Rare-events in turbulent fluid flow

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

In the 2018 Government Office for Science report, 'Computational Modelling: Technological Futures', Greg Clarke, the Secretary of State for Business Energy and Industrial Strategy, wrote "Computational modelling is essential to our future productivity and competitiveness, for businesses of all sizes and across all sectors of the economy". With its focus on computational models, the mathematics that underpin them, and their integration with complex data, the MathSys II CDT will generate diverse impacts beyond academia. This includes impacts on skills, on the economy, on policy and on society.

Impacts on skills.
MathSys II will produce a minimum of 50 PhD graduates to support the growing national demand for advanced mathematical modelling and data analysis skills. The CDT will provide each of them with broad core skills in the MSc, a deep knowledge of their chosen research specialisation in the PhD and a complementary qualification in transferable skills integrated throughout. Graduates will thus acquire the profiles needed to form the next generation of leaders in business, government and academia. They will be supported by an integrated pastoral support framework, including a diverse group of accessible leadership role models. The cohort based environment of the CDT provides a multiplier effect by encouraging cohorts to forge long-lasting professional networks whose value and influence will long outlast the CDT itself. MathSys II will seek to maximise the influence of these networks by providing topical training in Responsible Research and Innovation, by maintaining a robust Equality, Diversity & Inclusion policy, and by integration with Warwick's global network of international partnerships.

Economic impacts.
The research outputs from many MathSys II PhD projects will be of direct economic value to commercial, public sector and charitable external partners. Engagement with CDT partners will facilitate these impacts. This includes co-supervision of PhD and MSc projects, co-creation of Research Study Groups, and a strong commitment to provide placements/internships for CDT students. When commercial innovations or IP are generated, we will work with Warwick Ventures, the commercial arm of the University of Warwick, to commercialise/license IP where appropriate. Economic impact may also come from the creation of new companies by CDT graduates. MathSys II will present entrepreneurship as a viable career option to students. One external partner, Spectra Analytics, was founded by graduates of the preceding Complexity Science CDT, thus providing accessible role models. We will also provide in-house entrepreneurship training via Warwick Ventures and host events by external start-up accelerator Entrepreneur First.

Impacts on policy.
The CDT will influence policy at the national and international level by working with external partners operating in policy. UK examples include Department of Health, Public Health England and DEFRA. International examples include World Health Organisation (WHO) and the European Commission for the Control of Foot-and-mouth Disease (EuFMD). MathSys students will also utilise the recently announced UKRI policy internships scheme.

Impacts on society.
Public engagement will allow CDT students to promote the value of their research to society at large. Aside from social media, suitable local events include DataBeers, Cafe Scientifique, and the Big Bang Fair. MathSys will also promote a socially-oriented ethos of technology for the common good. Concretely, this includes the creation of open-source software, integration of software and data carpentry into our computational and data driven research training and championing open-access to research. We will also contribute to the 'innovation culture and science' strand of Coventry's 2021 City of Culture programme.