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BEGIN:VEVENT
DTSTAMP:20200922T172512Z
DTSTART:20201111T140000Z
DTEND:20201111T150000Z
SUMMARY:Dan Lucas - Stabilisation of exact coherent structures using time
-delayed feedback in two-dimensional turbulence
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}r10l-kfccj9
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DESCRIPTION:Dan Lucas (Keele) joins us for this virtual seminar in the Ph
ysical Applied Mathematics Series\n\nThis seminar will be held via Zoom.
Please email alice.thompson@manchester.ac.uk if you require the meeting
details.\n\nTitle: Stabilisation of exact coherent structures using tim
e-delayed feedback in two-dimensional turbulence\n\nAbstract: Time-delay
ed feedback control (Pyragas 1992 Phys. Letts. 170 (6) 421-428)\, is a m
ethod 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 `ga
in matrix' and T a time delay. The form of the delay term is such that i
t will vanish for any orbit of period T\, making it an orbit of the unco
ntrolled system. This non-invasive feature makes the method attractive f
or stabilising exact coherent structures in fluid turbulence. Here we va
lidate the method using the basic flow in Kolmogorov flow\; a two-dimens
ional incompressible viscous flow with a sinusoidal body force. Linear p
redictions for the laminar basic flow are well captured by direct numeri
cal simulation. This result demonstrates a work-around of the so-called
“odd-number” limitation in flows which have a continuous symmetry. By ap
plying an adaptive method to adjust the streamwise translation of the de
lay\, a known nonlinear travelling wave solution is able to be stabilise
d up to relatively high Reynolds number. Finally an adaptive method to c
onverge the period T is also presented to enable periodic orbits to be s
tabilised in a proof of concept study at low Reynolds numbers. These res
ults demonstrate that unstable ECSs may be found by timestepping a modif
ied set of equations\, thus circumventing the usual convergence algorith
ms.\n\n
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Via Zoom.
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