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Weak compressibility of surface wave turbulence

Published online by Cambridge University Press:  23 November 2007

MARIJA VUCELJA and
ITZHAK FOUXON
MARIJA VUCELJA
Affiliation:
Physics of Complex Systems, Weizmann Institute of Science, Rehovot, 76100, Israel
ITZHAK FOUXON
Affiliation:
Physics of Complex Systems, Weizmann Institute of Science, Rehovot, 76100, IsraelRacah Institute of Physics, Hebrew University of Jerusalem, Jerusalem, 91904, Israel
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Abstract

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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.

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 593 , 25 December 2007, pp. 281 - 296
Copyright
Copyright © Cambridge University Press 2007

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