Abstract:
We experimentally study
linear and nonlinear waves on the surface of a fluid covered by
an elastic sheet where both tension and flexural waves occur. An
optical method is used to obtain the full space–time wave field,
and the dispersion relation of the 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 scales, a regime of
hydroelastic 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.