Scaling of temperature- and stress-dependent viscosity convection

Simple scaling analysis of temperature- and stress-dependent viscosity convection with free-slip boundaries suggests three convective regimes: the small viscosity contrast regime which is similar to convection in a fluid whose viscosity does not depend on temperature, the transitional regime characterized by self-controlled dynamics of the cold boundary layer and the asymptotic regime in which the cold boundary becomes stagnant and convection involves only the hottest part of the lid determined by a rheological temperature scale. The first two regimes are usually observed in numerical experiments. The last regime is similar to strongly temperature-dependent viscosity convection with rigid boundaries studied in laboratory experiments.