Rotating Shallow Water Magnetohydrodynamics

Over the past decade, shallow-water magnetohydrodynamics (SWMHD) has been used as a model system to describe various waves and instabilities in thin astrophysical layers. This system is far simpler than the alternatives, and allows both mathematical analysis (e.g., linear stability) and nonlinear numerical simulations (e.g., transition to turbulence) to be performed.

This PhD project would expand upon recent research work on SWMHD at Leeds. A particular focus would be instabilities of shear flows with background rotation, and how the interaction of magnetic field and rotation either enhances or suppresses standard shear instabilities. There is the possibility of both asymptotics (e.g., the long-wave methodology of Drazin and Howard) and numerical simulation of the fully nonlinear instability.