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The stability of pipe flow Part 1. Asymptotic analysis for small wave-numbers

Published online by Cambridge University Press:  29 March 2006

W. P. Graebel
W. P. Graebel
Affiliation:
Department of Engineering Mechanics, The University of Michigan, Ann Arbor, Michigan
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Abstract

The instability of Poiseuille flow in a pipe is considered for small disturbances. An asymptotic analysis is used which is similar to that found successful in plane Poiseuille flow. The disturbance is taken to travel in a spiral fashion, and comparison of the radial velocity component with the transverse component in the plane case shows a high degree of similarity, particularly near the critical point where the disturbance and primary flow travel with the same speed. Instability is found for azimuthal wave-numbers of 2 or greater, although the corresponding minimum Reynolds numbers are too small to compare favourably with either experiments or the initial restrictions on the magnitude of the wave-number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 43 , Issue 2 , 28 August 1970 , pp. 279 - 290
Copyright
© 1970 Cambridge University Press

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