Thermal convection in rotating spherical shells

Linear and non-linear properties of thermal convection in rotating spherical shells of varying radius ratios are investigated numerically. The range of validity of the simple 'equatorial' approximation is determined through a comparison with the more complete numerical analysis based on the Galerkin approximation. The earlier work of Zhang and Busse (1987, Geophys. Astrophys. Fluid Dyn., 39: 119-147) is extended in order to classify the way in which different modes of convection become preferred in various parts of the parameter space. It is found that in the transition region between equator attached convection and columnar convection an intermediate mode with a multi-humped structure enters. Examples of non-linear vacillating convection in low Prandtl number fluids are discussed.