Subcritical Bifurcation Of Plane Poiseuille Flow


We apply the perturbation theory which was recently developed and justified by Joseph & Sattinger (1972) to determine the form of the time-periodic solutions which bifurcate from plane Poiseuille flow. The results a t lowest significant order seem to be in good agreement with those following from the formal perturbation method of Stuart (1960) as extended by Reynolds & Potter (1967). Given the numerical results of the present calculation, the rigorous theory guarantees that the only time-periodic solution which bifurcates from laminar Poiseuille flow is a two-dimensional wave. The wave which bifurcates at the lowest Reynolds number exists, but it is unstable when its amplitude is small. Solutions which escape the small domain of attraction of laminar Poiseuille flow snap through this unstable time-periodic solution with a small amplitude to solutions of larger amplitudes. © 1973, Cambridge University Press. All rights reserved.


Mechanical and Aerospace Engineering

International Standard Serial Number (ISSN)

1469-7645; 0022-1120

Document Type

Article - Journal

Document Version


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© 2023 Cambridge University Press, All rights reserved.

Publication Date

01 Jan 1973