Journal of Fluid Mechanics

Papers

Weak compressibility of surface wave turbulence

MARIJA VUCELJAa1 and ITZHAK FOUXONa1a2

a1 Physics of Complex Systems, Weizmann Institute of Science, Rehovot, 76100, Israel

a2 Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem, 91904, Israel

Abstract

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)

Metrics