On topography and geoid from 2‐D stagnant lid convection calculations

Abstract

Temperature‐dependent convection in the stagnant lid regime with a Frank‐Kamenetskii and Arrhenius viscosity formulation are compared. When properly scaled, the Nusselt number and root‐mean‐square velocity of the fluid for the two viscosity formulations are similar but the surface stresses and hence predicted dynamic topography and geoid differ significantly. The Arrhenius viscosity formulation results are insensitive to a viscosity cutoff at the high viscosity limit as long as the cutoff is 104 times the basal viscosity. The condition number for stagnant lid convection matrices using a penalty formulation is smaller than the penalty number times viscosity contrast value (a reasonable estimate of the condition number), explaining why large viscosity contrast convection problems with the penalty method agree with other formulations and analytic solutions. The difference in magnitude between the maximum and minimum dynamic topography could be used to constrain the magnitude of the viscosity contrast across the stagnant lid in planetary bodies.