Plume formation in strongly temperature-dependent viscosity fluids over a very hot surface

Plume formation in a strongly temperature-dependent viscosity fluid placed on a very hot surface involves an intermediate step-small-scale convection in the thermal boundary layer. We perform numerical simulations and suggest a simple analysis of this process using the stagnant lid convection theory and Canright and Morris' theory of Rayleigh-Taylor instability of two layers with different viscosities. We show that plume formation can approximately be predicted from the requirement that the growth of the large-scale instability becomes faster than the growth of the convecting thermal boundary layer.