The Phillips spectrum and a model of wind-wave dissipation

S. I. Badulin   ; V. E. Zakharov

Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 3, pp. 353-363

Résumé

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.

Détail

Keywords: Phillips spectrum, kinetic (Hasselmann) equation for water waves, Kolmogorov–Zakharov spectrum.

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