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On the stability of pipe-Poiseuille flow to finite-amplitude axisymmetric and non-axisymmetric disturbances

Published online by Cambridge University Press:  20 April 2006

P. K. Sen ,
D. Venkateswarlu  and
S. Maji
P. K. Sen
Affiliation:
Department of Applied Mechanics, Indian Institute of Technology, New Delhi 110016
D. Venkateswarlu
Affiliation:
Department of Mechanical Engineering, Delhi College of Engineering, Delhi 110006
S. Maji
Affiliation:
Department of Applied Mechanics, Indian Institute of Technology, New Delhi 110016
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Abstract

The stability of fully developed pipe-Poiseuille flow to finite-amplitude axisymmetric and non-axisymmetric disturbances has been studied using the equilibrium-amplitude method of Reynolds & Potter (1967). In both the cases the least-stable centre-modes were investigated. Also, for the non-axisymmetric case the mode investigated was the one with azimuthal wavenumber equal to one. Many higher-order Landau coefficients were calculated, and the Stuart-Landau series was analysed by the Shanks (1955) method and by using Padé approximants to look for the existence of possible equilibrium states. The results show in both cases that, for each value of the Reynolds number R, there is a preferred band of spatial wavenumbers α in which equilibrium states are likely to exist. Moreover, in both cases it was found that the magnitude of the minimum threshold amplitude for a given R decreases with increasing R. The scales of the various quantities obtained agree very well with those deduced by Davey & Nguyen (1971).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 158 , September 1985 , pp. 289 - 316
Copyright
© 1985 Cambridge University Press

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