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 $z\to -z$, 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.

• Received 5 June 2008

DOI:https://doi.org/10.1103/PhysRevLett.103.174503