The magnetohydrodynamic primitive equations

磁流体动力学（MHD）方程已被广泛用于理解恒星和行星大气和内部的流动动力学，包括磁场的产生。然而，当考虑具有稳定密度分层的薄层时，可以导出一组简化的所谓MHD原始方程，其可以被视为在气象学和海洋学中广泛使用的原始方程的磁流体动力学扩展。该项目的第一个目标是研究由MHD原始方程描述的动力学过程，例如旋转剪切流的不稳定性和由此产生的湍流，建立在气象学，海洋学和更复杂的MHD完整方程中的充分理解的过程上。第二个目的是调查在何种程度上的简化固有的MHD原始方程允许效率的节省，无论是在数学分析或计算建模，相对于完整的MHD方程。这项工作在两种恒星背景下都有重要的应用（例如，太阳速跃层的建模）和行星背景（例如，热蒸发器的建模）。

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).