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On the stability of flow in an elliptic pipe which is nearly circular

Published online by Cambridge University Press:  12 April 2006

A. Davey
A. Davey
Affiliation:
School of Mathematics, University of Newcastle upon Tyne, England
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Abstract

The linear stability of Poiseuille flow in an elliptic pipe which is nearly circular is examined by regarding the flow as a perturbation of Poiseuille flow in a circular pipe. We show that the temporal damping rates of non-axisymmetric infinitesimal disturbances which are concentrated near the wall of the pipe are decreased by the ellipticity. In particular we estimate that if the length of the minor axis of the cross-section of the pipe is less than about 96 ½% of that of the major axis then the flow will be unstable and a critical Reynolds number will exist. Also we calculate estimates of the ellipticities which will produce critical Reynolds numbers ranging from 1000 upwards.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 87 , Issue 2 , 26 July 1978 , pp. 233 - 241
Copyright
© 1978 Cambridge University Press

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References

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