Observation of the nonlinear dispersion relation and

spatial statistics of wave turbulence on the surface of a fluid

E. Herbert1, N. Mordant2 & E. Falcon1
1MSC, University Paris Diderot, CNRS - UMR 7057, 75 013 Paris, France
2LPS, Ecole Normale Supérieure, CNRS, 75 005 Paris, France


Physical Review Letters 105, 144502 (2010)

DOI: 10.1103/PhysRevLett.105.144502


We report experiments on gravity-capillary wave turbulence on the surface of a fluid. The wave amplitudes are measured simultaneously in time and space using an optical method. The full space-time power spectrum shows that the wave energy is localized on several branches in the wave-vector-frequency space. The number of branches depend on the power injected within the waves. The measurement of the nonlinear dispersion relation is found to be well described by a law suggesting that the energy transfer mechanisms involved in wave turbulence are not only restricted to purely resonant interaction between nonlinear waves. The power-law scaling of the spatial spectrum and the probability distribution of the wave amplitudes at a given wave number are also measured and compared to the theoretical predictions.

PACS : 47.35.+i  -  05.45.-a  - 47.52.+j

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