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Nonlinear waves on the surface of a fluid covered by an elastic sheet

Published online by Cambridge University Press:  23 September 2013

Luc Deike*
Affiliation:
Université Paris Diderot, Sorbonne Paris Cité, MSC, UMR 7057 CNRS, F-75 013 Paris, France
Jean-Claude Bacri
Affiliation:
Université Paris Diderot, Sorbonne Paris Cité, MSC, UMR 7057 CNRS, F-75 013 Paris, France
Eric Falcon
Affiliation:
Université Paris Diderot, Sorbonne Paris Cité, MSC, UMR 7057 CNRS, F-75 013 Paris, France
*
Email address for correspondence: luc.deike@univ-paris-diderot.fr

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.

Type
Papers
Copyright
©2013 Cambridge University Press 

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