Equilibria and stability of vortex clusters (BLYTHM_U26EMP)

A point vortex is an elementary, singular solution of the equations of inviscid fluid flow, and it is of fundamental importance for studying more complex fluids motions. Via mutually induced motion two point vortices either travel along parallel lines or co-rotate in a circular path. In either case, a change of reference frame makes the vortices stationary.

The aim of this project is to investigate vortex equilibria of this type more broadly, when there are N>>2 vortices present, and allowing for complex strength, so that each singularity represents a superimposed vortex-source/sink. Both stationary (in an inertial frame) and rotating clusters will be studied. Computation of equilibria, and an analysis of their stability will both be examined in detail.

The standard minimum entry requirement is 2:2 in Mathematics, Physics, Natural Sciences. This project is offered on a self-funding basis. It is open to applicants with funding or those applying to funding sources.

Details of tuition fees can be found here. A bench fee is also payable in addition to the tuition fee to cover specialist equipment or laboratory costs required for the research. Applicants should contact the primary supervisor for further information about the fee associated with the project.