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Abstract
Small amplitude oscillations of a uniformly rotating, density stratified, Boussinesq, electrically conducting, non-dissipative fluid are examined in the geometry of a spherical shell. The basic magnetic field is assumed to be toroidal and is allowed to be an arbitrary axisymmetrical function of space. The basic density distribution is allowed to be an arbitrary function of space, consistent with the gravitational potential and the toroidal magnetic field. Conserved energy integrals are constructed and these constraints are used to determine sufficient conditions for stability. The stable waves are, in general, spatially trapped. Explicit expressions are obtained for the “turning surfaces” that delineate the regions in which waves are trapped. These expressions are used to illustrate trapped hydromagnetic waves in the Earth's fluid core.
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