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SUMMARY:Thresholds for the formation of satellites in two--dimensional vor
 tices - Turner\, M (Exeter)
DTSTART:20081001T105000Z
DTEND:20081001T111000Z
UID:TALK13854@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We examine the evolution of a two--dimensional vortex which in
 itially consists of an axisymmetric monopole vortex with a perturbation of
  azimuthal wavenumber m=2 added to it. If the perturbation is weak then th
 e vortex returns to an axisymmetric state and the non--zero Fourier harmon
 ics generated by the perturbation decay to zero. However\, if a finite per
 turbation threshold is exceeded\, then a persistent nonlinear vortex struc
 ture is formed. This structure consists of a coherent vortex core with two
  satellites rotating around it.\n\nWe consider the formation of these sate
 llites by taking an asymptotic limit in which a compact vortex is surround
 ed by a weak skirt of vorticity. The resulting equations match the behavio
 ur of a normal mode riding on the vortex with the evolution of fine--scale
  vorticity in a critical layer inside the skirt. Three estimates of invisc
 id thresholds for the formation of satellites are computed and compared: t
 wo estimates use qualitative diagnostics\, the appearance of an inflection
  point or neutral mode in the mean profile. The other is determined quanti
 tatively by solving the normal mode/critical--layer equations numerically.
  These calculations are supported by simulations of the full Navier--Stoke
 s equations using a family of profiles based on the tanh function. 
LOCATION:Seminar Room 1\, Newton Institute
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