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SUMMARY:Numerical and analytical study of an asymptotic equation for defor
 mation of vortex lattices - Ohkitani\, K\, Al Sulti\, F (University of She
 ffield)
DTSTART:20120723T161000Z
DTEND:20120723T163000Z
UID:TALK39017@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:It is known that when two-dimensional flows are subject to a s
 uitable background rotation\, formation of vortex lattices are observed. W
 e can make use of critical points of the vorticity field and their connect
 ivity (so-called\, surface networks) to study reconnection of vorticity co
 ntours in 2D turbulence. In this talk we begin by noting how this method a
 pplies to the study of formation of vortex lattices. \n\nWe then study a c
 oarse-grained\, asymptotic equation which describes deformation vortex lat
 tices derived by Smirnov and Chukbar\, Sov. Phys. JETP vol 93\, 126-135(20
 01). It reads $phi_t=phi_{xx} phi_{yy}-phi_{xy}^2\,$ where $phi$ denotes d
 isplacement of vortex locations. This equation is particularly valid for g
 eostrophic Bessel vortices with a screened interaction. \n\nNumerical resu
 lts are reported which indicate an ill-posed nature of the time evolution.
  Self-similar blow-up solutions were already given by those authors\, whic
 h have an infinite total energy. We ask whether finite-time blow-up can ta
 ke place developing from smooth initial data with a finite energy. More ge
 neral self-similar blow-up solutions are sought\, but all are found to hav
 e infinite total energy. Finally\, remarks are made in connection with the
  Tkachenko-type lattice.\n
LOCATION:Seminar Room 1\, Newton Institute
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