Rogue Waves in the Ocean

by Kharif, Christian; Pelinovsky, Efim; Slunyaev, Alexey

• ISBN13: 9783540884187
• ISBN10: 3540884181
• Format: Hardcover
• Copyright: 2009-03-06
• Publisher: Springer Verlag

Summary

The book is written for specialists in the fields of fluid mechanics, applied mathematics, nonlinear physics, physical oceanography and geophysics, and also for students learning these subjects. It includes a wide range of observational data on rogue (or freak) waves in the seas and coastal waters, as well as presenting a basic statistical description of extreme water waves. The book describes the modern approaches, including theoretical and numerical models applied to explain the physical origin of such anomalous waves on the sea surface, taking into account wind flow above waves and also variable bathymetry and currents. Apart from these analytical and numerical approaches, laboratory experiments and in-situ observations are reported too.

Table of Contents

Introduction	p. 1
References	p. 9
Observation of Rogue Waves	p. 11
Historical Notes and Modern Testimonies	p. 11
Instrumental Registrations and Related Problems	p. 20
Keystones of the Rogue Wave Measurements	p. 20
Time-Series with Rogue Wave Occurrence	p. 22
SAR Registrations of Rogue Waves	p. 26
Sea States	p. 26
References	p. 29
Deterministic and Statistical Approaches for Studying Rogue Waves	p. 33
Deterministic Equations	p. 34
Mass and Momentum Conservation Equations	p. 34
Boundary Conditions	p. 37
Linearization: Equations for Small Amplitude Waves	p. 38
Dispersion Relation	p. 40
Statistical Description	p. 43
The Rayleigh Probability	p. 44
Wave Spectra	p. 48
Kinetic Models	p. 53
Possible Physical Mechanisms of Rogue Wave Generation	p. 56
Wave-Current Interaction	p. 57
Geometrical or Spatial Focusing	p. 58
Focusing Due to Dispersion: The Spatio-Temporal Focusing	p. 58
Focusing Due to Modulational Instability	p. 58
Soliton Collision	p. 58
References	p. 60
Quasi-Linear Wave Focusing	p. 63
Geometrical Focusing of Water Waves	p. 63
Dispersive Enhancement of Wave Trains	p. 69
Exact Solution for the Delta-Function	p. 72
Exact Solution for a Gaussian Wave Train	p. 73
Wave Focusing Under the Action of Wind	p. 78
Wave-Current Interaction as a Mechanism of Rogue Waves	p. 81
References	p. 87
Rogue Waves in Waters of Infinite and Finite Depths	p. 91
The Modulational Instability	p. 92
Within the Framework of the Fully Nonlinear Equations	p. 92
Within the Framework of the Nonlinear Schrodinger (NLS) Equation	p. 95
Rogue Wave Phenomenon within the Framework of the NLS Equation	p. 105
General Solution of the Cauchy Problem	p. 106
Nonlinear-Dispersive Formation of a Rogue Wave	p. 107
Solitons on a Background and Unstable Modes	p. 111
Rogue Wave Simulations within the Framework of the Fully Nonlinear Equations	p. 117
A High-Order Spectral Method	p. 117
A Boundary Integral Equation Method	p. 120
Numerical Simulation of Rogue Waves Due to Modulational Instability	p. 121
Numerical Simulation of Rogue Waves Due to Dispersive Focusing in the Presence of Wind and Current	p. 130
Numerical Simulation of Rogue Waves Due to Envelope-Soliton Collision	p. 135
Statistical Approach for Rogue Waves	p. 140
Laboratory Experiments of Dispersive Wave Trains with and without Wind	p. 143
Three-Dimensional Rogue Waves	p. 147
In Situ Rogue Waves	p. 154
Nonlinear Analysis of Measured Rogue Wave Time Series	p. 155
Statistics from Registrations of Natural Rogue Waves	p. 162
References	p. 165
Shallow-Water Rogue Waves	p. 173
Nonlinear Models of Shallow-Water Waves	p. 173
Nonlinear-Dispersive Focusing of Unidirectional Shallow-Water Wave Fields	p. 177
Numerical Modeling of Irregular Wave Fields in Shallow Water (KdV Framework)	p. 184
Three-Dimensional Rogue Waves in Shallow Water	p. 191
Anomalous High Waves on a Beach	p. 198
Waves at Vertical Walls	p. 199
Wave Run-up on a Plane Beach	p. 203
References	p. 207
Conclusion	p. 211
References	p. 212
Discretisation of the Boundary Integral Equation for the Potential	p. 213
Index	p. 215
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