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The neutral curves for periodic perturbations of finite amplitude of plane Poiseuille flow

Published online by Cambridge University Press:  29 March 2006

C. L. Pekeris  and
B. Shkoller
C. L. Pekeris
Affiliation:
Department of Applied Mathematics, The Weizmann Institute of Science, Rehovot, Israel
B. Shkoller
Affiliation:
Department of Applied Mathematics, The Weizmann Institute of Science, Rehovot, Israel
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Abstract

It is shown that there exist undamped solutions for perturbations of finite amplitude of plane Poiseuille flow, which are periodic in the direction of the axis of the channel. The shift in the ‘neutral curve’ as a function of the amplitude λ* of the disturbance is shown in figure 2. The solution is obtained by a perturbation method in which the eigenfunctions and the eigenvalue c are expanded in power series of the amplitude λ, as shown in (14), (15), (16) and (17). Near the neutral curve for a finite amplitude disturbance, the curvature of the mean flow shows a tendency to become negative (figure 5).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 39 , Issue 3 , 27 November 1969 , pp. 629 - 639
Copyright
© 1969 Cambridge University Press

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References

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