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SUMMARY:Inherent Instabilities in the Kuramoto-Sivashinsky Equation - Chri
 s Sear ( DAMTP)
DTSTART:20220207T150000Z
DTEND:20220207T160000Z
UID:TALK168395@talks.cam.ac.uk
CONTACT:Alistair Hales
DESCRIPTION:There is evidence to suggest that the boundary-layer equations
  are not the high-Reynolds number limit of solutions to the Navier-Stokes 
 equations. Numerical calculations by Brinckman and Walker show that at suf
 ficiently high Reynolds number\, a short-wavelength instability may appear
  before the separation time of solutions to the unsteady boundary-layer eq
 uations. Using the Kuramoto-Sivashinsky equation as a model for the proble
 m with key similarities and one spatial dimension\, we will show that a si
 milar short-wavelength instability can arise before the shock formation ti
 me of the kinematic-wave equation. We will then show that this instability
  can be explained through tracking exponentially-small terms in the asympt
 otic solution structure\, invisible to traditional matched asymptotics app
 roaches. These terms\, and their associated Stokes and anti-Stokes lines\,
  can be found by tracking singularities of the kinematic-wave equation in 
 the complex plane.
LOCATION:CMS\, MR11
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