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 silica te 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, co nvection beneath the lid is steady in time and characterized by cylindrical upwellings surrounded by cold sheet-like downwellings that exhibit dodecah edronal (l = 6, m = {0,5}) symmetry. The scaling relationship we obtain for the heat flux is very similar to results from two-dimensional numerical ex periments and asymptotic boundary layer analyses. It seems that the predict ions of two-dimensional models, in particular, low heat transport efficienc y and extensive melting, also apply in fully three-dimensional spherical ge ometry. (C) 1999 Elsevier Science B.V. All rights reserved.