Symmetry Induced Four-Wave Capillary Wave Turbulence

Abstract

We report theoretical and experimental results on 4-wave capillary wave turbulence. A system consisting of two immiscible and incompressible fluids of the same density can be written in a Hamiltonian way for the conjugated pair (eta, Psi). Adding the symmetry z --> -z, the set of capillary waves display a Kolmogorov-Zakharov spectrum k(-4) in wave vector space and f(-8/3) in the frequency domain. The wave system is studied experimentally with two immiscible fluids of almost equal densities (water and silicon oil) where the capillary surface waves are excited by a low-frequency random forcing. The probability density function of the local wave amplitude shows a quasi-Gaussian behavior and the power spectral density is shows a power-law behavior in frequency with a slope of -2.75. Theoretical and experimental results are in fairly good agreement with each other.