The combination of differential rotation and toroidal fields believed to exist in the solar tachocline should be unstable to global MHD modes, typically dominated by longitudinal wavenumber m = 1 modes for toroidal fields of peak value 30 kG and higher, and a broader range of low m values for weaker fields. For toroidal field bands, the high field instability takes the form of a ‘tipping’ of the band away from coincidence with circles of latitude. For a wide range of toroidal fields and differential rotations, and in both the overshoot and radiative parts of the tachocline, the unstable modes grow in a time short compared to a solar cycle, and are therefore of interest for the solar dynamo problem, as well as for creation of longitude-dependent magnetic patterns seen at the solar surface. The latitudinal momentum transport by Reynolds and Maxwell stresses associated with unstable modes provides a way to mix angular momentum in latitude, and help limit the thickness of the tachocline.

Introduction

The study of global MHD instabilities of differential rotation and toroidal fields that might be present in the solar tachocline began with Gilman & Fox (1997). Their original motivation was to see whether the magnetic field could destabilize the differential rotation of the tachocline, estimated to be stable to hydrodynamical disturbances by itself.