# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1701.05351