About the Project
Many problems in fluid mechanics can be investigated by using reduced models. In recent years, the trend has been to use neural networks or other model reduction techniques to learn solutions from high-resolution computations of the full-field equations, e.g. Navier--Stokes. A more classical approach is to choose a specific form of solution based on properties of the problem, e.g. assume axisymmetry or a particular form of the solution, and derive a simplified set of equations. The solutions of…
the reduced models can then be investigated using techniques of linear and nonlinear stability analysis. In cases in which there is uniqueness, one would naturally expect the solution of the reduced system to have a close relationship to the solution of the full system, but what about when there are multiple solutions? In such cases, the predictions of the reduced models can be both qualitatively and quantitatively wrong; or they can be extremely accurate. What is not understood is why the models work so well in some cases, but fail spectacularly in others.
The aim of this project is to investigate how nonlinear behaviour in reduced systems is related to that in the full system and, in particular, whether the influence of the reduced system on the full system and its accuracy can be determined a priori. The project will use a mixture of analytic and numerical techniques, including series solutions, linear and weakly nonlinear stability analysis, finite element methods and numerical bifurcation tracking within the C++ finite-element library oomph-lib.
This project should appeal to students with an interest in fluid flows, nonlinear systems, stability, solution of ODEs and PDEs as well as numerical methods and scientific computing.
This project is expected to start in September 2027.
Before you apply: We strongly recommend that you contact the supervisors for this project before you apply.
How to apply: To be considered for this project you must complete a formal application through our online application portal. If you already have an applicant account, this link will directly open an application for PhD School of Natural Sciences Scholarships. If you don’t already have an applicant account, please follow the instructions here.
When applying, please specify the full title and supervisor/s of the project, details of your previous study, and names and contact details of two referees. You must also upload a Supporting Statement describing your motivation to apply to the project, your CV and transcripts of awarded and in-progress university qualifications. Please note late or incomplete applications will not be considered.
Equality, diversity and inclusion are fundamental to the success of The University of Manchester and central to all our activities. A diverse research community strengthens creativity, productivity and quality, while increasing the societal and economic impact of our work. We welcome applicants from all career paths, backgrounds and sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation or transgender status.
We welcome applications from candidates returning to study after a career break or experience in other roles. Flexible study arrangements may be available, including part-time study at 50%, 60% or 80%, subject to the requirements of the project and funder.
Eligibility: The standard academic entry requirement for this PhD is an upper second-class (2:1) honours degree (or international equivalent) in Applied Mathematics or a discipline directly relevant to the PhD OR any upper-second class (2:1) honours degree and a Master’s degree at merit (or international equivalent) in Applied Mathematics or a discipline directly relevant to the PhD. Previous study of fluid mechanics and computer programming is essential.
This project will remain open until filled.
If your application is submitted by 1st November 2026, you can expect a decision by 18th December 2026.
If your application is submitted by 15th January 2027, you can expect a decision by 30th March 2027.
Self or externally funded students can also be considered for this project.
FSE_SoNS
Funding Notes
Funding covers tuition fees, an annual stipend at the UKRI minimum rate (currently £21,805 per year), and a research training support grant of up to £2,500 per year for the full 3.5-year programme.