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On the nonlinear evolution of three-dimensional disturbances in plane Poiseuille flow

Published online by Cambridge University Press:  29 March 2006

A. Davey ,
L. M. Hocking  and
K. Stewartson
A. Davey
Affiliation:
School of Mathematics, University of Newcastle upon Tyne
L. M. Hocking
Affiliation:
Department of Mathematics, University College, London
K. Stewartson
Affiliation:
Department of Mathematics, University College, London
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Abstract

The equations governing the nonlinear development of a centred three-dimensional disturbance to plane parallel flow at slightly supercritical Reynolds numbers are obtained, In contrast to the corresponding equation for two-dimensional disturbances, two slowly varying functions are needed to describe the development: the amplitude function and a function related to the secular pressure gradient produced by the disturbance. These two functions satisfy a pair of coupled partial differential equations. The equations derived in Hocking, Stewartson & Stuart (1972) are shown to be incorrect, Some of the properties of the governing equations are discussed briefly.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 63 , Issue 3 , 29 April 1974 , pp. 529 - 536
Copyright
© 1974 Cambridge University Press

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References

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