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SUMMARY:Verifying global stability of fluid flows despite transient growth
  of energy - David Goluskin\, University of Victoria
DTSTART:20220218T160000Z
DTEND:20220218T170000Z
UID:TALK168443@talks.cam.ac.uk
CONTACT:Prof. Jerome Neufeld
DESCRIPTION:Verifying nonlinear stability of a laminar fluid flow against 
 all perturbations is a classic challenge in fluid dynamics. All past resul
 ts rely on monotonic decrease of a perturbation energy or a similar quadra
 tic generalized energy. This "energy method" cannot show global stability 
 of any flow in which perturbation energy may grow transiently. For the man
 y flows that allow transient energy growth but seem to be globally stable 
 (e.g. pipe flow and other parallel shear flows at certain Reynolds numbers
 ) there has been no way to mathematically verify global stability. After e
 xplaining why the energy method was the only way to verify global stabilit
 y of fluid flows for over 100 years\, I will describe a different approach
  that is broadly applicable but more technical. This approach\, proposed i
 n 2012 by Goulart and Chernyshenko\, uses sum-of-squares polynomials to co
 mputationally construct non-quadratic Lyapunov functions that decrease mon
 otonically for all flow perturbations. I will present a computational impl
 ementation of this approach for the example of 2D plane Couette flow\, whe
 re we have verified global stability at Reynolds numbers above the energy 
 stability threshold. This energy stability result for 2D Couette flow had 
 not been improved upon since being found by Orr in 1907. The results I wil
 l present are the first verification of global stability – for any fluid
  flow – that surpasses the energy method. This is joint work with Federi
 co Fuentes (Universidad Católica de Chile) and Sergei Chernyshenko (Imper
 ial College London).
LOCATION:MR2\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
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