A cylindrical model for rotational MHD instabilities in aluminum reduction cells

Large-scale horizontal vortices associated with deformations of the aluminum-electrolyte interface have been observed in operating aluminum reduction cells as well as in physical and numerical models. To expose their importance, we analyze a particular class of magnetohydrodynamic (MHD) interfacial instabilities which are induced by rotation. As we focus on a single vortex, a cylindrical geometry is preferred. Two analytical models are proposed. In a first model based on the MHD shallow-water approximation, we consider a vortex that has a solid rotation profile to obtain a wave equation and a dispersion relation. A more realistic second model includes a viscous rotation profile and the treatment of the base-state interface deformation. Energetics of the flow gives further insight on how an initial perturbation evolves as an oscillatory or a non-oscillatory instability, depending on the direction of rotation. We find that the mechanism at the very origin of these instabilities is neither due to a shear between the two layers-and are therefore not Kelvin-Helmholtz instabilities-nor simply due to magnetic force alone, but rather to the indirect action of the centripetal pressure due to the rotation induced by magnetic force.