Stabilisation of exact coherent structures in fluid turbulence

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The unpredictable and multi-scale nature of fluid turbulence makes it a significant modelling challenge for many industries and natural systems. From designing planes, trains and ships, renewable energy technologies to sustainable ventilation systems, the list of situations where turbulent flows are important is almost endless. This means that there are considerable economic opportunities associated with understanding and influencing turbulent flows. After many years of intense research there is yet to emerge a rigorous predictive theory for turbulence, despite progress in modelling and analysing the governing equations. The main reason for this difficulty lies in the complexity such flows exhibit in space and time. Temporal complexity is manifest via the chaotic nature of the solutions to the governing equations; the solutions never repeat and are sensitive to initial conditions. Spatial complexity appears as turbulence being more intense in some regions than others, for no appreciable reason. It is possible, though currently difficult, to extract from this complexity, simpler solutions which underly the turbulent state. These solutions may be steady in time or time periodic but crucially they are unstable, and therefore never fully realised. The hypothesis is that these solutions are good proxies for the turbulence from which we can glean new insights and make rigorous predictions of the flow. This project will provide a new computationally efficient method for predicting fluid turbulence by developing a control method to stabilise simple unstable solutions embedded in the chaos. Until now these solutions require careful convergence which is a two-step process; first a guess needs to be found, then the solution converged using a sophisticated numerical algorithm. Our approach is to include new terms into the governing equations which will 'passively' stabilise solutions enabling the evolution to tend towards them without the need for guesses or convergences. The increases in efficiency afforded by our new method will allow us to tackle vastly more complex scenarios than previously possible enabling us to approach the true "spatiotemporal complexity" of real world turbulence.