Effect of shear and magnetic field on the heat-transfer efficiency of convection in rotating spherical shells

TL;DR

This study uses extensive numerical simulations to investigate how shear and magnetic fields influence heat transfer in rotating spherical shell convection, revealing that shear suppression enhances efficiency and magnetic fields can further improve heat transfer.

Contribution

It provides new insights into the combined effects of shear suppression and magnetic fields on heat transfer efficiency in rotating spherical shell convection.

Findings

Shear suppression can triple heat-transfer efficiency.

Magnetic fields can increase heat transfer by up to 30%.

Efficiency approaches non-rotating systems at high convective driving.

Abstract

We study rotating thermal convection in spherical shells. 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-B\'enard 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. Furthermore, we explore the influence of the magnetic field on the {\em 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\% (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.