Free oscillations of an incompressible inviscid fluid in a rotating spherical shell are studied by means of the ray method, which is different from the conventional approach. Axisymmetric modes covering the whole sphere and asymmetric modes trapped in equatorial regions bounded by critical circles of constant latitude as well as in regions off the equator bounded by caustics are discovered. The anomalies at poles and critical circles of the ray method expansion are removed by means of uniform asymptotic expansions. The equations for the resonance frequencies of each of the various modes of oscillation are studied numerically.
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London et al. (1979) studied this question.
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