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

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...

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Bibliographic Details
Published in:Journal of fluid mechanics 1984-11, Vol.148, p.193-205
Main Authors: Akylas, T. R., Demurger, J.-P.
Format: Article
Language:English
Subjects:
Exact sciences and technology
flow
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Hydrodynamic stability
numerical analysis
Physics
pipes
rotating bodies
stability
turbulence
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Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112084002305