Extreme Ocean Waves

This revised and updated second edition details the vast progress that has been achieved in the understanding of the physical mechanisms of rogue wave phenomenon in recent years. The selected articles address such issues as the formation of rogue waves due to modulational instability of nonlinear wave field, physical and statistical properties of extreme ocean wave generation in deep water as well as in shallow water, various models of nonlinear water waves, special analysis of nonlinear resonances between water waves and the relation between in situ observations, experimental data and rogue wave theories. In addition, recent results on tsunami waves due to subaerial landslides are presented. This book is written for specialists in the fields of fluid mechanics, applied mathematics, nonlinear physics, physical oceanography and geophysics, and for students learning these subjects. Preface 5 Contents 8 Contributors 10 Rogue Waves in Higher Order Nonlinear Schrödinger Models 13 1 Introduction 13 2 Background 16 2.1 Homoclinic Solutions of the NLS Equation as Candidates for Rogue Waves 18 2.2 Phase Modulated Rogue Waves 19 3 Noisy Rogue Waves 20 4 Melnikov Analysis 22 5 Random Oceanic Sea States and the Proximity to Homoclinic Data 25 6 Non-Gaussian Statistics and the Dependence of Kurtosis on the Proximity to Homoclinic Data 29 References 32 Freak-Waves: Compact Equation Versus Fully Nonlinear One 34 1 Introduction 34 2 Fully Nonlinear Conformal Equations 35 3 Compact Equation 37 4 Modulational Instability of Wave Train 39 5 Breathers 40 6 Conclusions 44 References 55 Occurrence of Extreme Waves in Finite Water Depth 56 1 Introduction 56 2 Data Sets 58 2.1 Laboratory Experiments 58 2.2 Numerical Simulations 60 2.3 Field Measurements: The Lake George Data Set 62 3 Evolution of Significant Wave Height and Wave Energy Spectrum 62 4 Wave Statistics 64 4.1 Skewness and Kurtosis 64 4.2 Probability Density Function 67 4.3 Wave Crest Distribution 68 5 Conclusion 70 References 71 Modeling of Rogue Wave Shapes in Shallow Water 74 1 Introduction 74 2 Theoretical Model 76 3 Numerical Model 78 4 Conclusions 82 References 83 Non-Gaussian Properties of Shallow Water Waves in Crossing Seas 85 1 Introduction 85 2 The Kadomtsev--Petviashvili Equation 87 3 Numerical Experiment 88 4 Skewness and Kurtosis of the Simulated Surface Elevation 90 5 Surface Elevation and Probability Density Function 93 6 Wave Height Distribution 97 7 Conclusions 99 References 100 Searching for Factors that Limit Observed Extreme Maximum Wave Height Distributions in the North Sea 102 1 Introduction 102 2 Data Sources 105 2.1 North Sea Data 105 2.2 WAM Model BFI 106 3 Results 107 4 Discussion 112 5 Conclusion 113 References 114 Extremes and Decadal Variations in the Baltic Sea Wave Conditions 115 1 Introduction 115 2 Long-Term Wave Measurements and Hindcasts in the Baltic Sea 118 2.1 Instrumental Data Sets 118 2.2 Visual Observations 121 2.3 Long-Term Wave Hindcasts 122 3 Wave Climate 124 3.1 Statistics of Wave Heights and Periods 124 3.2 Extreme Conditions 127 3.3 The Ratio of Extreme and Average Wave Heights 129 3.4 Sub-basins of the Baltic Sea 130 4 Extremes During Windstorm Gudrun 131 4.1 The Storm and Waves 132 4.2 Modelled Wave Fields 133 4.3 Maximum of the Wave Storm 134 5 Seasonal, Interannual and Long-Term Variations 136 5.1 Temporal Variations in the Wave Heights, Periods and Directions 136 5.2 Variations in the Wave Heights in Very Rough Seas in the Baltic Proper 138 5.3 Mismatch of Trends for the Averages and Extremes in the Gulf of Finland 139 6 Discussion 140 References 142 Runup of Long Irregular Waves on Plane Beach 149 1 Introduction 149 2 Theoretical Model of the Long Wave Runup 151 3 Runup of irregular waves 154 4 Conclusion 159 References 160 Numerical Study for Run-Up of Breaking Waves of Different Polarities on a Sloping Beach 162 1 Introduction 162 2 Mathematical Model 164 3 Run-Up of Breaking Waves of Positive Polarity on a Sloping Beach 165 4 Run-Up of breaking Waves of Negative Polarity on a Sloping Beach 170 5 Contrastive Analysis of Run-up Characteristics for Breaking