Stagnant lid convection in bottom-heated thin 3-D spherical shells: Influence of curvature and implications for dwarf planets and icy moons

Abstract

Because the viscosity of ice is strongly temperature dependent, convection in the ice layers of icy moons and dwarf planets likely operates in the stagnant lid regime, in which a rigid lid forms at the top of the fluid and reduces the heat transfer. A detailed modeling of the thermal history and radial structure of icy moons and dwarf planets thus requires an accurate description of stagnant lid convection. We performed numerical experiments of stagnant lid convection in 3-D spherical geometries for various ice shell curvatures f (measured as the ratio between the inner and outer radii), effective Rayleigh number Ram, and viscosity contrast Δ�� . From our results, we derived scaling laws for the average temperature of the well-mixed interior, �� m, and the heat flux transported through the shell. The nondimensional temperature difference across the bottom thermal boundary layer is well described by (1 − �� m )= 1.23 �� f 1.5 ,