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Transition to turbulence in plane Poiseuille and plane Couette flow

Published online by Cambridge University Press:  19 April 2006

Steven A. Orszag  and
Lawrence C. Kells
Steven A. Orszag
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139
Lawrence C. Kells
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139 Present address: 1929 Crisanto 907, Mountain View, CA 94040.
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Abstract

Direct numerical solutions of the three-dimensional time-dependent Navier-Stokes equations are presented for the evolution of three-dimensional finite-amplitude disturbances of plane Poiseuille and plane Couette flows. Spectral methods using Fourier series and Chebyshev polynomial series are used. It is found that plane Poiseuille flow can sustain neutrally stable two-dimensional finite-amplitude disturbances at Reynolds numbers larger than about 2800. No neutrally stable two-dimensional finite-amplitude disturbances of plane Couette flow were found.

Three-dimensional disturbances are shown to have a strongly destabilizing effect. It is shown that finite-amplitude disturbances can drive transition to turbulence in both plane Poiseuille flow and plane Couette flow at Reynolds numbers of order 1000. Details of the resulting flow fields are presented. It is also shown that plane Poiseuille flow cannot sustain turbulence at Reynolds numbers below about 500.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 96 , Issue 1 , 16 January 1980 , pp. 159 - 205
Copyright
© 1980 Cambridge University Press

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