Turbulent plumes, whether found in atmospheric gas dispersion or within high-energy fuel combustors, are central to applications across engineering, environmental science, and physics. These complex flows impact everything from air quality monitoring to fuel efficiency in combustion processes and are essential for fault diagnostics in aerospace propulsion. This project aims to explore whether it is feasible to image the concentration and temperature profile of gases within a turbulent plume using sparse optical measurements? Addressing this question requires modelling and analysis on how photons interact with highly dynamic media, combining principles from ill-posed inverse problems, and partial differential equations, such as radiative and heat transfer. Aside the harsh environment constraint that limits the amount of data that are feasible to collect, this endeavour is further complicated by the turbulent nature of the media itself. The challenge lies not only in reconstructing the complex features of these images from limited noisy data but also in establishing a rational way of parameterising and characterising the turbulence to suppress the uncertainty in the reconstructed images.

The research will delve into the study of random media and Bayesian inference frameworks as turbulent flows exhibit chaotic behaviour, and capturing data-consistent estimates of uncertainty will ensure the credibility of the reconstructed images. Moreover, the project offers an exciting opportunity to explore contemporary approaches in data-driven modelling of turbulence. Neural networks, including neural operators and diffusion models, show promise for efficiently representing the complex swirling and chaotic structures of turbulent flows, potentially offering an alternative or complement to traditional models.

This project provides a stimulating environment for mathematically inclined graduates, offering direct applicability to high-impact fields and the chance to contribute to pioneering research that bridges theory, computation, and practical application. Opportunities for direct collaboration with experts in gas metrology and aerospace to refine methods and validate results.