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

K. Stewartson, P. H. Roberts
1963 Journal of Fluid Mechanics  
Neglecting magnetic effects the precession of the mantle of the Earth is responsible for hydrodynamic motions in the liquid core because, (1) the velocity of the inner boundary of the mantle along its normal is non-zero unless the core boundary is a perfect sphere, (ii) there is a viscous coupling between core and mantle, (iii) there is a magnetic coupling between core and mantle because lines of geomagnetic force thread each. In this preliminary discussion of the problem, we suppose that the
more » ... re boundary is an oblate spheroid of eccentricity e; it is shown that the relative importance of (i) and (ii) depends in an essential way on the value of R we /0 where w is the angular velocity of rotation and Q ( c w) is the angular velocity of precession. Since R is almost certainly large for the Earth, the present discussion is limited to this case. 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 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 is a circulation with constant vorticity in planes perpendicular to w and Q, the streamlines being similar and similarly situated ellipses.
doi:10.1017/s0022112063001063 fatcat:ptbrcljlnnhvvc2a7egthadaqy