Heat transport in a convecting layer heated from within and below

Abstract

The heat transport scaling relationships for fluids heated from within and below are established based on numerical calculations of isoviscous Boussinesq convection at infinite Prandtl number. The internal temperatures scale in a way that is similar to the internally heated case but with an offset equal to the average of the two boundary temperatures, reflecting the underlying temperature structure of bottom‐heated convection. The heat fluxes through the boundaries scale as a linear combination of the end‐member modes of heat transport, consistent with the effects of internal heating on the interior temperature. The boundary layer thicknesses, however, depend on H and Ra in a nonintuitive way. As the internal temperature increases with the addition of internal heating, the upper thermal boundary layer thickens despite the increased temperature drop across the layer (the reverse is true for the bottom boundary layer). This is inconsistent with the idea that the boundary layer thickness is controlled by a stability condition on the local Rayleigh number, which would predict that the boundary layer would thin as the temperature drop increases. Deriving boundary layer thicknesses from the scalings for heat flux and boundary layer temperature drop provides an excellent fit to the model results and reveals the importance of plumes arriving from the other boundary layer in establishing the boundary layer thickness. This suggests that, although widely used, boundary layer stability analysis is not an accurate description of the processes controlling boundary layer thickness in systems with two active boundary layers at moderate Ra.