Horizontal infinite-Prandtl-number convection

Differential heating of a horizontal surface in a finite fluid volume, leading to so-called horizontal convection, is a hot topic for both the oceans and glass furnaces. Here we investigate the infinite-Prandtl-number limit relevant to the latter, using numerics and scaling arguments. Two regimes are identified, and universal scaling functions are found for the transition between the regimes. Conclusive numerical evidence is presented for the Rossby boundary-layer scaling for both rigid and shear-free boundary conditions. The surprising lack of dependence on the boundary condition is explained by showing that the return flow comprises of a horizontal intrusion at the bottom of the horizontal boundary layer, and a weak downwelling plume that returns at depth. We also present results for highly temperature-dependent viscosity.