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Mathematics and Mechanics

Russian Academy of Sciences
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in January 1936
(Translated from 1958)
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ISSN 0021-8928
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IssuesArchive of Issues2008-3pp.296-302

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L.D. Akulenko and S.A. Kumakshev, "Bifurcation of multimode flows of a viscous fluid in a plane diverging channel," J. Appl. Math. Mech. 72 (3), 296-302 (2008)
Year 2008 Volume 72 Issue 3 Pages 296-302
Title Bifurcation of multimode flows of a viscous fluid in a plane diverging channel
Author(s) L.D. Akulenko (Moscow, Russia)
S.A. Kumakshev (Moscow, Russia, kumak@ipmnet.ru)
Abstract The pattern of steady multimode flow of a viscous incompressible fluid in a plane diverging channel is constructed and investigated. It is shown that odd-mode flows have velocity profiles that are symmetrical about the axis of the channel and from one to three different flows with a fixed number of modes exist. The even-mode flows are asymmetric and exist as pairs. The existence of a denumerable set of finite ranges adjoining one another, in which a single-type of complex bifurcation of the flow occurs, is established in the case of an unbounded range of values of the Reynolds number. As the Reynolds number increases, transitions to flows with an increasing number of modes, containing domains of forward and backward flows, occur successively. Flow patterns with a smaller number of modes do not occur. An increase in the number of an range corresponding to an increase in the Reynolds number leads to an unlimited increase in the length of the range and the number of modes of permissible flows.
Received 14 April 2007
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