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New methods for computing exact coherent structures responsible for cascades of energy in fluid turbulence

   Faculty of Natural Sciences

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  Dr D Lucas  No more applications being accepted  Funded PhD Project (European/UK Students Only)

About the Project

A major challenge in the field of fluid mechanics exists in understanding the complex nonlinear behaviour of turbulence. This problem has an enormous number of engineering and geophysical applications. Recently this spatiotemporal chaos has begun to be unravelled by considering the turbulent trajectory from a dynamical systems perspective as fleetingly visiting the neighbourhoods of unstable exact solutions, for example, fixed points, travelling waves and periodic orbits. These solutions have great value as reduced descriptions of the complex turbulent attractor. However significant challenges exist in efficiently locating and converging upon such solutions. A further challenge is in computing them in sufficient abundance and at high enough Reynolds numbers to associate with them exchanges of energy across spatial scales. This project aims to address this problem using several new techniques and makes use of the latest numerical methods including using GPU acceleration. The successful candidate will learn the current state-of-the-art method (so-called “recurrent-flow analysis”), extend it and finally apply these new methods to new systems, ultimately broadening the parameter regimes for which these techniques are practical.
Further information including references can be found at

1 PhD available from September 2019.

Informal enquiries about the project should be made to the Project Lead: Dr Dan Lucas [Email Address Removed] and should include a CV.

To apply please go to
Please quote FNS GS 2019-11 on your application.

Funding Notes

Funding support is provided as follows:

100% UK/EU tuition fees for 3 years commencing Academic year 2019/2020 (UK/EU fees are £4,327 per annum for 2019/20). Stipend support for three years at Research Council rates (2019/20 stipend £15,009 per annum). Some support for conference attendance will be available.

Eligibility criteria:

Minimum of BSc (2:1 or higher) in applied mathematics or equivalent discipline, with strong preference for candidates with experience of computational modelling and/or fluid mechanics. Overseas students are eligible but need to pay the difference between UK/EU fees (£4,327 per annum for 2019/20) and overseas fees.

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