A Numerical Study of Magnetic and Non-Magnetic Geophysical Fluid Dynamics

The subject of fluid dynamics contains some of the last remaining unsolved challenges in classical physics. In particular, the dynamics of rotating fluids still pose many unanswered questions despite the availability of modern supercomputers. It is often the case that the parameter regimes in which we are interested are those which are the most difficult to reach. It is therefore common to focus on specific aspects of a problem rather than try to solve the complete set of governing equations. In the case of rotating fluid dynamics, one such aspect is that of inertial modes. These are oscillations of the fluid arising solely from the pressure and Coriolis forces in the momentum equation. In a sphere or spherical shell, inertial modes may be excited and maintained by precession of the rotation axis. In the first part of this thesis we shall consider the unforced inertial oscillations in spherical geometry. This simplified approach still gives us slowly decaying inertial modes which we believe will exhibit the same behaviour as their forced counterparts. The motivation for studying this problem is to try to explain the origin of the internal shear layers that are known to exist within the structure of these modes. In the second part of this thesis we move into the realm of Magnetohydrodynamics where the rotating fluid is now treated as an electrical conductor and can therefore conduct currents under the action of electromagnetic fields. Again we focus on one specific area, that of magnetic stability, as opposed to solving the full 3-D dynamo equations. Here we are interested in the stability of axisymmetric magnetic fields (generated via an alpha effect) to nonaxisymmetric perturbations. This analysis will help to determine how strong a field we can expect to find in the liquid iron core of the Earth and if it is possible for that field to equilibrate at lower field strengths than the critical onset value. This may be important in understanding the mechanism of geomagnetic reversals