From Geostrophic to Magnetically-Damped Turbulence in Liquid Metal Rotating Magnetoconvection

Understanding planetary core convection dynamics requires the study of convective flows in which the Coriolis and Lorentz forces attain a leading-order, so-called magnetostrophic balance. Experimental investigations of rotating magnetoconvection (RMC) in the magnetostrophic regime are therefore essential to broadly characterize the properties of local-scale planetary core flow. Towards this end, we present here the first thermovelocimetric measurements of magnetostrophic, liquid metal convection, which are made using liquid gallium as the working fluid, at moderate rotation rates (Ekman numbers $10^{-4} \leq Ek\leq 10^{-5}$) and in the presence of dynamically strong magnetic fields (Elsasser number $Λ=1$). Complementary rotating convection (RC) experiments are performed at the same rotation rates to serve as reference cases. Our RMC velocity measurements adequately follow a geostrophic turbulent scaling for cases in which local-scale convective inertial forces exceed the Lorentz forces in the fluid bulk. In cases where Lorentz forces exceed local-scale inertia ($N_\ell \gtrsim 3$), the root-mean-square RMC velocities are magnetically damped, yielding values below the geostrophic turbulent RC scaling prediction. An enhancement in heat transfer is observed, which we attribute to the increased coherence of vertically aligned magnetostrophic convective flow. Extrapolating these laboratory results, we predict that convection-scale flows in Earth's core occur in the magnetically damped $N_\ell \gtrsim 3$ regime with Rayleigh number values between $10^{24}$ and $10^{26}$.