Numerical studying mechanics of a stationary range formation in the wind-wave spectrum

TL;DR

This study numerically investigates the formation of stationary ranges in wind-wave spectra, revealing the absence of inertial intervals and emphasizing the importance of input-dissipation ratios in spectrum formation.

Contribution

It provides a detailed numerical analysis of the wind-wave spectrum formation, challenging the existence of inertial intervals and clarifying the role of input and dissipation mechanisms.

Findings

No inertial interval exists in real wind wave spectra.

The input-dissipation ratio governs stationary spectrum formation.

Proper modeling of input and dissipation reproduces known spectral forms.

Abstract

The process of a stationary range formation in the wind-wave spectrum is investigated numerically. The evolution equation for the two-dimensional wind-wave spectrum is numerically solved by using an exact calculation of the Hasselmann kinetic integral with exploring several parametrizations for the wave-pumping and wave-dissipation mechanisms. The following results are established. First, there is no any inertial interval in the spectral frequency band of real wind waves. Therefore, there is no reason for the Kolmogorov-type spectra formation in this case. Second, the ratio between the input and dissipation mechanisms is responsible for a stationary range formation in the wind-wave spectrum. Third, this ratio enables us to establish all known forms for a stationary range of the spectrum, if proper mathematical representations for the input and dissipation mechanisms are chosen.