Convection in a rotating medium above a thermally inhomogeneous horizontal surface

The linear stationary problem of convection in a medium rotating about a vertical axis above a thermally inhomogeneous horizontal surface is theoretically investigated. Attention is mainly focused on the case of a homogeneous medium, but certain stratification effects and especially the convection characteristics in binary mixtures (for example, in saline sea water) are also considered. When the rotation is rapid (large Taylor numbers) the convective cells are strongly elongated in the vertical direction, though they also contain a thin Ekman boundary layer. The importance of the boundary conditions on the horizontal surface (in parallel with the no-slip conditions, more general conditions that may follow from the quadratic turbulent friction model are considered) is shown. In the case of binary mixtures, the differential diffusion and rotation effects may together result in the appearance of “induced salt fingers”, the deep penetration of convection into an arbitrarily stably stratified medium. The convective motions may then have a considerable effect on the background vertical temperature and admixture distributions. Attention is drawn to an original manifestation of the analogy between the rotation and stratification effects: in a non-rotating, stably stratified medium, near a thermally inhomogeneous vertical surface, the convection also penetrates deep into the medium, but in the horizontal direction, so that, when the coordinate system is rotated through 90°, the solution coincides with the case of a rotating non-stratified fluid considered here.