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On the motion of liquid in a spheroidal cavity of a precessing rigid body

Published online by Cambridge University Press:  28 March 2006

K. Stewartson  and
P. H. Roberts
K. Stewartson
Affiliation:
Mathematics Research Center, University of Wisconsin, Madison, Wisconsin, U. S. A
Present address: Department of Mathematics, The University of Durham, Durham.
P. H. Roberts
Affiliation:
Yerkes Observatory, Williams Bay, Wisconsin, U. S. A.
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Abstract

The flow set up in an oblate cavity of a precessing rigid body is examined under the assumptions that the ellipticity of the spheroidal boundary of the fluid is large compared with Ω/ω and that the boundary-layer thickness is small compared with the deviations of the boundary from sphericity (ω is the angular velocity of the rigid body about the axis of symmetry, Ω is the angular velocity with which this axis precesses).

The motion of the fluid is found by considering an initial-value problem in which the axis of rotation of the spheroid is impulsively moved at a time t = 0; before that time this axis is supposed to be fixed in space, the fluid and envelope turning about it as a solid body. The solution is divided into a steady motion and transients, and, by evaluating the effects of the viscous boundary layer, the transients are shown to decay with time. The steady motion which remains consists of a primary rigid-body rotation with the envelope, superimposed on which is a circulation with constant vorticity in planes perpendicular to ω × (ω × Ω), the streamlines being similarly situated ellipses.

The possible effects of the luni-solar precession on the fluid motions in the Earth's core are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 17 , Issue 1 , September 1963 , pp. 1 - 20
Copyright
© 1963 Cambridge University Press

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References

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