Observation of nonlinear dispersion relation and spatial statistics of wave turbulence on the surface of a fluid

Eric Herbert (1) , Nicolas Mordant (2) , Eric Falcon (1)

1 MSC - Matière et Systèmes Complexes
2 LPS - Laboratoire de Physique Statistique de l'ENS

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.

Domaines: Dynamique des Fluides [physics.flu-dyn]; Dynamique Chaotique [nlin.CD]; Autre [cond-mat.other]; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Eric Herbert, Nicolas Mordant, Eric Falcon. Observation of nonlinear dispersion relation and spatial statistics of wave turbulence on the surface of a fluid. Physical Review Letters, 2010, 105 (14), pp.144502. ⟨10.1103/PhysRevLett.105.144502⟩. ⟨hal-00482731v2⟩