The self-consistent theory of the wind-driven sea is absolutely challenging problem for the scientist and is extremely important for the practical needs of weather broadcasting. The analytic theory of wind-driven sea can be developed due to the presence of natural small parameter ( are air and water densities). As a result, the average steepness of wind-driven waves, η)2>( is the shape of the surface), is small: The steepness μ is the measure of wave nonlinearity. The smallness of μ means that the average level of nonlinearity is low. Even in the situation of strong storm the wind-driven sea is basically weakly nonlinear. This weakly nonlinear sea is seeded by ”islands” of strong nonlinearity - the zones of ”white capping”, where the energy of dissipation takes place. This dissipation compensates the flux of energy from the wind.
In spite of presence of energy pumping from the wind and its dissipation in the white cap zones, the leading physical process in the wind-driven sea is the nonlinear interaction between waves with different wave vectors. This process provides the energy distribution along the spectrum and formation of quasistationary universal spectra, which depend on some parameters defined by the strength and the direction of the wind. These spectra can be studied by analytical methods, starting from the basic mathematical model of the sea. This model is based on the Euler equation for potential flow of incompressible fluid in the presence of the free surface. This is the Hamiltonian system described by an efficient Hamiltonian, which can be expressed in terms of complex canonical variables for propogating waves ak. The Hamiltonian H
is the standard ”collision term”, and are ”source functions” describing the energy flux from the wind and the dissipation due to wave capping. They should be determined empirically by matching with experimental data.
The kinetic equation has important stationary and self-similar solutions that can be found partly analytically, partly numerically. It admits on-line numerical simulation.
The results obtained by our group explain the majority of data accumulated during decades in field observations and wave-tank experiments. They make possible to create the operational model for prediction of the ”wave climate” in the costal area or in the scale of the ocean.