PhD Studentship - Nonlinear Waves Travelling On Liquid Cylinders (PARAUE_U26SCI)

Primary supervisor - Prof Emilian Parau

Inviscid liquid jets subject to surface tension and in the absence of gravity are known to be unstable under long-wave perturbations, a phenomenon described by the classical Rayleigh–Plateau instability. However, when vorticity and swirl are included, Erhard et al. (2022) have theoretically demonstrated the existence of nonlinear travelling-wave solutions on such jets — although their detailed properties remain unexplored. In this project, we will develop new computational methods to compute and characterize these novel wave solutions, with particular emphasis on solitary waves and on analysing their stability. We will also extend the study to related configurations, such as ferrofluid jets under vorticity and swirl. 

The mathematical and numerical techniques developed during this work will deepen our understanding of nonlinear wave phenomena in fluid mechanics and contribute to the broader theory of interfacial flows. 

This PhD project is in a competition for a Faculty of Science funded studentship. Funding is available to UK applicants and comprises ‘home’ tuition fees and an annual stipend for 3 years.

Entry requirements The standard minimum entry requirement is 2:1 in Mathematics, Physics.

Mode of study Full-time

Start date 1 October 2026

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