X
Contents
3.7 Numerical Integration of the Source FUnction .............. 65
3.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4
Study of Physical Mechanisms
Forming the Wind Wave Energy Spectrum
in Deep Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.1 Non-Linear Energy Transfer in Wind Wave Spectrum . . . . . . . 81
4.1.1 Problem Review.................................. 81
4.1.2 Optimal Algorithm of Computation
of Non-linear Energy Transfer...................... 85
4.1.3 Calculation Results of Non-linear Energy Transfer
in Wind Wave Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.1.4 Numerical Study of Non-Stationary Solution
of the Hasselmann Equation ....................... 105
4.2 Wind Wave Energy Input ............................... 123
4.3 Wave Energy Dissipation in Deep Water ................... 127
4.4 Influence of Mesoscale Effects on Wind Wave Evolution ..... 136
5 Wave Evolution in Non-uniform Currents in Deep Water . 153
5.1 Formulation of the Problem in the Local Coordinate System . 153
5.2 Frequency-Angular Spectrum Evolution in a Current ........ 155
5.3 Spectral Model of Rips .................................. 164
5.4 Estimation of Non-Linear Wave Interaction
in the Rip Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
5.5 Wave Element Transformations in Current,
Varying Along its Direction .............................. 183
5.6 Wave Diffraction Around a Caustic ....................... 190
5. 7 Wind Wave Transformation in Cross-Velocity Shear Current . 198
5.8 Freak Wave Problem .................................... 217
5.9 Influence of Vertical Non-Uniform Current
on Wind Wave Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
5.10 Wind Wave Generation in a Current ...................... 237
5.11 Some Practical Recommendations
for Estimation of Current Influence on Waves .............. 247
6 Wave Transformation in Shallow Water ................... 253
6.1 Spectrum Transformation Due to Wave Refraction
in Shallow Water ....................................... 253
6.2 Weak Non-Linear Wave Interaction in Shallow Water ....... 261
6.3 Joint Influence of Bottom and a Non-Uniform Current
on Wave Transformation ................................ 268
6.4 Wave Energy Dissipation in Shallow Water ................ 285
6.5 Numerical Model of Wind Wave Transformation
in a Coastal Area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293