Limited fetch revisited: comparison of wind input terms, in surface waves modeling

TL;DR

This paper compares different wind input models in numerical simulations of wind-driven surface waves, highlighting the effectiveness of the ZRP model in matching field observations and analyzing the impact of spectral dissipation on wave energy growth.

Contribution

It provides a comprehensive comparison of five source function models, including the novel ZRP model, for solving the Hasselmann kinetic equation in fetch-limited wave growth scenarios.

Findings

ZRP model aligns well with field data since 1947.

Quadruplet wave interactions dominate energy balance.

Spectral peak dissipation limits wave energy growth.

Abstract

Results pertaining to numerical solutions of the Hasselmann kinetic equation (HE), for wind driven sea spectra, in the fetch limited geometry, are presented. Five versions of source functions, including the recently introduced ZRP model, have been studied, for the exact expression of Snl and high-frequency implicit dissipation, due to wave-breaking. Four of the five experiments were done in the absence of spectral peak dissipation for various Sin terms. They demonstrated the dominance of quadruplet wave-wave interaction, in the energy balance, and the formation of self-similar regimes, of unlimited wave energy growth, along the fetch. Between them was the ZRP model, which strongly agreed with dozens of field observations performed in the seas and lakes, since 1947. The fifth, the WAM3 wind input term experiment, used additional spectral peak dissipation and reproduced the results of a previous, similar, numerical simulation, but only supported the field experiments for moderate fetches, demonstrating a total energy saturation at half of that of the Pierson-Moscowits limit. The alternative framework for HE numerical simulation is proposed, along with a set of tests, allowing one to select physically-justified source terms.