Deep Water Gravity Waves

Introduction to water waves....Pages 1-16
More comments on mathematical techniques....Pages 17-26
The Hamiltonian for an isolated gravity wave field....Pages 27-39
Deep water eigenmodes....Pages 40-47
Resonant interactions and dynamics equations....Pages 48-60
Resonance among gravity waves....Pages 61-76
Resonant instabilities and the nonlinear Schröndinger equation....Pages 77-91
Unstable finite amplitude waves and envelope functions....Pages 92-100
Stability vs. instability....Pages 101-120
Kolmogorov\'s average Hamiltonian technique....Pages 121-132
Modification of the Hamiltonian to couple with the wind....Pages 133-144
Langrangian formulation....Pages 145-153
Linear stochastic differential equation (Langevin model)....Pages 154-163
Steady-state gravity-capillary spectrum....Pages 164-176
Steady-state linear wave field....Pages 177-189
Linear stochastic differential equation (cumulant expansions)....Pages 190-201
Gravity wave instability....Pages 202-209
Stochastic nonlinear gravity waves....Pages 210-220
Steady-state nonlinear wave field....Pages 221-234
Phase space equation of evolution....Pages 235-248
Entropy and the Fokker-Planck approximation....Pages 249-262
State of minimum entropy production....Pages 263-272
Entropy generation in the approach to the steady-state....Pages 273-287
Closure of the moment transport equations....Pages 288-295
Non-homogenous transport equation....Pages 296-306
Example calculations....Pages 307-321
Areas for further study....Pages 322-328