Dan Lucas

University of St Andrews


Stabilising travelling waves from fluid turbulence. 


Fluids and Materials Seminar


24th October 2024, 2:00 pm – 3:00 pm
Fry Building, 1.11


An attractive approach to tackling the complexity of a turbulent fluid flow is to view the behaviour from a dynamical systems perspective. That is, we might imagine a trajectory navigating a high dimensional phase space directed by the stable and unstable manifolds of simple invariant states. In a fluid system such invariant states might take the form of steady equilibria, travelling waves or time periodic orbits. In many cases isolating such states is challenging due to their high instability. In this talk we will introduce the method of “time-delayed feedback control” as a method to passively stabilise travelling wave solutions to the Navier-Stokes equations. We will survey recent results in this project where we successfully stabilise states from two-dimensional turbulence and turbulence in a rectilinear periodic pipe. In both cases travelling waves can be stabilised at relatively large Reynolds numbers, and in each situation we outline some novel approaches to improve the performance of the control. Along the way we perform linear stability analyses and use methods from control theory to validate our results and help us gain additional insight into the mechanisms underpinning successful control. We also demonstrate gradient descent methods to help optimise control parameters to avoid laborious searching and enable states to be obtained from speculative guesses.






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