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Perturbed bifurcation theory for Poiseuille annular flow

Published online by Cambridge University Press:  20 April 2006

Gary S. Strumolo
Gary S. Strumolo
Affiliation:
Schlumberger–Doll Research, Old Quarry Road, Ridgefield, Connecticut 06877
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Abstract

The consequence of imposing an axisymmetric travelling-wave disturbance on the Poiseuille flow between two concentric cylinders is examined. A nonlinear analysis is taken, using perturbed bifurcation and singular perturbation theory, to determine how resonant wall oscillations affect flow stability. Subcritical, stable, finite-amplitude perturbations to the basic Poiseuille flow are found and conjectures on their significance are given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 130 , May 1983 , pp. 59 - 72
Copyright
© 1983 Cambridge University Press

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References

Hall, P. 1978 The effect of external forcing on the stability of plane Poiseuille flow Proc. R. Soc. Lond. A359, 453.Google Scholar
Joseph, D. D. 1976 Stability of Fluid Motions. Springer.
Joseph, D. D. & Chen, T. S. 1974 Friction factors in the theory of bifurcating Poiseuille flow through annular ducts J. Fluid Mech. 66, 189.Google Scholar
Karnitz, M. A. et al. 1974 An experimental investigation of transition of a plane Poiseuille flow. Trans. A.S.M.E. 384.
Keller, H. B. & Cebeci, T. Numerical methods for the Orr–Sommerfeld equation. (Unpublished.)
Lessen, M. & Huang, P. 1976 Poiseuille flow in a pipe with axially symmetric wavy walls Phys. Fluids 19, 945.Google Scholar
Matkowsky, B. J. & Reiss, E. L. 1977 Singular perturbations of bifurcations SIAM J. Appl. Maths 33, 230.Google Scholar
Meksyn, D. & Stuart, J. T. 1951 Stability of viscous motion between parallel planes for finite disturbance Proc. R. Soc. Lond. A208, 517.Google Scholar
Orszag, S. A. 1971 Accurate solution of the Orr–Sommerfeld stability equation J. Fluid Mech. 50, 689.Google Scholar
Pekeris, C. & Shkoller, B. 1967 Stability of plane Poiseuille flow to periodic disturbances of finite amplitude in the vicinity of the neutral curve J. Fluid Mech. 29, 31.Google Scholar
Reiss, E. L. 1977 Imperfect bifurcation. Advanced Seminar on Bifurcation Theory. Univ. of Wisconsin.
Reynolds, W. C. & Potter, M. C. 1967 Finite-amplitude instability of parallel shear flows J. Fluid Mech. 27, 465.Google Scholar
Stewartson, K. & Stuart, J. T. 1971 A non-linear instability theory for a wave system in plane Poiseuille flow J. Fluid Mech. 48, 529.Google Scholar
Strumolo, G. S. 1978 Perturbed bifurcation theory for plane Poiseuille flow. Ph.D. thesis, Courant Institute of Mathematical Sciences, N.Y.U., N.Y.
Strumolo, G. S. & Reiss, E. L. 1981 Poiseuille channel flow with driven walls. (Unpublished.)
Stuart, J. T. 1960 On the non-linear mechanics of wave disturbances in stable and unstable parallel flows. Part 1. The basic behaviour in plane Poiseuille flow J. Fluid Mech. 9, 353.Google Scholar
Subbotin, V. I. 1978 Flow in pipes with regular, artificially-produced wall roughness. Fluid Mech.–Sov. Res. 7.
Watson, J. 1960 On the non-linear mechanics of wave disturbances in stable and unstable parallel flows. Part 2. The development of a solution for plane Couette flow J. Fluid Mech. 14, 336.Google Scholar
Wygnanski, I. J. & Champagne, F. H. 1973 On transition in a pipe. Part 1. The origins of puffs and slugs and the flow in a turbulent slug J. Fluid Mech. 59, 281.Google Scholar
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