratory That Produced the Nonlinear Waves -- 3.2. The Digital Camera and Setup -- 3.3. Experimental Images of Nonlinear Waves -- 3.4. EMD/HHT Analysis on Images of Nonlinear Waves -- 3.4.1. Components, Contour and Surface Visualization -- 3.4.2. Volume Computations and Isosurface Visualization -- 3.4.3. Use of EML/HHT in Image Decomposition -- 4. Summary -- Acknowledgements -- References.

Chapter 3: Wave Structure Interaction.