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SUMMARY:Exact solutions in the 2-dimensional viscoelastic channel flow - M
 orozov\, A (Edinburgh)
DTSTART:20080912T092000Z
DTEND:20080912T094000Z
UID:TALK13388@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Recently\, it has been discovered that flows of polymer soluti
 ons can become unstable and exhibit turbulent-like behaviour at very small
  Reynolds numbers. As a rule\, viscoelastic flows with curved streamlines 
 are linearly unstable\, while parallel shear flows are believed to exhibit
  a subcritical transition to a turbulent state. In the absence of inertia\
 , these instabilities are driven by anisotropic elastic stresses. \n\nHere
  I try to identify exact solutions in the 2D viscoelastic channel flow. St
 arting from the exact solutions of the Navier-Stokes equation found by Th.
  Herbert\, solutions for the Oldroyd-B viscoelastic model are obtained by 
 analytic continuation from the Newtonian case. It is found that these solu
 tions persist at relatively small Reynolds numbers if the normal-stress di
 fference is large enough. Nevertheless\, so far I was unsuccessful in trac
 king these solutions down to the Re=0 limit. Other types of analytic conti
 nuation will be discussed as well.\n
LOCATION:Seminar Room 1\, Newton Institute
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