Routes to turbulence in low Prandtl number rotating magnetoconvection

The magnetic fields of terrestrial planets are generated by the turbulent convective processes occurring in their liquid metal cores. Here, we focus on the fundamental flow physics in the polar region by studying rotating magnetoconvection in a low Prandtl number fluid, Pr = 0.025, in a cylindrical domain. We present results from direct numerical simulations, where we follow the pathways from the onset of convection to the turbulent state by gradually increasing the Rayleigh number Ra for fixed Elsasser numbers in the range 0.01 ≤ Λ ≤ 10.0. A vertical magnetic field is externally imposed and the induced magnetic field is assumed to be negligible such that the quasi-static approximation can be employed. Thermal instability can onset in four basic manners in this configuration: stationary high-wavenumber geostrophic convection, stationary low-wavenumber magnetostrophic convection, oscillatory convection and wallmode convection. Since the critical Rayleigh number Ra_c of the possible instabilities is strongly dependent on Λ , we can follow several distinct pathways, where the order in which these types of convection set in, as well as their respective range, varies. Hence, through the successive increase of Ra, we can explore the individual instabilities, analyse their imprints on the flow, trace their evolution, and also investigate their interactions. We find, that the signatures of the underlying instabilities remain present up to relatively high supercriticalities, leading generally to highly multi-modal flows. However, it is neither necessarily the onset nor the latest instability setting in that determines the overall flow.