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SUMMARY:Instability by weak precession of the flow in a rotating sphere - 
 Kida\, S (Kyoto University)
DTSTART:20120726T130000Z
DTEND:20120726T134000Z
UID:TALK39073@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The linear stability analysis is performed of the steady flow 
 in a weakly precessing sphere of rapid rotaion. It is well-known that all 
 the disturbances damp with decay rate proportional to Re^{-1/2} without pr
 ecession\, where Re is the Reynolds number defined by the sphere radius\, 
 the the spin angular velococity\, and the kinematic viscosity of fluid. We
  show by an asymptotic analysis for large Re and small Gamma\, the ratio o
 f the precession and spin angular velocities\, that with weak precession o
 f Gamma of order Re^{-1/2} destabilizes the disturbances by the coupling b
 etween an symmetric (with respect to the spin axis) mode and (2\,1\,1) mod
 e through "the conical shear layers" emanating from the critical circles a
 long the sphere boundary. It is found the critical curve for the instabili
 ty behaves as Gamma = 7.9 Re^{-0.5}$ asymptotically\, which agrees well wi
 th an observation in an precessing spheroid of ellipticity $0.9$ by Goto {
 it et al.} (2011).\n
LOCATION:Seminar Room 1\, Newton Institute
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