Wave turbulence served up on a plate

TL;DR

This study experimentally investigates wave turbulence in a thin elastic plate using Fourier transform profilometry, revealing that the energy concentrates on a nonlinear dispersion surface close to the linear relation, with deviations linked to nonlinear effects.

Contribution

The paper introduces a novel experimental technique to measure the full space-time deformation field, enabling detailed analysis of wave turbulence spectra and validation of theoretical dispersion relations.

Findings

Energy concentrates on a 2D surface in ($ extbf{k}, oldsymbol{ extomega}$) space.

The nonlinear dispersion relation closely matches the linear one, validating common analysis methods.

Deviations from linearity increase with input power, indicating weak nonlinear effects.

Abstract

Wave turbulence in a thin elastic plate is experimentally investigated. By using a Fourier transform profilometry technique, the deformation field of the plate surface is measured simultaneously in time and space. This enables us to compute the wavevector-frequency Fourier ($\mathbf k, \omega$) spectrum of the full space-time deformation velocity. In the 3D ($\mathbf k, \omega$) space, we show that the energy of the motion is concentrated on a 2D surface that represents a nonlinear dispersion relation. This nonlinear dispersion relation is close to the linear dispersion relation. This validates the usual wavenumber-frequency change of variables used in many experimental studies of wave turbulence. The deviation from the linear dispersion, which increases with the input power of the forcing, is attributed to weak non linear effects. Our technique opens the way for many new extensive quantitative comparisons between theory and experiments of wave turbulence.