We experimentally study linear and nonlinear waves on the surface of a fluid
covered by an elastic sheet where both tension and flexural waves take place.
An optical method is used to obtain the full space-time wave field, and the
dispersion relation of waves. When the forcing is increased, a significant
nonlinear shift of the dispersion relation is observed. We show that this shift
is due to an additional tension of the sheet induced by the transverse motion
of a fundamental mode of the sheet. When the system is subjected to a random
noise forcing at large scale, a regime of hydro-elastic wave turbulence is
observed with a power-law spectrum of the scale in disagreement with the wave
turbulence prediction. We show that the separation between relevant time scales
is well satisfied at each scale of the turbulent cascade as expected
theoretically. The wave field anisotropy, and finite size effects are also
quantified and are not at the origin of the discrepancy. Finally, the
dissipation is found to occur at all scales of the cascade contrary to the
theoretical hypothesis, and could thus explain this disagreement.Comment: Journal of Fluid Mechanics (2013
