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Instability by weak precession of the flow in a rotating sphere

Thursday 26th July 2012 - 14:00 to 14:40
INI Seminar Room 1
Session Chair: 
Marie Farge
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 precession, 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 of the precession and spin angular velocities, that with weak precession of Gamma of order Re^{-1/2} destabilizes the disturbances by the coupling between an symmetric (with respect to the spin axis) mode and (2,1,1) mode through "the conical shear layers" emanating from the critical circles along the sphere boundary. It is found the critical curve for the instability behaves as Gamma = $7.9 Re^{-0.5}$ asymptotically, which agrees well with an observation in an precessing spheroid of ellipticity $0.9$ by Goto {\it et al.} (2011).
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons