Steady Convective Motion in a Horizontal Layer of Fluid Heated Uniformly from Above and Cooled Non-uniformly from Below

Abstract

A gravitationally stable fluid layer is heated non-uniformly (sinusoidally) at the bottom (or top) and a thermal convection regime is established. Examples are worked out for cases (i) without rotation (ii) with uniform rotation, and (iii) with non-uniform rotation (beta-plane).