Symmetry Induced 4-Wave Capillary Wave Turbulence

Abstract

We report theoretical and experimental results on 4-wave capillary wave turbulence. A system consisting of two inmiscible and incompressible fluids of the same density can be written in a Hamiltonian way for the conjugated pair $(\eta ,\Psi )$. When given the symmetry $z\to -z$, the set of weakly non-linear interacting waves display a Kolmogorov-Zakharov (KZ) spectrum $n_k\sim k^{-4}$ in wave vector space. The wave system was studied experimentally with two inmiscible fluids of almost equal densities (water and silicon oil) where the capillary surface waves are excited by a low frequency random forcing. The power spectral density (PSD) and probability density function (PDF) of the local wave amplitude are studied. Both theoretical and experimental results are in fairly good agreement with each other.

6 pages, 2 figures

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• Gravity surface wave turbulence in a laboratory flume
• Observation of wave turbulence in vibrating plates
• Observation of intermittency in wave turbulence
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Cited by in corpus (11)

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• Numerical Simulation of Collinear Capillary-Wave Turbulence
• Wave turbulence in a two-layer fluid: coupling between free surface and interface waves
• Turbulence of capillary waves forced by steep gravity waves
• Capillary wave turbulence experiments in microgravity
• Self-similar formation of an inverse cascade in vibrating elastic plates
• An exact result in strong wave turbulence of thin elastic plates
• Phenomenological model for predicting stationary and non-stationary spectra of wave turbulence in vibrating plates
• Path integral description and direct interaction approximation for elastic plate turbulence