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Finite-amplitude bifurcations in plane Poiseuille flow: two-dimensional Hopf bifurcation

Soibelman, Israel and Meiron, Daniel I. (1991) Finite-amplitude bifurcations in plane Poiseuille flow: two-dimensional Hopf bifurcation. Journal of Fluid Mechanics, 229 . pp. 389-416. ISSN 0022-1120.

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We examine the stability to superharmonic disturbances of finite-amplitude two-dimensional travelling waves of permanent form in plane Poiseuille flow. The stability characteristics of these flows depend on whether the flux or pressure gradient are held constant. For both conditions we find several Hopf bifurcations on the upper branch of the solution surface of these two-dimensional waves. We calculate the periodic orbits which emanate from these bifurcations and find that there exist no solutions of this type at Reynolds numbers lower than the critical value for existence of two-dimensional waves ([approximate]2900). We confirm the results of Jiménez (1987) who first detected a stable branch of these solutions by integrating the two-dimensional equations of motion numerically.

Item Type:Article
Additional Information:Copyright © 1991 Cambridge University Press. Reprinted with permission. (Received 13 March 1990 and in revised form 21 January 1991) We wish to acknowledge helpful discussions with Philip Saffman and Dwight Barkley. This work was supported by the Department of Energy, Office of Energy Sciences (DE-AS03-76ER-72012), Applied Mathematical Sciences (KC-07-01-01).
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Deposited On:16 Apr 2008
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