Stagnant lid convection in a spherical shell

A compelling explanation for the observed lack of mobile surface plates on the terrestrial planets is that the strong temperature dependence of silicate rheology leads to a quasi-rigid stagnant lid at the cool surface of the convecting planetary mantle. We investigate such stagnant lid convection in an internally heated spherical shell. For the parameter range we study, convection beneath the lid is steady in time and characterized by cylindrical upwellings surrounded by cold sheet-like downwellings that exhibit dodecahedronal (l = 6, m = {0,5}) symmetry. The scaling relationship we obtain for the heat flux is very similar to results from two-dimensional numerical experiments and asymptotic boundary layer analyses. It seems that the predictions of two-dimensional models, in particular, low heat transport efficiency and extensive melting, also apply in fully three-dimensional spherical geometry.