About the Project
Supervisory team: Dr Davide Lasagna
Which disturbances produce the largest response in a turbulent flow? This project will develop mathematical and computational methods to answer this question while accounting for the changing flow state. Combining fluid mechanics, dynamical systems and chaos theory, you will investigate how turbulence amplifies disturbances and generates organised patterns of motion.
Turbulent flows contain organised structures despite their irregular motion. Understanding how these structures arise is important for explaining turbulence and identifying ways to influence it. Analysing the Navier–Stokes equations linearised around the mean flow has helped explain features such as streaks near walls and very large scale motions. In resolvent analysis, these structures are studied as amplified responses to external forcing or to forcing generated by nonlinear interactions within the flow.
However, the mean flow averages over the evolving turbulent motion. It therefore omits the instantaneous flow states and their sequence, which may strongly influence the response to disturbances. This project will investigate how optimal perturbations depend on the turbulent trajectory and what this reveals about coherent structures in wall-bounded flows.
You will develop a chaotic resolvent framework: a method for analysing forcing and response along chaotic flow trajectories. The research will combine mathematical analysis with algorithm development and numerical implementation, drawing on dynamical systems and chaos theory to address the sensitivity of turbulent trajectories to perturbations.
You will formulate appropriate measures of amplification, compute optimal forcing and response structures and test their physical interpretation using turbulent flow simulations.
The intended outcomes are computational tools and a clearer understanding of when instantaneous flow dynamics change the predictions of mean-flow analysis.
You will develop expertise in fluid mechanics, numerical linear algebra and scientific computing while tackling an open problem at the intersection of turbulence and applied mathematics.
The School of Engineering is committed to promoting equality, diversity inclusivity as demonstrated by our Athena SWAN award. We welcome all applicants regardless of their gender, ethnicity, disability, sexual orientation or age, and will give full consideration to applicants seeking flexible working patterns and those who have taken a career break. The University has a generous maternity policy, onsite childcare facilities, and offers a range of benefits to help ensure employees’ well-being and work-life balance. The University of Southampton is committed to sustainability and has been awarded the Platinum EcoAward.
Entry requirements
You must have a UK 2:1 honours degree, or its international equivalent, in one of the following:
- aerospace engineering
- mechanical engineering
- physics
- mathematics
- a closely related discipline
Essential skills:
- mathematical skills in linear algebra, differential equations and calculus, with experience analysing mathematical models
- a basic understanding of fluid mechanics
- programming experience sufficient to implement numerical algorithms and analyse simulation data, demonstrated through coursework, an independent project or research
Desirable skills:
- experience with numerical methods, dynamical systems, computational fluid dynamics or scientific software development
Fees and funding
We offer a range of funding opportunities for both UK and international students. Horizon Europe fee waivers automatically cover the difference between overseas and UK fees for qualifying students.
Competition-based Presidential Bursaries from the University cover the difference between overseas and UK fees for top-ranked applicants.
Competition-based studentships offered by our schools typically cover UK-level tuition fees and a stipend for living costs for top-ranked applicants.
Funding will be awarded on a rolling basis, so apply early for the best opportunity to be considered.
For more information, please visit our postgraduate research funding pages.
How to apply
Apply now
You need to:
- choose programme type (Research), 2027/28, Faculty of Engineering and Physical Sciences
- select Full time or Part time
- search for programme PhD Engineering & the Environment (7175)
- add name of the supervisor in section 2 of the application
Applications should include:
- research proposal
- your CV (resumé)
- 2 academic references
- degree transcripts and certificates to date
- English language qualification (if applicable)
Contact us
Faculty of Engineering and Physical Sciences
For questions about applying, doctoralcollege-admissions@soton.ac.uk.
Project leader
For an initial conversation, davide.lasagna@soton.ac.uk.