Onset of convection in internally heated fluids with strongly temperature-dependent viscosity

We investigate the onset of convection in internally heated fluids with strongly temperature-dependent viscosity by solving numerically a non-linearized system of thermal convection equations in two dimensions for viscosity contrasts up to ∼ 10 35. As the viscosity contrast increases, a high-viscosity stagnant lid develops at the upper surface and convection occurs in a sublayer beneath it. The transition to stagnant-lid convection occurs at about the same viscosity contrast as in Rayleigh-Bénard convection. We obtain asymptotic scaling relationships for the critical Rayleigh number and other parameters in the stagnant-lid regime. We also investigated the possibility of subcritical convection. In contrast to the Rayleigh-Bénard problem, we did not detect a subcritical region for internally heated convection in two-dimensional simulations. The results of this study can help improve our understanding of the conditions under which convection occurs in planetary interiors.