Onset of convection in fluids with strongly temperature-dependent, power-law viscosity

The onset of convection in the power-law creep regime on the terrestrial planets and icy satellites is poorly constrained. The major difficulty is that the viscosity of power-law fluids approaches infinity when the perturbation amplitudes approach zero and thus the methods of linear theory are inapplicable. Here, we determine the critical Rayleigh number for the onset of convection by starting in the convective regime and gradually decreasing the Rayleigh number in small increments until the solution collapses to the conductive state. For Newtonian viscosity, this approach constraints the subcritical branch and determines the critical Rayleigh number for the cessation of convection. For power-law viscosity, this gives a perturbation-independent critical Rayleigh number below which no steady-state convection solution can exist. The calculations are performed in the stagnant lid regime of temperature-dependent viscosity convection and for several values of the stress exponent. The results approximately agree with earlier theoretical estimates.