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The Rotation of a Gravitating Sphere in a Monatomic Gas, II
Author(s) -
Foster M. R.
Publication year - 1970
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1970493259
Subject(s) - prandtl number , boundary layer , rotation (mathematics) , mechanics , hydrostatic equilibrium , physics , classical mechanics , plane (geometry) , monatomic gas , jet (fluid) , flow (mathematics) , boundary layer thickness , monatomic ion , boundary (topology) , geometry , convection , mathematics , mathematical analysis , quantum mechanics
The purpose of this work is to study the fluid motion caused by the high speed rotation of a gravitating sphere in a monatomic gas. It has been possible to find a stable steady solution only for very small Prandtl number, which can be interpreted to mean an optically thick gas. The flow is characterized by a flat radial jet in the equatorial plane and a viscous boundary layer on the spherical surface which, in some cases, lies beneath a thermal boundary layer. That the outer region must be hydrostatic puts very stringent constraints on the associated velocity field which necessitate still another boundary layer on the sphere. This last layer is shown to be unstable to small disturbances in certain temperature ranges. Finally, a similar solution that exists for order one Prandtl number must be disregarded because this last boundary layer is always unstable.