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The effect of rigid rotation on the finite-amplitude stability of pipe flow at high Reynolds number

Published online by Cambridge University Press:  20 April 2006

T. R. Akylas  and
J.-P. Demurger
T. R. Akylas
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
J.-P. Demurger
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
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Abstract

A theoretical study is made of the stability of pipe flow with superimposed rigid rotation to finite-amplitude disturbances at high Reynolds number. The non-axisymmetric mode that requires the least amount of rotation for linear instability is considered. An amplitude expansion is developed close to the corresponding neutral stability curve; the appropriate Landau constant is calculated. It is demonstrated that the flow exhibits nonlinear subcritical instability, the nonlinear effects being particularly strong owing to the large magnitude of the Landau constant. These findings support the view that a small amount of extraneous rotation could play a significant role in the transition to turbulence of pipe flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 148 , November 1984 , pp. 193 - 205
Copyright
© 1984 Cambridge University Press

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