Abstract
Various mechanisms of nonlinear saturation of water wave growth under the action of a light wind are discussed. The unstable wind may be saturated by nonlinear dissipation due to the energy transfer to the damping harmonics of the wave. Other nonlinear saturation mechanisms: nonlinear frequency shift, self-modulation or self-focusing of a wave packet may be effective in certain wavenumber regions. In case the wind speed is close to the critical one, an equation is derived for the complex wave amplitude. This equation describes all these nonlinear effects in near-critical systems. In the one-dimensional case this is the nonlinear Shrodinger equation with complex coefficients. Its solutions under various conditions are discussed.
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