Experimental study of the inverse cascade in gravity wave turbulence

Univ Paris Diderot, Sorbonne Paris Cité, MSC, UMR 7057 CNRS - F-75 013 Paris, France, EU

^a luc.deike@univ-paris-diderot.fr
^b eric.falcon@univ-paris-diderot.fr

Received: 14 June 2011
Accepted: 15 September 2011

Abstract

We perform experiments to study the inverse-cascade regime of gravity wave turbulence on the surface of a fluid. Surface waves are forced at an intermediate scale corresponding to the gravity capillary wavelength. In response to this forcing, waves at larger scales are observed. The spectrum of their amplitudes exhibits a frequency power law at high enough forcing. Both observations are ascribed to the upscale wave action transfers of gravity wave turbulence. The spectrum exponent is close to the value predicted by the weak-turbulence theory. The spectrum amplitude is found to scale linearly with the mean injected power. We measure also the distributions of the injected power fluctuations in the presence of upscale (inverse) transfers or in the presence of a downscale (direct) cascade in gravity wave turbulence.