3D MHD Shear instabilities in the Solar Tachocline

In the past decade, linear analysis has shown that the latitudinal differential rotation in the solar tachocline is unstable in the presence of a toroidal field under a wide range of field amplitudes and configurations. The most unstable modes are generally tipping modes whereby a band of toroidal field evolves such that its central axis tips away from the rotation axis. Previous studies of these instabilities have been based on two-dimensional (latitude-longitude) models or on the MHD shallow-water approximation in which horizontal velocities and fields are still independent of height but are no longer required to be divergenceless. Recently we have extended these linear analyses to 3D using a thin-shell model. Here we present nonlinear simulations of these 3D MHD shear instabilities.