Nonlinear waves on liquid cylinders (BLYTHM_U27EMPSFP)
Key details
- Application Deadline
- 31 July 2026 (11:59 pm UK time)
- Location
- UEA
- Funding Type
- Self-funded (Home students only)
- Start Date
- 1 October 2026
- Mode of Study
- Full or Part time
- Programme Type
- PhD
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Project Description
Primary Supervisor: Prof. Mark Blyth(opens in a new window)
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.
Entry Requirements
The minimum entry requirement is 2:1 in mathematics or physics.
Funding
This project is offered on a self-funded basis. It is open to applicants who are self-funded or who are in the process of securing external funding. Details of tuition fees can be found here.
A bench fee is payable in addition to the tuition fee, to cover the cost of specialist equipment and laboratory facilities required for the research. Applicants should contact the primary supervisor for details of the bench fee applicable to this project.
If you are part of the UEA alumni community, you may be eligible for a tuition fee discount. The UEA Alumni 10% Tuition Fee Discount Scheme(opens in a new window) offers a 10% reduction for eligible alumni, while the and UEA 30% Final Year Undergraduate Continuation Scholarship(opens in a new window) offers a reduction of up to 30% for qualifying applicants. Visit each scholarship page for full eligibility details.
For information on doctoral funding, visit our Postgraduate Student Loans(opens in a new window) page.
References
2014 M. G. Blyth & E. I. Parau, Solitary waves on a ferrofluid jet. J. Fluid Mech. 750, 401-420
1998 J-M. Vanden-Broeck, T. Miloh & B. Spivak, Axisymmetric capillary waves, Wave Motion, 27, 245-256.
2022 A. H. Earhart, E. Wahlen, J.Weber, Bifurcation analysis for axisymmetric capillary
Water waves with vorticity and swirl, Studies in Appl. Math., 149.