On the Rayleigh number dependence of convection with a strongly temperature-dependent viscosity

Abstract

The strong dependence of the rheology of a fluid on temperature has a great impact on the style of thermally driven convection. When the viscosity contrast is sufficiently large, the viscosity of the coldest fluid at the top of a bottom-heated box is so high that this fluid layer becomes very stiff and a so-called cold “stagnant lid” develops on top of a hot convecting layer. Studying this style of convection is relevant for planetary mantles since the rheology of mantle material is likely to be very strongly temperature dependent. In this paper, the Rayleigh number dependence of stagnant-lid convection with a viscosity contrast of 106 is studied numerically in two and three dimensions in wide Cartesian domains. Like in constant-viscosity cases, the convection in the layer underneath the stagnant lid undergoes the typical transition from steady to time-dependent with the thinning of plumes and with the appearance of boundary layer instabilities as the Rayleigh number increases. A stagnant-lid style of convection was obtained in 2D and 3D for all supercritical Rayleigh numbers considered and the interior temperature appeared not to depend on the Rayleigh number. We have compared our results with other theoretical and numerical results and we found a close agreement.