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
(η,Ψ). When given the symmetry z→−z, the set of weakly non-linear
interacting waves display a Kolmogorov-Zakharov (KZ) spectrum nk∼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.Comment: 6 pages, 2 figure