a1 Physics of Complex Systems, Weizmann Institute of Science, Rehovot, 76100, Israel
a2 Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem, 91904, Israel
We study the growth of small-scale inhomogeneities in the density of particles floating in weakly nonlinear small-amplitude surface waves. Despite the small amplitude, the accumulated effect of the long-time evolution may produce a 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 the turbulence of surface waves is weakly compressible and alone it cannot be a realistic mechanism of the clustering of matter on liquid surfaces.
(Received March 12 2007)
(Revised August 23 2007)