The Propagation and Stability of Hydromagnetic Waves in a Rotating Cylindrical Annulus with Distorted End-Surfaces

The linear stability of a differentially heated cylindrical annulus, of finite length, containing a dissipationless fluid and rotating uniformly in a nonuniform toroidal magnetic field is studied. The analysis is restricted to the situation where the instabilities are driven by buoyancy. If the end-surfaces are flat, the unstable waves propagate against the basic flow, i.e. westward. When the effect of slight distortions in the end-surfaces on the propagation speeds of these waves are investigated, it is found that these distortions can decrease or increase the propagation speeds depending on a variety of conditions. The application of these results to Hide's (1969) theory on the effects of bumps on the core-mantle interface of the Earth indicates that these topographical features may lead to irregular fluctuations in the westward drift.