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Nonlinear cellular motions in Poiseuille channel flow

Published online by Cambridge University Press:  29 March 2006

J.-P. Zahn ,
Juri Toomre ,
E. A. Spiegel  and
D. O. Gough
J.-P. Zahn
Affiliation:
Department of Mathematics, New York University and Astronomy Department, Columbia University, New York 10027[dagger]
Juri Toomre
Affiliation:
Department of Mathematics, New York University and Goddard Institute for Space Studies, New York 10025
E. A. Spiegel
Affiliation:
Astronomy Department, Columbia University, New York 10027
D. O. Gough
Affiliation:
Goddard Institute for Space Studies, New York 10025
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Abstract

We expand the equations describing plane Poiseuille flow in Fourier series in the co-ordinates in the plane parallel to the bounding walls. There results an infinite system of equations for the amplitudes, which are functions of time and of the cross-stream co-ordinate. This system is drastically truncated and the resulting set of equations is solved accurately by a finite difference method. Three truncations are considered: (I) a single mode with dependence only on the downstream co-ordinate and time, (II) the mode of (I) plus its first harmonic, (III) a single three-dimensional mode. For all three cases, for a variety of initial conditions, the solutions evolve to a steady state as seen in a particular moving frame of reference. No runaways are encountered.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 64 , Issue 2 , 19 June 1974 , pp. 319 - 346
Copyright
© 1974 Cambridge University Press

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