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Note on Howard's semicircle theorem

Published online by Cambridge University Press:  19 April 2006

G. T. Kochar  and
R. K. Jain
G. T. Kochar
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kanpur
R. K. Jain
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kanpur
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Abstract

For a steady plane parallel flow of an inviscid incompressible fluid of variable density under gravity, it is shown that the complex wave velocity for any unstable mode lies in a semi-ellipse whose major axis coincides with the diameter of Howard's semicircle, while its minor axis depends on the stratification.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 91 , Issue 3 , 11 April 1979 , pp. 489 - 491
Copyright
© 1979 Cambridge University Press

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References

Banerjee, M. B., Gupta, J. & Gupta, S. K. 1974 On reducing Howard's semicircle. J. Math. Phys. Sci. 8, 475–484a.Google Scholar
Banerjee, M. B. & Jain, R. K. 1972 A unified instability criterion of heterogeneous shear flows. The Math. Student 40, 111–119.Google Scholar
Howard, L. N. 1961 Note on a paper of John W. Miles. J. Fluid Mech. 10, 509–512.Google Scholar
Howard, L. N. & Drazin, P. G. 1966 Adv. in Appl. Mech. 9, 1–85.