Effect of shear and magnetic field on the heat-transfer efficiency of convection in rotating spherical shells. Issue 2 (16th December 2015) - Yadav, R.K.; Gastine, T.; Christensen, U.R.; Duarte, L.D.V.; Reiners, A.
Abstract: We study rotating thermal convection in spherical shells as prototype 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 −5 . The supercriticality of the convection reaches about 1000 in some models. Four sets of simulations are considered: non-magnetic simulations and dynamo simulations with either free-slip or no-slip flow boundary conditions. The non-magnetic setup with free-slip boundaries generates the strongest zonal flows. Both non-magnetic simulations with no-slip flow boundary conditions and self-consistent dynamos with free-slip boundaries have drastically reduced zonal-flows. Suppression of shear leads to a substantial gain in heat-transfer efficiency, increasing by a factor of 3 in some cases. Such efficiency enhancement occurs as long as the convection is significantly influenced by rotation. At higher convective driving the heat-transfer efficiency tends towards that of the classical non-rotating Rayleigh–Bénard system. Analysis of the latitudinal distribution of heat flow at the outer boundary reveals that the shear is most effective at suppressing heat-transfer in the equatorial regions. Simulations with convection zones of different thickness show that the zonal flows become less energetic in thicker shells, and, therefore, their effect on heat-transfer efficiency decreases. Furthermore, we explore the influence of the magnetic field on the non-zonal flow components of the convection. For this we compare the heat-transfer efficiency of no-slip non-magnetic cases with that of the no-slip dynamo simulations. We find that at E = 10 −5 magnetic field significantly affects the convection and a maximum gain of about 30 per cent (as compared to the non-magnetic case) in heat-transfer efficiency is obtained for an Elsasser number of about 3. Our analysis motivates us to speculate that convection in the polar regions in dynamos at E = 10 −5 is probably in a 'magnetostrophic' regime.