The Phillips spectrum and a model of wind-wave dissipation

S. I. Badulin, V. E. Zakharov

Research output: Contribution to journalArticlepeer-review


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 (US)
Pages (from-to)309-318
Number of pages10
JournalTheoretical and Mathematical Physics(Russian Federation)
Issue number3
StatePublished - Mar 1 2020


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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Fingerprint Dive into the research topics of 'The Phillips spectrum and a model of wind-wave dissipation'. Together they form a unique fingerprint.

Cite this