I. Fluid flow in a precessing spherical cavity. II. Electromagnetic radiation from an expanding sphere in a magnetic field

Abstract

In Part I the flow of an incompressible fluid inside a precessing spherical cavity is studied. The precession angle is assumed small and the equations of motion are linearized. For the case of large viscosity an expansion is developed in inverse powers of the viscosity by expanding the velocity field in vector spherical harmonics. The flow obtained is essentially rigid body motion. The case of low viscosity is also studied. At low precession rates difficulties arise in the boundary layer treatment and the inviscid equations. A modified boundary layer equation is derived and an approximate solution obtained. The flow consists essentially of rotation about the average axis of rotation. Some geophysical aspects of the problem, and in particular its relevance to dynamo theories of the earth's magnetic field are discussed. Part II deals with the electromagnetic fields about a perfectly conducting sphere which is placed in a uniform magnetic field. The radiation fields that result when the radius of the sphere is allowed to change are investigated. Explicit expressions are obtained for the cases of a sphere expanding or collapsing at a uniform rate. In the latter case it is found that wave propagation and energy propagation are in opposite directions. Constant speed oscillations are also investigated and the effect of the amplitude on the power radiated is considered. The case of arbitrary motions of the radius is also discussed.