Subcritical Bifurcation Of Plane Poiseuille Flow
Abstract
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.
Recommended Citation
T. S. Chen and D. D. Joseph, "Subcritical Bifurcation Of Plane Poiseuille Flow," Journal of Fluid Mechanics, vol. 58, no. 2, pp. 337 - 351, Cambridge University Press, Jan 1973.
The definitive version is available at https://doi.org/10.1017/S0022112073002624
Department(s)
Mechanical and Aerospace Engineering
International Standard Serial Number (ISSN)
1469-7645; 0022-1120
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2023 Cambridge University Press, All rights reserved.
Publication Date
01 Jan 1973
