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CATEGORIES:Partial Differential Equations seminar
SUMMARY:On the subcritical transition of the 3D Couette fl
ow - Jacob Bedrossian\, University of Maryland
DTSTART;TZID=Europe/London:20160111T160000
DTEND;TZID=Europe/London:20160111T170000
UID:TALK63345AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/63345
DESCRIPTION:We discuss the dynamics of small perturbations of
the plane\, periodic Couette flow in the 3D incomp
ressible Navier-Stokes equations at high Reynolds
number. For sufficiently regular initial data\, we
determine the stability threshold for small pertu
rbations and characterize the long time dynamics o
f solutions near this threshold. For rougher data\
, we obtain an estimate of the stability threshold
which agrees closely with numerical experiments.
The primary linear stability mechanism is an aniso
tropic enhanced dissipation resulting from the mix
ing caused by the large mean shear\; the main line
ar instability is a non-normal instability known a
s the lift-up effect. Understanding the variety of
nonlinear resonances and devising the correct nor
ms to estimate them form the core of the analysis
we undertake. Joint work with Pierre Germain and N
ader Masmoudi.
LOCATION:CMS\, MR11
CONTACT:Amit Einav
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