Global MHD instabilities in a thin-shell model of the solar tachocline

Previous studies have demonstrated that strong toroidal fields in the solar tachocline are unstable to 2D and shallow-water tipping instabilities, fed by the latitudinal differential rotation. Here we have extended these analyses to three dimensions using a model based on the thin-shell limit of the Boussinesq MHD equations. For strongly stable stratification and relatively weak field strengths, the thinshell results coincide with the 2D and SW unstable modes, with peak growth rates of several months. However, if the stratification is nearly adiabatic or if the toroidal fields are strongly super-equipartition, we find a distinct mode of instability characterized by nonzero vertical wavenumbers and high growth rates (∼ days). Under these conditions, our Boussinesq model formally breaks down but preliminary results from a self-consistent anelastic thin-shell model indicate that the high-growth-rate modes are still present, but may be altered.