Effect of shear and magnetic field on the properties of convection in rotating spherical shells

Abstract:

We study thermal convection in rotating spherical shells as prototype models for flow in the cores of terrestrial planets, gas planets or in stars. We base our analysis on a set of about 450 direct numerical simulations of the (magneto)hydrodynamic equations under the Boussinesq approximation. The Ekman number ranges from 10^-3 to 10^-6. The supercriticality of the convection reaches about 1000 in some models. Four sets of simulations are considered: non-magnetic as well as dynamo simulations with either free-slip or no-slip flow boundary conditions. The hydrodynamic set-up with free-slip boundaries generates the strongest zonal flows. We then perform simulations with ingredients which would quench such shear flows: non-magnetic simulations with no-slip boundaries and self-consistent dynamos with free-slip boundaries. Both set-ups have drastically reduced zonal-flows. Suppression of zonal-flows leads to a substantial gain in heat-transfer efficiency, reaching 300% increase in some cases. Such efficiency enhancement occurs as long as the convection is significantly influenced by rotation (i.e. small enough Rossby numbers). At higher convective driving, both of these set-ups have a reduced heat-transfer efficiency. Analysis of the latitudinal distribution of heat coming out at the outer boundary reveals that the shear is most effective at suppressing heat-transfer at low-latitudes (near the equator). We also try to narrow down the influence of the magnetic field on the non-zonal flow components to test the idea of `magnetostrophic' convection. For this purpose, the flow boundary conditions are kept no-slip and hydrodynamic simulations are compared with new self-consistent dynamo simulations. We find that even at an Ekman number of 10^-5, the polar regions are already significantly affected by the presence of dynamo-generated magnetic field. Near the equator, however, only subtle changes are observed. We then run few simulations at even lower Ekman number of 10^-6 and see dramatic changes in flow structure at all latitudes due to the presence of the magnetic field. Simulations at such low Ekman numbers indicate that we are approaching the magnetostrophic regime of convection.