### Abstract

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 language | English (US) |
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Pages (from-to) | 309-318 |

Number of pages | 10 |

Journal | Theoretical and Mathematical Physics(Russian Federation) |

Volume | 202 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1 2020 |

### Keywords

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

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

*Theoretical and Mathematical Physics(Russian Federation)*,

*202*(3), 309-318. https://doi.org/10.1134/S0040577920030034