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Nonlinear stability of parallel flows with subcritical Reynolds numbers. Part 2. Stability of pipe Poiseuille flow to finite axisymmetric disturbances

Published online by Cambridge University Press:  12 April 2006

Nobutake Itoh
Nobutake Itoh
Affiliation:
National Aerospace Laboratory, Chofu, Tokyo, Japan
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Abstract

A theoretical study is presented of the spatial stability of flow in a circular pipe to small but finite axisymmetric disturbances. The disturbance is represented by a Fourier series with respect to time, and the truncated system of equations for the components up to the second-harmonic wave is derived under a rational assumption concerning the magnitudes of the Fourier components. The solution provides a relation between the damping rate and the amplitude of disturbance. Numerical calculations are carried out for Reynolds numbers R between 500 and 4000 and βR [les ] 5000, β being the non-dimensional frequency. The results indicate that the flow is stable to finite disturbances as well as to infinitesimal disturbances for all values of R and βR concerned.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 82 , Issue 3 , 27 September 1977 , pp. 469 - 479
Copyright
© 1977 Cambridge University Press

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