Jets, Vortices and Turbulence in Quasi-Geostrophic Magnetohydrodynamics

Abstract

In this thesis, we model the dynamics of the solar tachocline and the Earth's molten core using a shallow, rapidly rotating, and electrically conducting fluid on an f-plane. We explore the effects of a strong uniform magnetic field with and without a weak free-surface in three different physical problems. We start with large coherent vortices to build an understanding of the local interactions between the field and vortical structures. Magnetic field lines are expelled from the vortex cores for weaker fields and vortices are disrupted for stronger ones, along with a generation of small scale features in the potential vorticity. Including a weak free-surface makes the flow more compact and inhibits the field-induced anisotropy. We then study freely-decaying turbulence using the shape of the energy spectra and the spectral energy fluxes. Kinetic energy is sent to smaller length scales while magnetic energy moves to larger scales for increasing field strength. In the mid to large wavenumbers, the downscale transfer of energy is due to the Lorentz force. Including a free-surface adds an additional downscale transfer at smaller wavenumbers, provided the field is weak enough. Finally, we study the linear stability and nonlinear evolution of an unstable Bickley jet. The field and free-surface are confirmed to be individually stabilizing to the jet and the combined effects show increased stability.