Linear stability analysis on the influences of the spatial variations in thermal conductivity and expansivity on the flow patterns of thermal convection with strongly temperature-dependent viscosity

Abstract

A series of linear stability analysis is carried out on the onset of thermal convection in the presence of spatial variations of viscosity, thermal conductivity and expansivity. We consider the temporal evolution of an infinitesimal perturbation superimposed to a static (motionless) and conductive state in a basally-heated planar layer. From the changes in flow patterns with increasing the amplitudes of temperature dependence of viscosity, we identified the transition into the “stagnant-lid” (ST) regime, where the convection occurs only beneath a thick and stagnant-lid of cold fluid at the top surface. Detailed analysis showed a significant increase of the aspect ratio of convection cells in ST regime induced by the spatial variations in thermal conductivity and/or expansivity: the horizontal length scale of ST convection can be enlarged by up to 50% with 10 times increase of thermal conductivity with depth. We further developed an analytical model of ST convection which successfully reproduced the mechanism of increasing horizontal length scale of ST regime convection cells for given spatial variations in physical properties. Our findings may highlight the essential roles of the spatial variation of thermal conductivity on the convection patterns in the mantle.