to water waves.- More comments on mathematical techniques.- The Hamiltonian for an isolated gravity wave field.- Deep water eigenmodes.- Resonant interactions and dynamics equations.- Resonance among gravity waves.- Resonant instabilities and the nonlinear Schröndinger equation.- Unstable finite amplitude waves and envelope functions.- Stability vs. instability.- Kolmogorov's average Hamiltonian technique.- Modification of the Hamiltonian to couple with the wind.- Langrangian formulation.- Linear stochastic differential equation (Langevin model).- Steady-state gravity-capillary spectrum.- Steady-state linear wave field.- Linear stochastic differential equation (cumulant expansions).- Gravity wave instability.- Stochastic nonlinear gravity waves.- Steady-state nonlinear wave field.- Phase space equation of evolution.- Entropy and the Fokker-Planck approximation.- State of minimum entropy production.- Entropy generation in the approach to the steady-state.- Closure of the moment transport equations.- Non-homogenous transport equation.- Example calculations.- Areas for further study.
