Symmetry Induced 4-Wave Capillary Wave Turbulence

TL;DR

This paper investigates 4-wave capillary wave turbulence in a symmetric two-fluid system, combining theoretical Hamiltonian analysis with experiments using water and silicon oil, revealing a specific wave spectrum and confirming theoretical predictions.

Contribution

It presents the first combined theoretical and experimental study of symmetry-induced 4-wave capillary wave turbulence in a two-fluid system with nearly equal densities.

Findings

Observed a Kolmogorov-Zakharov spectrum n_k ~ k^{-4}

Experimental PSD and PDF match theoretical predictions

Validated Hamiltonian formulation for symmetric two-fluid wave systems

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.