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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

Davey, A. & Stewartson, K. 1974 Proc. Roy. Xoc. A To appear.
Eagles, P. M. 1971 J. Fluid Mech. 49, 529–550.
Hocking, L. M. 1974 Submitted for publication.
Hocking, L. M. & Stewartson, K. 1971 Mathematiaka, 18, 219–239.
Hocking, L. M. & Stewartson, K. 1972 Proc. Roy. Soc. A 326, 289–313.
Hocking, L. M., Stewartson, K. & Stuart, J. T. 1972 J. Fluid Mech. 51, 705–735.
Orszag, S. A. 1971 J. Fluid Mech. 50, 689–703.
Reynolds, W. C. & Potter, M. C. 1967 J. Fluid Mech. 27, 465–492.
Squire, H. B. 1933 Proc. Roy. Soc. A 142, 621–628.
Stewartson, K. B. Stuart, J. T. 1971 J. Fluid Mech. 48, 529–545.
Stuart, J. T. 1958 J. Fluid Mech. 4, 1–22.
Stuart, J. T. & Diprima, R. 1974 To be submitted for publication.