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The instability to long waves of unbounded parallel inviscid flow

Published online by Cambridge University Press:  28 March 2006

P. G. Drazin  and
L. N. Howard
P. G. Drazin
Affiliation:
Mathematics Department, University of Bristol
L. N. Howard
Affiliation:
Mathematics Department, Massachusetts Institute of Technology
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Abstract

Formulas for the determination of the instability characteristics of unbounded parallel flow are obtained for the case of long waves, and applied, together with some general results, to give a qualitative description of the different modes of instability of such flows. It is found that there is a finite number of different modes unstable to long waves, essentially one for each relative maximum and minimum of the velocity profile. These modes appear to become stable when the wavelength is sufficiently small, reducing to neutral solutions associated with inflexion points as stability is approached. The formulas are also useful for quantitative calculation of instability characteristics.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 14 , Issue 2 , October 1962 , pp. 257 - 283
Copyright
© 1962 Cambridge University Press

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