Geoid and topography of Earth-like planets: A comparison between compressible and incompressible models for different rheologies

A systematic study of 2D-axisymmetric, spherical shell models of compressible and incompressible mantle convection with constant and variable viscosity and constant and depth-dependent thermodynamic properties is presented. To account for compressibility effects, we employ the anelastic liquid approximation. In the case of variable viscosity, an Arrhenius law with strongly temperature and pressure dependent viscosity is considered. We show that assuming compressible convection with depth-dependent thermodynamic properties strongly influence the geoid undulations. Using compressible convection with constant thermodynamic properties is physically inconsistent and may lead to spurious results for the geoid and convection pattern. In addition, we examine the impact of compressibility as well as different rheologies on the power law relation that connects the Nusselt number to the Rayleigh number. We discover that the power law index of the Nu–Ra relationship is controlled by the rheology, independent of which approximation is used. Instead, the bound of this relation is controlled by a combination of different approximation and rheology.