Contents
Introduction..................................................
1
1
General Problem Formulation of Wind Wave Modelling
in a Non-Uniform Ocean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.1 Hydrodynamic Problem of Surface Wave Generation
by Air Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2 Geometric Optics Approximation. . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3 Wave Action Conservation Law . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.4 Statistical Wind Wave Description . . . . . . . . . . . . . . . . . . . . . . . . 23
1.5 Kinetic Equation of the Evolution
of the Wind Wave Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.6 General Problem Formulation for Determining
the Wave Action Spectral Density in the Ocean . . . . . . . . . . . . 28
1. 7 Spatial-Temporal Scale Considerations
in the Analysis of Problem Solution . . . . . . . . . . . . . . . . . . . . . . . 32
2
Mathematical Simulation of Wave Propagation
at Global Distances....................................... 35
2.1 Problem Formulation of Ocean Wind Wave Modelling
Using Spherical Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.2 Correspondence of Local and Global Coordinate Systems . . . . 38
2.3 Numerical Simulation of Swell Propagation
Using the Method of Characteristics . . . . . . . . . . . . . . . . . . . . . . 39
2.4 The Influence of Current on the Evolution of Waves
at the Global Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3
Numerical Implementation
of the Wave Energy Balance Equation . . . . . . . . . . . . . . . . . . . . 49
3.1 Statement of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2 Formulation of the Wave Propagation Problem............. 51
3.3 Standard Numerical Propagation Schemes . . . . . . . . . . . . . . . . . 53
3.4 Elimination of the "Garden Sprinkler Effect" . . . . . . . . . . . . . . . 54
3.5 Interpolation-Ray (INTERPOL) Method . . . . . . . . . . . . . . . . . . 59
3.6 Comparison of Results
of Numerical Wave Propagation Schemes . . . . . . . . . . . . . . . . . . 60
Introduction..................................................
1
1
General Problem Formulation of Wind Wave Modelling
in a Non-Uniform Ocean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.1 Hydrodynamic Problem of Surface Wave Generation
by Air Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2 Geometric Optics Approximation. . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3 Wave Action Conservation Law . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.4 Statistical Wind Wave Description . . . . . . . . . . . . . . . . . . . . . . . . 23
1.5 Kinetic Equation of the Evolution
of the Wind Wave Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.6 General Problem Formulation for Determining
the Wave Action Spectral Density in the Ocean . . . . . . . . . . . . 28
1. 7 Spatial-Temporal Scale Considerations
in the Analysis of Problem Solution . . . . . . . . . . . . . . . . . . . . . . . 32
2
Mathematical Simulation of Wave Propagation
at Global Distances....................................... 35
2.1 Problem Formulation of Ocean Wind Wave Modelling
Using Spherical Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.2 Correspondence of Local and Global Coordinate Systems . . . . 38
2.3 Numerical Simulation of Swell Propagation
Using the Method of Characteristics . . . . . . . . . . . . . . . . . . . . . . 39
2.4 The Influence of Current on the Evolution of Waves
at the Global Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3
Numerical Implementation
of the Wave Energy Balance Equation . . . . . . . . . . . . . . . . . . . . 49
3.1 Statement of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2 Formulation of the Wave Propagation Problem............. 51
3.3 Standard Numerical Propagation Schemes . . . . . . . . . . . . . . . . . 53
3.4 Elimination of the "Garden Sprinkler Effect" . . . . . . . . . . . . . . . 54
3.5 Interpolation-Ray (INTERPOL) Method . . . . . . . . . . . . . . . . . . 59
3.6 Comparison of Results
of Numerical Wave Propagation Schemes . . . . . . . . . . . . . . . . . . 60