Space-Time Resolved Wave Turbulence in a Vibrating Plate

COBELLI, PABLO JAVIER; PETITJEANS, PHILIPPE; MAUREL, AGNES; PAGNEUX, VINCENT; MORDANT, NICOLAS

PHYSICAL REVIEW LETTERS

AMER PHYSICAL SOC

Año: 2009 vol. 103 p. 2043011 - 2043014

0031-9007

Wave turbulence in a thin elastic plate is experimentally investigated. By using a Fourier transform pro- filometry technique, the deformation field of the plate surface is measured simultaneously in time and space. This enables us to compute the wave-vector-frequency (k, w) Fourier spectrum of the full space-time deformation velocity. In the 3D (k, w) 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 wave-number-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 nonlinear effects. Our technique opens the way for many new extensive quantitative comparisons between theory and experiments of wave turbulence.