Fluctuations of the Energy Flux in Wave Turbulence

S. Aumaître, E. Falcon & S. Fauve
SPEC, DSM, CEA-Saclay, CNRS, 91 191 Gif-sur-Yvette, France, UE
Univ Paris Diderot, Sorbonne Cité, MSC, CNRS, UMR 7057, F-75 013 Paris, France, UE
LPS, ENS Paris, CNRS, 24 rue Lhomond, 75 005 Paris, France, UE


"Advances in Wave Turbulence", Chapter 2, pp. 53-72 (World Scient. Series on Nonlinear Series A, Vol. 83, V. Shrira  & S. Nazarenko Eds, 2013)

URL: http://www.worldscientific.com/worldscibooks/10.1142/8269
ISBN: 978-981-4366-93-9


The key governing parameter of wave turbulence is the energy flux that drives the waves and cascades to small scales through nonlinear interactions. In the inertial range, the energy flux is conserved across the scales, and is assumed to be constant in most theoretical approaches. It is only recently that measurements of the injected power into wave turbulence have been performed at the scale of the wave maker (integral scale). In this review, we focus on the statistical properties of the injected power fluctuations in gravity-capillary wave turbulence in a stationary regime. Fluctuations of the injected power have been found much larger than their mean value. In addition, events related to a negative injected power, i.e. an instantaneous reversed energy flux, occur with a fairly large probability. Both features are well described using a Langevin type equation. Finally, we consider the experimental dependence of the scaling law of the wave spectrum with the mean injected power and discuss possible reasons for the discrepancy with weak turbulence theory..

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Advances in Wave Turbulence

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