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.