Waves of Different Polarity 172 6 Conclusion 176 References 177 Tsunami Waves Generated by Cliff Collapse: Comparison Between Experiments and Triphasic Simulations 180 1 Introduction 180 2 Experimental Investigations 184 2.1 Experimental Setup 184 2.2 Evolution of Amplitude During the Propagation of the Wave 185 3 Numerical Simulations 190 3.1 Parameters of the Simulations 190 3.2 Comparison of Numerical and Experimental Results 191 3.3 Evolution of the Amplitude During Propagation 192 4 Conclusion 194 References 194 An Analytical Model of Large Amplitude Internal Solitary Waves 198 1 Introduction 198 2 Basic Equations 199 3 The Model Equation 202 4 Solitary Waves 204 5 Conclusion 207 References 208 Symbolic Computation for Nonlinear Wave Resonances 209 1 Introduction 209 2 Mathematical Background 211 3 Equations for Wave Amplitudes 213 3.1 Method Description 213 3.2 The Implementation 214 3.3 Obstacles 218 3.4 Results 219 4 Resonance Conditions 221 4.1 Method Description 222 4.2 The Implementation 223 4.3 Results 225 5 Structure of the Solution Set 226 5.1 Method Description 226 5.2 Implementation 227 5.3 Results 228 5.4 Important Remark 231 6 A Web Interface to the Software 232 6.1 The Interface 233 6.2 The Implementation 234 6.3 Extensions 237 7 Discussion 238 References 239 Index 241 This revised and updated second edition details the vast progress that has been achieved in the understanding of the physical mechanisms of rogue wave phenomenon in recent years. The selected articles address such issues as the formation of rogue waves due to modulational instability of nonlinear wave field, physical and statistical properties of extreme ocean wave generation in deep water as well as in shallow water, various models of nonlinear water waves, special analysis of nonlinear resonances between water waves and the relation between in situ observations, experimental data and rogue wave theories. In addition, recent results on tsunami waves due to subaerial landslides are presented.This book is written for specialists in the fields of fluid mechanics, applied mathematics, nonlinear physics, physical oceanography and geophysics, and for students learning these subjects. Throughout the book, in fact, the reader will find a combination of theoretical and statistical/empirical treatment necessary for the complete examination of this subject. ... Overall, 'Extreme Ocean Waves' is a valuable contribution to the literature on wave theory and statistics, helping fill an important gap in our knowledge of a variety of unusual waves. It should be of great interest to scientists and engineers studying physical oceanography, wave dynamics and observations, nonlinear physics, and applied mathematics." (Eric L. Geist, Pure and Applied Geophysics, Vol. 168, 2011) Front Matter....Pages i-xiii Rogue Waves in Higher Order Nonlinear Schrödinger Models....Pages 1-21 Freak-Waves: Compact Equation Versus Fully Nonlinear One....Pages 23-44 Occurrence of Extreme Waves in Finite Water Depth....Pages 45-62 Modeling of Rogue Wave Shapes in Shallow Water....Pages 63-73 Non-Gaussian Properties of Shallow Water Waves in Crossing Seas....Pages 75-91 Searching for Factors that Limit Observed Extreme Maximum Wave Height Distributions in the North Sea....Pages 93-105 Extremes and Decadal Variations in the Baltic Sea Wave Conditions....Pages 107-140 Runup of Long Irregular Waves on Plane Beach....Pages 141-153 Numerical Study for Run-Up of Breaking Waves of Different Polarities on a Sloping Beach....Pages 155-172 Tsunami Waves Generated by Cliff Collapse: Comparison Between Experiments and Triphasic Simulations....Pages 173-190 An Analytical Model of Large Amplitude Internal Solitary Waves....Pages 191-201 Symbolic Computation for Nonlinear Wave Resonances....Pages 203-234 Back Matter....Pages 235-236 Extreme, freak, rogue or giant waves correspond to the large-amplitude waves that suddenly appear on the sea surface. They can cause serious damage to the offshore industry and navigation. This book highlights the recent progress that has been achieved in understanding the physical mechanisms of these waves