Eur. Phys. J. B 76, 537-545 (2010)
https://doi.org/10.1140/epjb/e2010-00197-y

Fourier analysis of wave turbulence in a thin elastic plate

Laboratoire de Physique Statistique, École Normale Supérieure & CNRS, 24 rue Lhomond, 75005 Paris, France

Corresponding author: ^a nmordant@ens.fr

Received: 18 March 2010
Revised: 28 May 2010
Published online: 29 June 2010

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.