Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-28T07:55:37.198Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.