Weak compressibility of surface wave turbulence
Chaotic Dynamics
2012-10-23 v1 Fluid Dynamics
Geophysics
Abstract
We study the growth of small-scale inhomogeneities of the density of particles floating in weakly nonlinear, small-amplitude, surface waves. Despite the amplitude smallness, the accumulated effect of the long-time evolution may produce strongly inhomogeneous distribution of the floaters: density fluctuations grow exponentially with a small but finite exponent. We show that the exponent is of sixth or higher order in wave amplitude. As a result, the inhomogeneities do not form within typical time-scales of the natural environment. We conclude that turbulence of surface waves is weakly compressible and alone it cannot be a realistic mechanism of the clustering of matter on liquid surfaces.
Cite
@article{arxiv.nlin/0703019,
title = {Weak compressibility of surface wave turbulence},
author = {M. Vucelja and I. Fouxon},
journal= {arXiv preprint arXiv:nlin/0703019},
year = {2012}
}