THE INFLUENCE OF SURFACE-TOPOGRAPHY ON ROTATING CONVECTION

Busse's annulus is considered as a model of thermal convection inside the Earth's liquid core. The conventional tilted base and top are modi fied by azimuthal sinusoidal corrugations so that the effects of surfa ce topography can be investigated. The annulus rotates rapidly about i ts axis of symmetry with gravity directed radially inwards towards the rotation axis. An unstable radial temperature gradient is maintained and the resulting Boussinesq convection is considered at small Ekman n umber. Since the corrugations on the boundaries cause the geostrophic contours to be no longer circular, strong geostrophic flows may be dri ven by buoyancy forces and damped by Ekman suction. When the bumps are sufficiently large, instability of the static state is dominated by s teady geostrophic flow with the convection pattern locked to the bumps . As the bump size is decreased, oscillatory geostrophic flow is possi ble but the preferred mode is modulated on a long azimuthal length sca le and propagates as a wave eastwards. This mode only exists in the pr esence of bumps and is not to be confused with the thermal Rossby wave s which are eventually preferred as the bump height tends to zero. Lik e thermal Rossby waves, the new modes prefer to occupy the longest ava ilable radial length scale. In this long-length-scale limit, two finit e-amplitude states characterized by uniform geostrophic flows can be d etermined. The small-amplitude state resembles Or & Busse's (1987) mea n flow instability. On losing stability the solution jumps to the more robust large-amplitude state. Eventually, for sufficiently large Rayl eigh number and bump height, it becomes unstable to a long-azimuthal-l ength-scale travelling wave. The ensuing finite-amplitude wave and the mean flow, upon which it rides, are characterized by a geostrophic fl ow, which is everywhere westward.