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

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 (ωis the angular velocity of the rigid body about the axis of symmetry,Ωis 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 timet= 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 toω× (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.