Observation of Gravity-Capillary Wave Turbulence

Abstract

We report the observation of the crossover between gravity and capillary wave turbulence on the surface of mercury. The probability density functions of the turbulent wave height are found to be asymmetric and thus non-Gaussian. The surface wave height displays power-law spectra in both regimes. In the capillary region, the exponent is in fair agreement with weak turbulence theory. In the gravity region, it depends on the forcing parameters. This can be related to the finite size of the container. In addition, the scaling of those spectra with the mean energy flux is found in disagreement with weak turbulence theory for both regimes.

Turbulent parametric surface waves

“…Quite recent experiments on directly driven gravitycapillary waves on the surface of mercury were reported by Falcon et al 16 Unlike all previous experiments in this regime of wavelengths, those experiments were noise driven. The surface elevation was measured using a capacitive wire sensor piercing the surface.…”

“…Also the energy input was measured in Ref. 16 but, in contrast to weak wave turbulence, which predicts the power spectral density to be proportional to 1/2 for capillary waves, they found E͑ ͒ϳ . The point signal of surface gradients was found to be strongly non-Gaussian, and anomalous scaling exponents were determined.…”

“…The instrumentation of a point measurement is relatively easy and many frequency spectra of point measurements have been published. [12][13][14][15][16] However, since the spectral energy drops very steeply with increasing frequency, ͓E͑ ͒ϳ −17/6 ͔, the height detector should be linear and should have a large dynamical range.…”

Wave turbulence in magnetized plasmas

“…Wave turbulence is a very common natural phenomenon with applications, for example, in capillary waves (Kolmakov et al, 2004;Abdurakhimov et al, 2008), gravity waves (Falcon et al, 2007), superfluid helium and processes of Bose-Einstein condensation (Kolmakov et al, 1995;Lvov et al, 2003), nonlinear optics (Dyachenko et al, 1992), inertial waves (Galtier, 2003;Morize et al, 2005) or Alfvén waves (Galtier et al, 2000;Kuznetsov, 2001;Chandran, 2005). The most important difference between plasmas and incompressible neutral fluids is the plethora of linear waves supported by the former.…”

Fundamental Research to Support Direct Phase-Resolved Simulation of Nonlinear Ocean Wavefield Evolution

“…We considered the inertial range spectrum of capillary wave turbulence. Recent experimental measurements (Falcon et al 2007) reported a linear scaling of surface elevation spectrum <|η k | 2 > with energy flux P. This is in apparent disagreement with weak turbulence theory (WTT) which predicts <|η k | 2 > ∼ P 1/2 (Zakharov and Filonenko 1967). We conducted a direct numerical investigation of the problem by using SNOW (with a modification for capillarity wave dynamics).…”