Fourier analysis of wave turbulence in a thin elastic plate

TL;DR

This study uses high-speed Fourier transform profilometry to analyze wave turbulence in a vibrating elastic plate, finding qualitative agreement with Weak Turbulence theory but noting some quantitative discrepancies likely due to dissipation effects.

Contribution

It provides experimental evidence of wave turbulence behavior in elastic plates and measures the spectral properties, including dispersion relation and nonlinearity, contributing to the understanding of wave turbulence in elastic media.

Findings

Isotropic continuous wave spectrum observed

Nonlinear dispersion relation slightly shifted from linear theory

Quantitative mismatch possibly due to dissipation effects

Abstract

The spatio-temporal dynamics of the deformation of a vibrated plate is measured by a high speed Fourier transform profilometry technique. The space-time Fourier spectrum is analyzed. It displays a behavior consistent with the premises of the Weak Turbulence theory. A isotropic continuous spectrum of waves is excited with a non linear dispersion relation slightly shifted from the linear dispersion relation. The spectral width of the dispersion relation is also measured. The non linearity of this system is weak as expected from the theory. Finite size effects are discussed. Despite a qualitative agreement with the theory, a quantitative mismatch is observed which origin may be due to the dissipation that ultimately absorbs the energy flux of the Kolmogorov-Zakharov casade.