# Dan Lucas - Stabilisation of exact coherent structures using time-delayed feedback in two-dimensional turbulence

Dates: | 11 November 2020 |
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Times: | 14:00 - 15:00 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, External researchers, Current University students |

Dan Lucas (Keele) joins us for this virtual seminar in the Physical Applied Mathematics Series

This seminar will be held via Zoom. Please email alice.thompson@manchester.ac.uk if you require the meeting details.

Title: Stabilisation of exact coherent structures using time-delayed feedback in two-dimensional turbulence

Abstract: Time-delayed feedback control (Pyragas 1992 Phys. Letts. 170 (6) 421-428), is a method known to stabilise periodic orbits in chaotic dynamical systems. A system dx/dt = f(x) is supplemented with G(x(t)-x(t-T) where G is a `gain matrix' and T a time delay. The form of the delay term is such that it will vanish for any orbit of period T, making it an orbit of the uncontrolled system. This non-invasive feature makes the method attractive for stabilising exact coherent structures in fluid turbulence. Here we validate the method using the basic flow in Kolmogorov flow; a two-dimensional incompressible viscous flow with a sinusoidal body force. Linear predictions for the laminar basic flow are well captured by direct numerical simulation. This result demonstrates a work-around of the so-called “odd-number” limitation in flows which have a continuous symmetry. By applying an adaptive method to adjust the streamwise translation of the delay, a known nonlinear travelling wave solution is able to be stabilised up to relatively high Reynolds number. Finally an adaptive method to converge the period T is also presented to enable periodic orbits to be stabilised in a proof of concept study at low Reynolds numbers. These results demonstrate that unstable ECSs may be found by timestepping a modified set of equations, thus circumventing the usual convergence algorithms.