Nonlinear evolution of 2D tachocline instabilities

A spectral method is used to explore the nonlinear evolution of known linea r 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 spectacular ly, the 'clam instability', which occurs for solar differential rotation an d a strong broad toroidal magnetic field structure, results in the field ti pping over by 90 degrees and reconnecting. A common characteristic of all t he simulations though is that the nonlinear instabilities produce a strong angular momentum mixing effect which pushes the rotation towards a solid bo dy form. It is argued that this may be the mechanism required by the model of Spiegel and Zahn to limit the tachocline's thickness.