Abstract
The discussion of stability of plane parallel shear flow in an infinite rotating layer heated from below requires a mathematical analysis of this problem in dependence on four parameters. These are the Reynolds- and Rayleigh-number, controlling the strength of the shear flow and the heating power, respectively, the Prandtl-number, which measures the relative influence of viscosity and thermal conductivity, and the rotation rate of the layer. After discussing some physical background, possible applications and laboratory experiments two major problems are addressed: i) To find out the cases where unconditional (global) stability up to criticality takes place. In these situations theory makes the clearest predictions and coincidence between experiments and mathematical theory can be expected. ii) To prove that the (monotonic) energy-stability limit is assumed by 2-dimensional (with respect to the spatial variables) perturbations. The solution of this variational problem shows that in certain situations the critical perturbations are 2-dimensional. In these situations, at least, the stability problem is completely solved.
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