Wave propagation in a rotating fluid of spherical configuration

Abstract

An asymptotic approximation to the solution of the time-dependent linearized equations governing the motion of an incompressible, inviscid rotating fluid of spherical configuration having uniform density, variable depth and a free upper surface is obtained using the ray method without a shallow water assumption. This result is then modified to obtain a ray approximation to the solution of the time-reduced problem and the free oscillations of the fluid are studied. Axisymmetric modes covering the whole sphere and asymmetric modes trapped in both equatorial and non-equatorial regions are discovered, and all these modes are shown to have countably many resonance frequencies. A shallow water limit is defined and this limit of the time-reduced approximation is obtained. Most of the modes of free oscillation are lost in this limit and the limiting axisymmetric modes are shown to be trapped in the equatorial region and are singular at the wave region boundaries. The limiting approximation is compared to previous results obtained under a shallow water assumption.