Abstract
A spectral method is used to explore the nonlinear evolution of known linear instabilities in a 2D differentially rotating magneto-hydrodynamic shell, representing the solar tachocline. Several simulations are presented, with a range of outcomes for the magnetic field configuration. Most spectacularly, the `clam instability', which occurs for solar differential rotation and a strong broad toroidal magnetic field structure, results in the field tipping over by 90° and reconnecting. A common characteristic of all the simulations though is that the nonlinear instabilities produce a strong angular momentum mixing effect which pushes the rotation towards a solid body form. It is argued that this may be the mechanism required by the model of Spiegel and Zahn to limit the tachocline's thickness.
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