Numerical Modelling of Extreme Waves/Численное моделирование экстремальных волн

Издание на английском языке
The book is devoted to the study of extreme waves in the context of climate change and active ocean exploration. She emphasizes the importance of developing numerical models to predict the formation of extreme waves, which can cause significant damage to floating structures such as ships and pose a danger to life and the environment. The authors systematically investigate various numerical wave models with different levels of nonlinearity, comparing their results with laboratory observations. The book also analyzes statistical differences in simulations, the effect of nonlinearity on the formation of extreme waves, and the probability of exceeding the height of waves in comparison with theoretical models. In addition, the initial conditions and their effect on the generation of extreme waves, including noise in deterministic sequences and uncertainties in stochastic wave trains, are considered.

Contents
1 Introduction
1.1 Motivation
1.1.1 Threat of Extreme Waves
1.1.2 Physical Mechanisms of Extreme Wave Formation
1.2 Literature Review
1.2.1 Wave Modelling
1.2.2 Wave Statistics
1.3 Outline of Chapters
2 Laboratory Experiments Related to Extreme Waves
2.1 Basic Theory
2.1.1 Carrier Wave Envelope Representation
2.1.2 Longuet-Higgins Joint Distribution
2.1.3 Modified Longuet-Higgins Joint Distribution I
2.1.4 Modified Longuet-Higgins Joint Distribution II
2.1.5 Nonlinear Models of Wave Height Distribution
2.2 Unidirectional Wave Experiments in Two Wave Basins
2.2.1 Marintek Wave Basin
2.2.2 CEHIPAR Wave Basin
2.2.3 Experimental Data for Comparative Analysis
2.3 Verification and Validation of Extreme Wave Experiments
2.3.1 Sea State Parameters
2.3.2 Wave Spectrum
2.3.3 Joint Distribution of Wave Heights and Wave Periods
2.3.4 Exceedance Distribution of Wave Heights
2.3.5 Probability Distribution of Wave Periods
2.4 Modified Theoretical Models for Joint Distributions
2.4.1 Spatial Variation of Basic Wave Parameters
2.4.2 Comparison of Joint Distributions
2.5 Dynamic Pressure Under Crests of Nonlinear Waves
2.5.1 Introduction
2.5.2 Theoretical Pressure Models for Regular and Irregular Waves
2.5.3 Layout of the Experimental Setup
2.5.4 Dynamic Pressure in Regular Waves
2.5.5 Dynamic Pressure in Irregular Waves
2.5.6 Comparison of Pressures Between Regular and Irregular Waves
2.5.7 Dynamic Pressure in Focused Waves
2.6 Evolutionary Property of Multidirectional Waves
2.6.1 Directional Spectrum
2.6.2 Higher-Order Statistics
2.6.3 Surface Elevation Probabilities
2.7 Conclusion
3 Modelling Extreme Waves with 2D NLS Equation
3.1 Basic Theory
3.1.1 Cubic Nonlinear Schrodinger Equation
3.1.2 Theoretical Distribution Models of Wave Heights
3.1.3 Numerical Schemes
3.2 Typical Wave Envelopes
3.3 Simulation of Laboratory Experiments in Marintek
3.3.1 General Comparisons
3.3.2 Comparison of Wave Height Distribution
3.4 Simulation of Laboratory Experiments in CEHIPAR
3.4.1 Exceedance Distribution of Wave Heights
3.4.2 Statistics on Maximum Wave Heights
3.5 Conclusion
4 Modelling Extreme Waves with 2D Dysthe Equation
4.1 Basic Theory
4.1.1 2D Dysthe Equation
4.1.2 Statistical Models
4.2 Effects of Fourth-Order Terms in Dysthe Equation
4.3 Comparison Between NLS and Dysthe Models
4.3.1 Statistical Moments
4.3.2 Surface Elevation
4.3.3 Wave Height
4.3.4 Wave Crest
4.3.5 Wave Trough
4.3.6 Wave Period
4.4 Conclusion
5 Modelling Extreme Waves with 3D Dysthe Equation.
5.1 Basic Theory
5.1.1 Temporal and Spatial Versions of 3D MNLS Equation.
5.1.2 Initial Random Multidirectional Wave Field
5.2 Numerical Schemes
5.3 Difference Between Temporal and Spatial Evolutions
5.4 Numerical Simulation of Multidirectional Waves
5.4.1 Coefficients of Skewness and Kurtosis
5.4.2 Surface Elevation
5.4.3 Wavenumber Spectrum
5.5 Conclusion
6 Modelling Extreme Waves with the HOS Method
6.1 Basic Theory
6.1.1 High-Order Spectral Method
6.1.2 Breather Solutions of Nonlinear Schrodinger Equation.
6.2 Experimental and Numerical Setup
6.2.1 Wave Basin and Ma Breather Solution
6.2.2 Numerical Schemes
6.3 Experimental and Numerical Results
6.3.1 Experimental Results
6.3.2 Numerical Simulation of Ma Breather Solution
6.3.3 Numerical Simulation of Peregrine Breather Solution
6.4 Conclusion
7 Modelling Extreme Waves with the Chalikov-Sheinin Model
7.1 Basic Theory
7.1.1 Chalikov-Sheinin Model
7.1.2 Numerical Schemes
7.2 Comparison Between HOS Method and Chalikov-Sheinin Model
7.2.1 Capability of the Chalikov-Sheinin Model
7.2.2 Modulation of Stokes Wave Train Due to Type I Instability
7.2.3 Evolution of Wave Packet
7.2.4 Collision of Two Wave Groups
7.3 Comparison Between Dysthe Equation and CS Model
7.3.1 Statistical Parameters
7.3.2 Distributions Related to Free Surface Elevation
7.4 Conclusion
8 Effect of Initial Conditions on Extreme Wave Formation
8.1 Disturbance of Noise in Deterministic Wave Train
8.1.1 Regular Background Waves
8.1.2 Irregular Background Waves
8.2 Influence of Uncertainty in a Stochastic Wave Train
8.2.1 Introduction
8.2.2 Case Study
8.2.3 Definition of Maximum Waves
8.2.4 Sensitivity Analysis
8.2.5 Aleatory Uncertainty
8.2.6 Epistemic Uncertainty
8.2.7 Mixed Uncertainty
8.3 Conclusion
References