Nonlinear Resonance: Mathematics and Computation, Mathematics – PhD (Funded) Ref: 3394

About the award


Professor Beth Wingate, University of Exeter


Mathematics, Streatham Campus, Exeter

The University of Exeter’s College of Engineering, Mathematics and Physical Sciences, is inviting applications for a fully-funded PhD studentship to commence in September 2019 or as soon as possible thereafter.  For eligible students the studentship will cover UK/EU/International tuition fees plus an annual tax-free stipend of at least £14,777 for 3.5 years full-time, or pro rata for part-time study.  The student would be based in the Department of Mathematics in the College of Engineering, Mathematics and Physical Sciences at the Streatham Campus in Exeter.

Project Description:
When a bell is struck, its shape creates resonances that produce its primary strike-tone and harmonic spectra. A central question explored in this project is how nonlinear resonance in fluids, rather than in solids, create low frequency, long-lasting dynamical patterns or ‘mean’ flows, as well as characterizing their evolution and life cycles.
The student will explore the mathematical nature of resonance in fluids, primarily with applications to the atmosphere, ocean, and magnetic field in idealized configurations. In particular the project will seek to understand how nonlinear oscillations give rise to low-frequency mean flows in time-scale separated phenomenon. What creates nonlinear resonance in fluids? How does it depend on the parameters of the physics such as background ocean stratification or magnetic field? Can numerical analysis shed new light on how we can approximate the phenomenon with numerical computation?  This project will involve a combination of theoretical fluid dynamics, numerical analysis and simulation to seek answers to these questions. The student will choose the direction of the project in consultation with the supervisors.  This project also has the unique potential of allowing for the possibility of collaboration with Dr. Terry Haut in the Center for Applied Scientific Computing ( at Lawrence Livermore National Laboratory located near San Francisco, United States.
The successful student will join the Centre for Geophysical and Astrophysical Fluid Dynamics which is part of the Department of Mathematics.

Entry requirements

Applicants for this studentship must have obtained, or be about to obtain, a First or Upper Second Class UK Honours degree, or the equivalent qualifications gained outside the UK, in an appropriate area of science or technology including mathematics, engineering, or the physical sciences. 
If English is not your first language you will need to have achieved at least 6.0 IELTS and no less than 6.0 in any section by the start of the project.  Alternative tests may be acceptable (see

How to apply

In the application process you will be asked to upload several documents. 
• CV
• Letter of application (outlining your academic interests, prior research experience and reasons for wishing to undertake the project).
• Research proposal
• Transcript(s) giving full details of subjects studied and grades/marks obtained (this should be an interim transcript if you are still studying)
• Names of two referees familiar with your academic work. You are not required to obtain references yourself. We will request references directly from your referees if you are shortlisted.
• If you are not a national of a majority English-speaking country you will need to submit evidence of your proficiency in English
The closing date for applications is midnight on 21 January 2019.  Interviews will be held on the University of Exeter Streatham the week commencing 11 February 2019.
If you have any general enquiries about the application process please email or phone +44 (0)1392 722730 or +44 (0)1392 725150.  Project-specific queries should be directed to the main supervisor.


Application deadline:21st January 2019
Number of awards:1
Duration of award:per year