Metastability of Geophysical Turbulent Flows

The dynamics of geophysical turbulent flows, such as the Earth's atmosphere and oceans play a critical role in determining the long-term climate of our planet. Therefore, the understanding and modelling of their long-term mean dynamics becomes increasingly important for studying the effect of climate change. However, the equations of motions of these systems are incredibly complex and require high resolution numerical simulations computed over long computation times in order to acquire long-term flow statistics. I propose a PhD project that builds upon theory developed by my MSc supervisor Dr Jason Laurie concerning the prediction of mean flow profiles in these geophysical flows [1,2]. The plan of the project will be to develop a kinetic theory approach [3] to determine a stochastic Reynolds equation for the mean flow dynamics that depends on the Reynolds stresses of the underlying turbulent fluctuations. We will go beyond the typical quasi-linear approximation to include stochastic feedback correlated to the underlying turbulence. This will yield a set of equations that will be highly accurate, and computationally efficient and applicable to studying metastability using large deviation and instanton methods [4]. The benefits of this approach could be substantial for climate scientists. Indeed, the problem of modelling these phenomena typically necessitates the use of parallel computing, and as such we plan to develop new CUDA-enabled high-performance parallel codes using the computational facilities of Dr Jason Laurie.
The project will further allow for me to build upon the point-vortex theory I have been working on with Dr Laurie during my MSc by Research at Aston University. Our point-vortex calculations can be used to study the dynamics of idealised setups of 2D classical and quantum turbulence and can be used to gain further insight into the mathematics regarding vortex scattering and sound emission.
I have worked with Dr Laurie during my MSc by Research at Aston University on point-vortex dynamics. This project has given me an extensive introduction to fluid dynamics and theoretical physics as a whole; including topics such as Hamiltonian mechanics, phase-plane analysis, solutions of elliptic integrals, turbulence, vortex dynamics, etc. For this project, I have developed substantial experience in numerical methods and programming in C++ that will prove invaluable in this PhD position. The PhD project will provide a natural progression of my research interests in fluid mechanics and geophysical turbulence and further develop my scientific computing skills.
I undertook the MSc by Research at Aston University following my undergraduate BSc in Mathematics, also at Aston University, in which I achieved the result of a high first class with honours. It was during this time that I developed my understanding of various different aspects of advanced mathematics, for example; chaos and dynamical systems, probabilistic modelling, numerical methods, and more.