About the project
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.
