The Phillips spectrum and a model of wind-wave dissipation

S. I. Badulin, V. E. Zakharov

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1 Citation (Scopus)


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(ω) ~ ω−4 to the Phillips spectrum E(ω) ~ ω−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.

Original languageEnglish
Pages (from-to)309-318
Number of pages10
JournalTheoretical and Mathematical Physics
Issue number3
Publication statusPublished - 1 Mar 2020


  • kinetic (Hasselmann) equation for water waves
  • Kolmogorov-Zakharov spectrum
  • Phillips spectrum


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