On inertial waves in a rotating fluid sphere

Several new results are obtained for the classical problem of inertial wave s in a rotating fluid sphere which was formulated by Poincare more than a c entury ago. Explicit general analytical expressions for solutions of the pr oblem are found in a rotating sphere for the first time. It is also discove red that there exists a special class of three-dimensional inertial waves t hat are nearly geostrophic and always travel slowly in the prograde directi on. On the basis of the explicit general expression we are able to show tha t the internal viscous dissipation of all the inertial waves vanishes ident ically for a rotating fluid sphere. The result contrasts with the finite va lues obtained for the internal viscous dissipation for all other cases in w hich inertial waves have been studied.