Influences of the depth-dependence of thermal conductivity and expansivity on thermal convection with temperature-dependent viscosity

In this paper we carried out numerical experiments of a time-dependent thermal convection in a two-dimensional Cartesian box of aspect ratio (width/height) of 6, in order to study the influences on the convecting flow patterns of the spatial variations in physical properties (viscosity η, thermal conductivity k and expansivity α). A series of calculations by systematically varying the magnitude of spatial variations in these properties showed that the strongly temperature-dependent η induces the change in flow pattern into the “stagnant lid” (ST) regime, regardless of the increase in k and/or decrease in α with depth, where the convection occurs only beneath a stagnant lid of cold fluid at the top surface. In particular, we found that the increase in thermal conductivity k with depth significantly affects the convecting flow patterns in the presence of strong temperature-dependence in η. Compared with those with uniform k, the patterns of ST convection with non-uniform k are characterized by (i) thinner top thermal boundary layers or lids and (ii) larger horizontal length scales of convection cells beneath the stagnant lid. In addition, the variation in k with depth decreases the threshold values of the temperature-dependence in η above which the ST-mode of convection takes place, which may also help stabilize the convection cells of large horizontal length scales beneath stagnant lids. Our results may highlight the potential importance of the increase in thermal conductivity with depth (or pressure) in controlling the planforms of thermal convection in the mantle of terrestrial planets.