Mechanisms of the equilibrium-range formation in the wind-wave spectrum. Numerical simulation

TL;DR

This paper uses direct numerical simulation to investigate how the equilibrium range in wind-wave spectra forms, emphasizing the balance of wind input and dissipation mechanisms in establishing the spectrum's stationary part.

Contribution

It demonstrates that the equilibrium part of the wind-wave spectrum can be prescribed by balancing wind input and dissipation, using modified parametrizations and exact kinetic integral calculations.

Findings

Balance of wind input and dissipation forms the stationary spectrum.

Proper parametrizations allow prescribing the equilibrium spectrum.

Exact calculation of the Hasselmann integral enhances simulation accuracy.

Abstract

The issue of the equilibrium-range formation in the wind-wave spectrum is studied by a direct numerical simulation. The evolution equation of wind-wave spectrum is numerically solved with using an exact calculation of the Hasselmann kinetic integral and involving various modifications of known parametrizations for the wave-pumping mechanism due to wind and the wave-dissipation mechanism due viscosity of the upper layer. It is shown that the balance of the last two mechanisms is responsible for a formation of stationary part of the wind-wave spectrum. This balance allows establishing any prescribed form of the equilibrium part of the spectrum, if the proper representations of input and dissipation mechanisms are chosen.