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Laminar channel flow driven by accelerating walls

Published online by Cambridge University Press:  16 July 2009

P. Watson ,
W. H. H. Banks ,
M. B. Zaturska  and
P. G. Drazin
P. Watson
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, Great Britain
W. H. H. Banks
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, Great Britain
M. B. Zaturska
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, Great Britain
P. G. Drazin
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, Great Britain
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Abstract

The two-dimensional flow of a viscous incompressible fluid in a channel with accelerating walls is analysed by use of Hiemenz's similarity solution. Steady flows and their instabilities are calculated, and unsteady flows are computed by solving the initial-value problem for the governing partial-differential system. Thereby, these exact solutions of the Navier–Stokes equations are found to exhibit turning points, pitchfork bifurcations, Hopf bifurcations and Takens–Bogdanov bifurcations along the route to chaos. The substantial physical result is that the chaos previously found for flows with symmetrically accelerating walls is easily destroyed by a little asymmetry.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 2 , Issue 4 , December 1991 , pp. 359 - 385
Copyright
Copyright © Cambridge University Press 1991

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