  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.
