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Non-linear theory of unstable plane Poiseuille flow

Published online by Cambridge University Press:  29 March 2006

E. H. Dowell
E. H. Dowell
Affiliation:
Princeton University
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Abstract

A theoretical study of plane Poiseuille flow is made using the full non-linear Navier-Stokes equations. The mathematical technique employed is to use a Fourier decomposition in the streamwise spatial variable, a Galerkin expansion in the lateral variable and numerical integration with respect to time. By retaining the non-linear terms, the limit cycle oscillations of an unstable (in a linear sense) flow are obtained. A brief investigation of the possibility of instability due to large (non-linear) disturbances is also made. The results are negative for the cases examined. Comparisons with results previously obtained by others from linear theory illustrate the accuracy and efficacy of the method.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 38 , Issue 2 , 3 September 1969 , pp. 401 - 414
Copyright
© 1969 Cambridge University Press

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