The Phillips spectrum and a model of wind-wave dissipation

TL;DR

This paper extends the kinetic wave equation to include wave breaking dissipation, enabling better modeling of the transition from turbulence spectra to the Phillips spectrum observed in experiments.

Contribution

It introduces a dissipation function dependent on spectral energy flux into the kinetic equation, improving wave modeling accuracy.

Findings

The extended equation models the transition from Kolmogorov-Zakharov to Phillips spectrum.

The dissipation function can be expressed in terms of the energy spectrum for practical use.

The model aligns with experimental observations of wave spectrum transitions.

Abstract

We consider an extension of the kinetic equation developed by Newell & Zakharov (A.C. Newell and V.E. Zakharov. The role of the generalized Phillips' spectrum in wave turbulence. Phys.Lett.A, 372:4230-4233, 2008). The new equation takes into account not only the resonant four-wave interactions but also the dissipation associated with the wave breaking. A dissipation function that depends on the spectral energy flux is introduced into the equation. This function is determined up to a functional parameter, which optimal choice should be made based on comparison with the experiment. A kinetic equation with this dissipation function describes the transition from the Kolmogorov-Zakharov spectrum to the Phillips spectrum usually observed experimentally. The version of the dissipation function expressed in terms of the energy spectrum can be used for wave modeling and prediction of sea waves.