Evolution of Spectra for Mechanical and Wind Waves in a Large Tank

TL;DR

This study analyzes the evolution of wave spectra in a large tank, showing that both mechanical and wind waves develop spectra with specific tail decays, supported by empirical data and numerical solutions, revealing insights into wave dynamics.

Contribution

It provides new empirical spectra measurements for mechanical and wind waves and demonstrates their evolution aligns with theoretical models and numerical solutions, highlighting the natural evolution of nonlinear surface waves.

Findings

Mechanical wave spectra evolve to S(f) ~ f^-4.2 at high steepness.

Wind wave spectra develop to S(f) ~ f^-4.0 at large fetches.

Spectral tail intensities follow a modified Toba ratio involving wind speed and fetch.

Abstract

Empirical spectra for mechanical and wind waves measured in a large tank of the First Institute of Oceanography of China are presented. Analysis for the first and the second type of waves is done separately. It is shown that, in the case of mechanical waves with a steepness more than 0.2, the frequency spectra of waves evolve to ones with the tail decay S(f) ~ (f to power -4.2), whilst the shape of spectra at large fetches is self-similar. Numerical solutions of the four-wave kinetic equation, written in the fetch-limited version, result in the same spectra. This allows treating the empirical observations for mechanical waves as the natural evolution of free nonlinear surface waves. In the case of wind waves, the wave spectra evolve to ones with the tail decay S(f) ~ (f to power -4.0) at fetches X greater than 8 meters, under any applied winds. The well-known Toba three-second relation, H ~ (T to power 3/2), between the mean wave height, H, and the peak period, T, is well fulfilled. Though, the intensities of spectra tails do not follow the Toba ratio, S(f) ~ (gu)(f to power -4), rather they better correspond to the ratio , S(f) ~ ((u to power 2)/Xg)(to power p)(gu)(f to power -4) with p = 1/3. Moreover, the shape of the wind-wave spectra is not self-similar. Discussion of the results is presented.