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

最近对土星和木星的探测任务已经在这两颗行星的两极产生了惊人的漩涡图像。因此，这些涡旋是如何产生的，以及是什么决定了它们的大小，是人们非常感兴趣的研究课题。该项目将集中研究磁场对涡旋形成和结构的影响，特别关注气体巨行星表面附近电导率的急剧下降。该项目的一个关键目标将是确定磁场是否是确定涡旋径向范围的决定性因素。该项目将从考虑空间可变电导率（以及磁扩散率）在磁对流线性稳定性经典问题中的作用开始，最初没有旋转，目的是研究Boussinesq和非弹性体制下的问题。然后将介绍旋转的影响，这显然不是微不足道的。我们将特别感兴趣的是稳定模态和振荡模态之间的竞争。项目的最后一部分将考虑涡旋形成在旋转对流中的作用——这是一种非线性现象，将进行计算研究——以调查磁场的影响和空间依赖的磁扩散率的作用。

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.