There is a recent upsurge of interest world-wide in the self-structuring properties of quasi two-dimensional flows, motivated by the need to control transport in next-step fusion energy experiments and understand variations in planetary circulations mediated by climate change. What is the deeper physics behind the remarkable fact that in such flows ordered structures and patterns can arise from chaotic or turbulent fluid motions? Since thermodynamics tells us that disorder or entropy tends to increase, such behaviour may seem counterintuitive. In this module we shall study equations of motion for planetary flows in the geostrophic approximation and for magnetic fusion plasmas in the electrostatic approximation, and compare and contrast the physics expressed by each system.
Suitable for students who have completed MATH2405 and MATH2305 and some physics.