Numerical experiments on thermal convection of highly compressible fluids with variable viscosity and thermal conductivity in 2-D cylindrical geometry: implications for mantle convection of super-Earths

Abstract

SUMMARY We conduct a series of numerical experiments of thermal convection of highly compressible fluids in 2-D cylindrical annulus, in order to study the mantle convection on super-Earths. The variations in thermodynamic properties (thermal expansivity and reference density) with depth are taken to be relevant for the super-Earths with 10 times the Earth’s mass, while those in transport properties (viscosity and thermal conductivity) are modelled by an exponential dependence on temperature and/or depth. From our experiments we identified a distinct regime of convecting flow patterns induced by the interplay between the adiabatic temperature change and the spatial variations in viscosity and thermal conductivity. That is, for the cases with strong temperature-dependent viscosity and large increase in thermal conductivity with depth, a ‘deep stratosphere’ of stable thermal stratification is formed at the base of the mantle, in addition to thick stagnant lids at their top surfaces. In the ‘deep stratosphere’, the fluid motion is insignificant particularly in the vertical direction in spite of smallest viscosity owing to its strong dependence on temperature. From the comparison with the experiments with the Cartesian geometry, we also found that the occurrence of ‘deep stratosphere’ tends to be suppressed for the cases with cylindrical geometry, owing to the reduction of the surface area with depth which helps increase the temperature gradient in the lowermost mantle. Our finding may further imply that both the effects of adiabatic compression and those of spherical (or cylindrical) geometry of mantle are of crucial importance in understanding the mantle dynamics of massive super-Earths in the presence of spatial variations in physical properties.