Shear Flow Instabilities in Rotating Shallow-Water MHD

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One of the most exciting observational discoveries in solar physics was that of the tachocline, a thin region of high velocity shear, and strong magnetic field, at the base of the convection zone. This project will consider the possible instabilities of this region, incorporating the influence of rotation; the small depth of the tachocline will be accommodated by using the shallow water MHD equations. The project will start with the linear instability of idealised flows and magnetic fields, which will be studied analytically, before moving on to more general flow and field profiles, which will require a numerical approach. The project will then move on to consider the nonlinear evolution of these instabilities, andtheir relevance to transport in the solar interior.