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Tuesday 08 Oct 2019Dynamics Seminar: Towards the control of transitional flows

Anton Pershin - University of Leeds

Harrison 103 13:30-15:30

Shear flows are driven either by internal forcing (e.g. a pressure gradient) or by boundary forcing (e.g. the differential motion of the walls). They represent the simplest configurations in which we can observe bistability between the laminar (unidirectional) flow and turbulence (a state of spatio-temporal chaos). Transition is typically triggered by imposing a suitable finite-amplitude perturbation to the laminar flow. Using plane Couette flow (viscous flow between two differentially moving walls) as an example, we will first characterise transition in a small domain by means of a novel probabilistic protocol to approximate the size of the basin of attraction of the laminar state. We will then show how it can be used to quantify the efficiency of control strategies aimed at suppressing or promoting the instability. Next, we will turn to transition in large domains, which usually involves spatially localised seeds and for which we will use the paradigm of spatially localised solutions (and homoclinic snaking) to create a reproducible framework. By time-integrating these solutions for a range of subcritical Reynolds numbers, we unravelled various dynamical regimes involving oscillatory dynamics, spot splitting, front growth and connections between exact solutions. We will characterise all these regimes in a schematic of parameter space. If time permits, we will explore laminarisation control and its assessment in large domains.

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