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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Numerical and analytical study of an asymptotic eq
uation for deformation of vortex lattices - Ohkita
ni\, K\, Al Sulti\, F (University of Sheffield)
DTSTART;TZID=Europe/London:20120723T171000
DTEND;TZID=Europe/London:20120723T173000
UID:TALK39017AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/39017
DESCRIPTION:It is known that when two-dimensional flows are su
bject to a suitable background rotation\, formatio
n of vortex lattices are observed. We can make use
of critical points of the vorticity field and the
ir connectivity (so-called\, surface networks) to
study reconnection of vorticity contours in 2D tur
bulence. In this talk we begin by noting how this
method applies to the study of formation of vortex
lattices. \n\nWe then study a coarse-grained\, as
ymptotic equation which describes deformation vort
ex lattices derived by Smirnov and Chukbar\, Sov.
Phys. JETP vol 93\, 126-135(2001). It reads $phi_t
=phi_{xx} phi_{yy}-phi_{xy}^2\,$ where $phi$ denot
es displacement of vortex locations. This equation
is particularly valid for geostrophic Bessel vort
ices with a screened interaction. \n\nNumerical re
sults are reported which indicate an ill-posed nat
ure of the time evolution. Self-similar blow-up so
lutions were already given by those authors\, whic
h have an infinite total energy. We ask whether fi
nite-time blow-up can take place developing from s
mooth initial data with a finite energy. More gene
ral self-similar blow-up solutions are sought\, bu
t all are found to have infinite total energy. Fin
ally\, remarks are made in connection with the Tka
chenko-type lattice.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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