On Dissipation Function of Ocean Waves due to Whitecapping

The Hasselmann kinetic equation [1] provides a statistical description of waves ensemble. Several catastrophic events are beyond statistical model. In the case of gravity waves on the surface of the deep fluid may be the most frequent and important events of such kind are whitecapping and wave breaking. It was shown earlier that such effects leads to additional dissipation in the energy contaning region around waves spectral peak, which can be simulated by means of empiric dissipative term in kinetic equation. In order to find dependence of this term with respect to nonlinearity in the system (steepness of the surface) we preformed two numerical experiments: weakly nonlinear one in the framework of 3D hydrodynamics and fully nonlinear one for 2D hydrodynamic. In spite of significantly different models and initial conditions, both these experiments yielded close results. Obtained data can be used to define analytical formula for dependence of the dissipative term of dissipation coefficient with respect to mean steepness of the surface.