Analytic Theory of WindDriven Sea
Abstract
Winddriven sea is characterized by the spatial energy spectrum E(k), k  is a wave vector. The spectrum has a sharp maximum at k ≈ kp is defined by the wind velocity U and by the "waveage"  degree of the sea development. For the"well developed sea" kp ≈ g/U2. For a typical value of U ≈ 15 m/sec (moderate gale) λp = 2π/kp≈ 100m. The minimalscale λcap < 103m, thus λp/λcap ≈ 105. Obviously, the winddriven sea needs its statistical description. The wholekspace can be separated in two main regions:1. Energycapacitive region λp > λ > λcrit, λcrit ≈ 102λp. This range of scales contains more then 90% of wave energy. Wave dissipation in this range is negligibly small.2. Region of energy dissipation λ < λcrit. This region contains no more than 10% of wave energy but provides dissipation of all wave energy.If the wind velocity is smooth U < 5m/sec, the sea is also smooth and the dissipation is provided by transformation of gravity waves to capillary waves. For strong winds the dissipation is realized due to wave breaking. In this case one can observe the range of scales 5•102m < λ < λcrit which can be called " the Phillips sea". The main message of this lecture is the following. The most interesting energycapacitive range of wave scales can be selfconsistently discribed by the method of theoretical physics. The statistical description of this part of the wind driven sea is described by the Hasselmann kinetic equation for the energy spectrum. This kinetic equation has a rich family of exact solutions, both stationary and timedependent. It allows a comfortable and fast numerical simulations. Putting together results of the analytical theory and numerical simulations of waves it is possible to explain a bulk of facts, accumulated by experimentalists for decades.
 Publication:

AGU Fall Meeting Abstracts
 Pub Date:
 December 2016
 Bibcode:
 2016AGUFMNG33C..01Z
 Keywords:

 4420 Chaos;
 NONLINEAR GEOPHYSICS