Experimental and numerical studies of magnetoconvection in a rapidly rotating spherical shell

Abstract

Thermal magnetoconvection in a rapidly rotating spherical shell is investigated numerically and experimentally in electrically conductive liquid gallium (Prandtl number P = 0.025), at Rayleigh numbers R up to around 6 times critical and at Ekman numbers E ∼ 10−6. This work follows up the non-magnetic study of convection presented in a companion paper (Gillet et al. 2007). We study here the addition of a z-invariant toroidal magnetic field to the fluid flow. The experimental measurements of fluid velocities by ultrasonic Doppler velocimetry, together with the quasi-geostrophic numerical simulations incorporating a three-dimensional modelling of the magnetic induction processes, demonstrate a stabilizing effect of the magnetic field in the weak-field case, characterized by an Elsasser number Λ < (E/P)1/3. We find that this is explained by the changes of the critical parameters at the onset of convection as Λ increases. As in the non-magnetic study, strong zonal jets of characteristic length scales ℓβ (Rhines length scale) dominates the fluid dynamics. A new characteristic of the magnetoconvective flow is the elongation of the convective cells in the direction of the imposed magnetic field, introducing a new length scale ℓφ. Combining experimental and numerical results, we derive a scaling law $\overline{U} \,{\sim}\, (\widetilde{U}_s \widetilde{U}_{\phi})^{2/3} \,{\sim}\, \widetilde{U}_s{}^{4/3} (\ell_{\phi}/\ell_{\beta})^{2/3}$ where U is the axisymmetric motion amplitude, Ũs and Ũφ are the non-axisymmetric radial and azimuthal motion amplitudes, respectively.