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On the stability of fully developed flow in a pipe

Published online by Cambridge University Press:  28 March 2006

Gilles M. Corcos  and
John R. Sellars
Gilles M. Corcos
Affiliation:
The University of California and The Ramo-Wooldridge Corporation
John R. Sellars
Affiliation:
The University of California and The Ramo-Wooldridge Corporation
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Abstract

The stability of infinitesimal axially symmetric disturbances in fully developed pipe flow is examined anew. The classical eigenvalue problem is treated in part by asymptotic methods and leads to an algebraic relation between the eigenvalue c, the disturbance wavelength 2π/α, and the Reynolds number. Examination of the limiting cases of this relation reveals the existence of two families of characteristic numbers, the value of which tends to unity and to zero as the Reynolds number increases without bounds. For the latter, a more accurate solution is required and given. It is found that all eigenvalues yield stable solutions and that for a given wave number and Reynolds number only a finite number of eigenvalues exists.

The limitations of the analysis are discussed in the light of a recent experimental study of the same problem.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 5 , Issue 1 , January 1959 , pp. 97 - 112
Copyright
© 1959 Cambridge University Press

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