Spectral Theory for Dissipation Mechanism of Wind Waves

TL;DR

This paper develops a spectral theory for wind wave dissipation, emphasizing viscosity and turbulence interactions, and validates the model with numerical simulations showing improved accuracy over existing models.

Contribution

It introduces a new spectral dissipation mechanism model based on viscosity and turbulence, validated through numerical models like WAM and WAEWATCH.

Findings

The dissipation function is a power series starting from quadratic terms.

The proposed model shows superior performance in numerical simulations.

The theory aligns with recent experimental findings in wind wave research.

Abstract

A systematic and full description of the theory for a dissipation mechanism of wind wave energy in a spectral representation is given. As a basis of the theory, the fundamental is stated that the most general dissipation mechanism for wind waves is provided by the viscosity due to interaction between wave motions and turbulence of the water upper layer. The latter, in turn, is supposed to be induced by the whole aggregate of dissipation processes taking place at the air-sea interface. In the frame of phenomenological constructions of nonlinear closure for Reynolds stresses, it is shown that the dissipation function is generally a power series with respect to wave spectrum, starting from a quadratic term. Attracting previous results of the author, a simplified parameterization of the general theoretical result is done. Physical meaning for parameters of the dissipation function and its compliance with the new experimental facts established in this field for the last 5-10 years is discussed. Summarized theoretical results were verified in the mathematical shells of the well known numerical models for wind waves, WAM and WAEWATCH. Evidence is given, illustrating a superiority of the proposed model modifications. Prospects for elaboration of the theory are discussed.