2-D numerical experiments of thermal convection of highly viscous fluids under strong adiabatic compression: implications on mantle convection of super-Earths with various sizes

Abstract We conduct a series of numerical experiments of thermal convection of compressible fluids with temperature-dependent viscosity, in order to study how the adiabatic compression and model geometries affect the mantle convection on super-Earths. A two-dimensional basally heated convection is considered under the truncated anelastic liquid approximation (TALA), either in a rectangular box or in a cylindrical annulus. We varied the magnitude of adiabatic heating and the Rayleigh number as well as the depth profile of thermodynamic properties (thermal expansivity and reference density) in accordance with the planetary sizes. From our calculations by varying the planetary sizes up to 10 times the Earth’s mass, we confirmed that the adiabatic compression affects the thermal convection more strongly for larger planets. The activity of hot plumes originating from the core–mantle boundary is significantly suppressed in the terrestrial planets whose mass is larger than the Earth’s by a factor of about 3 regardless of the model geometries. We also developed scaling relationships between the vigor of thermal convection and the planetary mass by appropriately incorporating the effect of adiabatic compression into those of Boussinesq (or incompressible) cases. Our scaling relationships suggest that the stress level in the top cold thermal boundary layers is almost independent of the planetary mass, which may further imply that the emergence of plate tectonics is not likely to be enhanced for massive terrestrial planets whose composition is similar to the Earth’s. Graphical Abstract