Optimization in Fluid Mechanics

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This project aims to realise the full potential of optimisation as a theoretical tool to study fluid mechanics motivated by our need to better understand and control flows around us. As an exemplar, the drag experienced by vehicles as they move through either air or water is a huge consumer of energy and source of carbon emissions which the UK urgently needs to reduce. In the past, optimisation has generally only been used with simplified constraints such as the linearised Navier-Stokes equations to keep problems tractable. Recently, however, two breakthroughs now strongly suggest that the solutions to more sophisticated optimisation problems can be successfully computed and a recent experiment highlights what may be achieved using clever geometry design. This project will seek to exploit these exciting advances by developing new optimisation-based approaches to treat three key problems in fluid mechanics: 1) how to systematically search for new nonlinear flow solutions to the governing Navier-Stokes equations; 2) how to manipulate nonlinear stability via boundary geometry to design more energy-efficient fluid flows in pipelines; and 3) how to calculate the best rigorous upper estimates of energy consumption (or drag) in fully turbulent shear and convective flows.