Exact solutions in the 2-dimensional viscoelastic channel flow

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• Morozov, A (Edinburgh)
• Friday 12 September 2008, 10:20-10:40
• Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact Mustapha Amrani.

The Nature of High Reynolds Number Turbulence

Recently, it has been discovered that flows of polymer solutions 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.

Here I try to identify exact solutions in the 2D viscoelastic channel flow. Starting 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 solutions persist at relatively small Reynolds numbers if the normal-stress difference is large enough. Nevertheless, so far I was unsuccessful in tracking these solutions down to the Re=0 limit. Other types of analytic continuation will be discussed as well.

This talk is part of the Isaac Newton Institute Seminar Series series.

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