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Finite-amplitude neutral disturbances in plane Poiseuille flow

Published online by Cambridge University Press:  29 March 2006

W. D. George ,
J. D. Hellums  and
B. Martin
W. D. George
Affiliation:
Department of Chemical Engineering, Rice University, Houston, Texas 77001 Present address: Getty Oil Company, Houston, Texas.
J. D. Hellums
Affiliation:
Department of Chemical Engineering, Rice University, Houston, Texas 77001
B. Martin
Affiliation:
Department of Chemical Engineering, Rice University, Houston, Texas 77001 Present address: Department of Mathematics, University of Aston, Birmingham.
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Abstract

Finite-amplitude disturbances in plane Poiseuille flow are studied by a method involving Fourier expansion with numerical solution of the resulting partial differential equations in the coefficient functions. A number of solutions are developed which extend to relatively long times so that asymptotic stability or instability can be established with a degree of confidence. The amplitude for neutral stability is established for a fixed wavenumber for two values of the Reynolds number. Details of the neutral velocity fluctuation are presented. These and earlier results are expressed in terms of the asymptotic amplitude and compared with results obtained by prior workers. The results indicate that the expansion methods used by prior workers may be valid only for amplitudes considerably smaller than 0·01.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 63 , Issue 4 , 15 May 1974 , pp. 765 - 771
Copyright
© 1974 Cambridge University Press

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