Flux expulsion in shallow water magnetohydrodynamics

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Magnetic fluids of the Earth, Sun, stars and galaxies are generated by the motion of electrically conducting fluid, for example hydrogen plasma in the case of the Sun, liquid metal for the Earth. The project concerns a fundamental process in the interaction of magnetic field and fluid called flux expulsion, where field is expelled from regions of closed streamlines, for example a fluid vortex. This process was first identified by Nigel Weiss in the 1960s, but it was only recently that studies included the magnetic field feedback on the flow through the Lorentz force, e.g. Gilbert, Mason and Tobias (2016). The goal of the project is to study flux expulsion in a thin layer using the equations of shallow water magnetohydrodynamics (MHD) where the fluid motion is coupled to gravity waves. Such models are relevant to the solar tachocline and other systems where the fluid is stratified. The study would initially use numerical simulations in periodic geometry, but the goal would be also to develop scaling laws and analytical models.