Scaling relationships and physics for mixed heating convection in planetary interiors: Isoviscous spherical shells

Abstract

AbstractWe use a suite of 3‐D numerical experiments to test and expand 2‐D planar isoviscous scaling relationships of Moore (2008) for mixed heating convection in spherical geometry mantles over a range of Rayleigh numbers (Ra). The internal temperature scaling of Moore (2008), when modified to account for spherical geometry, matches our experimental results to a high degree of fit. The heat flux through the boundary layers scale as a linear combination of internal (Q) and basal heating, and the modified theory predictions match our experimental results. Our results indicate that boundary layer thickness and surface heat flux are not controlled by a local boundary layer stability condition (in agreement with the results of Moore (2008)) and are instead strongly influenced by boundary layer interactions. Subadiabatic mantle temperature gradients, in spherical 3‐D, are well described by a vertical velocity scaling based on discrete drips as opposed to a scaling based on coherent sinking sheets, which was found to describe 2‐D planar results. Root‐mean‐square (RMS) velocities are asymptotic for both low Q and high Q, with a region of rapid adjustment between asymptotes for moderate Q. RMS velocities are highest in the low Q asymptote and decrease as internal heating is applied. The scaling laws derived by Moore (2008), and extended here, are robust and highlight the importance of differing boundary layer processes acting over variable Q and moderate Ra.