Technion - Israel Institute of Technology
 
Department of Mathematics
 
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                        PDE AND APPLIED MATHEMATICS SEMINAR
 
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DATE: Tuesday, January 18, 2011
 
SPEAKER: Marija Vucelja, NYU
 
TITLE: Weak compressibility of surface wave turbulence
 
PLACE: Room 814, Amado Mathematics Building, Technion
 
TIME: 14:30
 
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Abstract:
 
Clustering of matter on the surface of lakes and pools and of oil
slicks and seaweed on the sea surface is well-known empirically but
there is no theory that describes it. Since surface flows are always
compressible, such a theory should be based on the description of the
development of density of inhomogeneities in a compressible flow.  We
studied 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 have shown 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. Thus the
turbulence of surface waves is weakly compressible and alone it cannot
be a realistic mechanism of the clustering of matter on liquid
surfaces.
However if besides waves there are also currents, the interplay of
waves with currents, might be in some cases responsible for the
patchiness of the floaters.
 
For further info: Gershon Wolansky,  <gershonw@math.technion.ac.il>
For past and future Applied Math/PDE seminars:
 <http://www.math.technion.ac.il/pde/seminar.html>
 
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Technion Math. Net (TECHMATH)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Gershon Wolansky   <gershonw@math.technion.ac.il>