[School of Natural Sciences PhD Scholarships] Models of three-dimensional instability in high-speed flow

About the project

About the Project This project investigates the use of asymptotic methods to predict and understand three-dimensional instabilities arising from separated flows at high Reynolds and Mach numbers. High-speed flow over surfaces with bumps or ramps commonly induces flow separation, leading to the formation of three-dimensional, streak-like structures. While Direct Numerical Simulation (DNS) can reproduce these phenomena, it is computationally expensive and yields complex data due to the numerous governing parameters – leaving fundamental aspects of the underlying instability mechanisms still open to interpretation. Previous asymptotic work has demonstrated the prediction of three-dimensional instability onset at small spanwise wavelengths [1], with ongoing efforts focused on modelling re-stabilisation at larger wavelengths. This approach offers several key advantages: (i) explicit capture of dominant length and time scales, (ii) significant reduction in parameter space enabling broader applicability through simple re-scaling, (iii) illumination of essential physical mechanisms, and (iv) a unifying framework for interpreting results from DNS. This project builds on this foundation by exploring the following novel directions: Investigating the role of nonlinearity in perturbation evolution. Extending the methodology beyond planar geometries to more complex configurations. Exploring potential secondary instabilities arising from nonlinear three-dimensional states. Determining whether these instability mechanisms also occur in alternative flow regimes, such as subsonic flows. 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 Mathematics, Physics, or Engineering OR any upper-second class (2:1) honours degree and a Master’s degree at merit (or international equivalent) Mathematics, Physics, or Engineering. A strong mathematical foundation and background in fluid mechanics is desired. The ideal candidate will be enthusiastic about combining analytical, asymptotic, and computational techniques to address challenging problems in fundamental fluid dynamics. 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. FSESoNS

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