The influence of magnetic fields and electrical conductivity variations on vortex formation

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Recent missions to Saturn and Jupiter have produced striking images of vortices at the poles of both planets. How these vortices arise, and what determines their size, are therefore topics of great research interest. This project will concentrate on the influence of the magnetic field on vortex formation and structure, paying particular attention to the sharp decrease in electrical conductivity close to the surfaces of the gas giant planets. One of the key aims of the project will be to determine whether the magnetic field is the defining element in determining the radial extent of the vortices.The project will start by considering the role of spatially variable electrical conductivity (and hence magnetic diffusivity) in the classical problem of the linear stability of magnetoconvection, initially without rotation, with the aim of investigating the problem in both the Boussinesq and anelastic regimes. The influence of rotation, which is decidedly non-trivial, will then be introduced. We shall be particularly interested in the competition between steady and oscillatory modes of instability. The final part of the project will be to consider the role of vortex formation in rotating convection - a nonlinear phenomenon, that will be studied computationally - to investigate the influence of the magnetic field and the role of the spatially-dependent magnetic diffusivity.