On trapped oscillations of a rotating fluid in a thin spherical shell II

Abstract

The study of the structure of free oscillations of fluid in a spherical shell, trapped near the equatorial plane, carried out by Stewartson (1971) is extended to include all members of the continuous set discovered by Israeli (1971). In the more general trapped mode it is not necessary for the limit cycle bounding the oscillation to touch the inner sphere but the pathological features discussed in I are also present here. The width of the band of continuous periods of oscillation is also found in terms of the number of reflections of the limit cycle at the outer sphere.