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CATEGORIES:Waves Group (DAMTP)
SUMMARY:Inherent Instabilities in the Kuramoto-Sivashinsky
Equation - Chris Sear ( DAMTP)
DTSTART;TZID=Europe/London:20220207T150000
DTEND;TZID=Europe/London:20220207T160000
UID:TALK168395AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/168395
DESCRIPTION:There is evidence to suggest that the boundary-lay
er equations are not the high-Reynolds number limi
t of solutions to the Navier-Stokes equations. Num
erical calculations by Brinckman and Walker show t
hat at sufficiently high Reynolds number\, a short
-wavelength instability may appear before the sepa
ration time of solutions to the unsteady boundary-
layer equations. Using the Kuramoto-Sivashinsky eq
uation as a model for the problem with key similar
ities and one spatial dimension\, we will show tha
t a similar short-wavelength instability can arise
before the shock formation time of the kinematic-
wave equation. We will then show that this instabi
lity can be explained through tracking exponential
ly-small terms in the asymptotic solution structur
e\, invisible to traditional matched asymptotics a
pproaches. These terms\, and their associated Stok
es and anti-Stokes lines\, can be found by trackin
g singularities of the kinematic-wave equation in
the complex plane.
LOCATION:CMS\, MR11
CONTACT:Alistair Hales
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