The magnetohydrodynamic primitive equations

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The equations of magnetohydrodynamics (MHD) have been widely used to understand the dynamics of flows in stellar and planetary atmospheres and interiors, including the generation of magnetic fields. However, when considering thin layers with a stable density stratification, it is possible to derive a simplified set of so-called MHD primitive equations, which can be regarded as a magnetohydrodynamic extension of the primitive equations that are widely used in meteorology and oceanography. The first aim of this project is to study dynamical processes as described by the MHD primitive equations, such as instabilities of rotating shear flows and the turbulence that results, building upon well-understood processes in meteorology, oceanography, and the more complex full equations of MHD. The second aim is to investigate to what extent the simplifications inherent in the MHD primitive equations allow efficiency savings in either mathematical analysis or computational modelling, relative to the full equations of MHD. There are important applications of this work in both stellar contexts (e.g., modelling of the solar tachocline) and planetary contexts (e.g., modelling of Hot Jupiters).