Rare-events in turbulent fluid flow

Lead Research Organisation: University of Warwick
Department Name: Mathematics

Abstract

The proposed PhD will focus on developing and building up on current statistical theory with modelling the occurrence and stability of large-scale structures in fluids (an atmosphere for example). We analyse stability of large structures in spatially extended stochastic systems with large time-scale separation. Concretely, we are looking at planetary atmospheres, where large zonal jets are stable structures driven by fast turbulent fluctuations. Methods from Large Deviation Theory, statistical modelling, and Data Science (such as clustering algorithms), are used to learn about the stability and lifetimes of these structures.
Possible applications are manifold:
Observations of exoplanets are restricted to the spectra emitted from their atmosphere. By modelling exoplanetary atmospheres, one can in principle deduce other characteristics, such as planetary radius, temperature differences in the atmosphere, and wind patterns, from spectral observations. A very popular research topic is currently finding possible signs of life on exoplanets which can be made easier if the dynamics of an atmosphere are known.
For fusion energy, plasma confinement in Tokamak fusion reactors deals with very similar equations, where the stability of the boundary layer is perturbed by the emergence of jets, and understanding their stability and lifetimes is crucial for confining plasmas efficiently to generate energy.
Further, understanding Earth's climate and the stability of structures such as the meandering jet stream or the Gulf stream are essential for predicting earths weather systems which are notoriously difficult to model.
The context of the research - Large-scale structures such as jets occur in turbulent fluid flow which when studied, can shed light on the dynamics of fluids in atmospheres or plasma flows for example. These structures can evolve over time and have various stable configurations with rare events such as creation of new jets also occurring. Investigating these configurations and transitions between configurations will lead to a much better understanding of these and similar stochastic systems in the real-world.
The aims and objectives of the research - This research aims to develop a statistical theory for analysing zonal jet configurations in a general context. We will then apply this theory to exoplanet atmospheres, plasma flows in Tokamaks and other systems with zonal jets. We will also study these configurations in a rare-events setting where rare transitions in these systems can be predicted.
The novelty of the research methodology - The novelty of the research is the application of methods from stochastic averaging and homogenization to large scale flows in order to describe both the expected mean behaviour of large-scale structures on a turbulent background, as well as typical fluctuations and rare excitations away from typical states.
The potential impact, applications, and benefits - The ability to accurately model and predict large structures in an exoplanet's atmosphere will allow extensive research into the processes occurring in these atmospheres and therefore better understand the planets themselves. This research will help with understanding the Earths weather systems which are affected by jets and can currently be very unpredictable with climate change. Predicting jets in thermonuclear fusion reactors (Tokamaks) is also very important for current research into fusion power and confinement.
Research area; Energy, Mathematical Sciences, Physical Sciences
External partner - MetOffice

Publications

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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/S022244/1 01/10/2019 31/03/2028
2271245 Studentship EP/S022244/1 23/09/2019 30/09/2023 Nayef Shkeir