The Phillips spectrum and a model of wind-wave dissipation

We consider an extension of the kinetic equation developed by Newell and Zakharov in 2008. The new equation takes not only the resonant four-wave interactions but also the dissipation associated with the wave breaking into account. In the equation, we introduce a dissipation function that depends on the spectral energy flux. This function is determined up to a functional parameter, which should be optimally chosen based on a comparison with experiment. A kinetic equation with this dissipation function describes the usually experimentally observed transition from the Kolmogorov–Zakharov spectrum $E(\omega)\sim\omega^{-4}$ to the Phillips spectrum $E(\omega)\sim \omega^{-5}$. The version of the dissipation function expressed in terms of the energy spectrum can be used in problems of numerically modeling and predicting sea waves.