Fluid systems often have an underlying Hamiltonian structure, where associated symmetries in the system can be linked to conservation laws via Noether's theorem (via the Lagrangian), which can then be utilised accordingly, for example for deriving reduced models, properly defined wave actions, and stability theorems. The project will review some of the existing literature for Hamiltonian fluid mechanics, principally with a focus on stability theorems (methods due originally to Arnol'd), but also on wave actions, with the view to derive results in systems of geophysical and astrophysical relevance. Another possible direction the project could towards is on the statistical mechanics of point vortices, possibly with some application to quantum turbulence.

The applicant should have a good command of calculus and classical mechanics (via a maths and/or physics course, or otherwise). Experience with fluid mechanics, statistical mechanics, geometry, topology or some group theory would be desirable but not strictly necessary. The main activity will be on review of the technical literature, with forays into new analytical research and/or numerical computations where appropriate.