Hostname: page-component-7479d7b7d-k7p5g Total loading time: 0 Render date: 2024-07-12T01:00:29.251Z Has data issue: false hasContentIssue false
  • English
  • Français

On the behaviour of small disturbances in plane Couette flow. Part 3. The phenomenon of mode-pairing

Published online by Cambridge University Press:  29 March 2006

A. P. Gallagher
A. P. Gallagher
Affiliation:
Department of Engineering Mathematics, The Queen's University of Belfast
Get access Rights & Permissions [Opens in a new window]

Abstract

In two earlier papers (Gallagher & Mercer 1962, 1964) the results for the first four eigenvalues of the problem of the stability of plane Couette flow were given. The first twelve eigenvalues have been calculated by the same method and the results show that the manner in which the eigenvalues join to form complex pairs depends on α, the wavenumber of the disturbance. They also would appear to indicate that mode-crossing always occurs.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 65 , Issue 1 , 12 August 1974 , pp. 29 - 32
Copyright
© 1974 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

Davey, A. 1973 On the stability of plane Couette flow to infinitesimal disturbances J. Fluid Mech. 57, 369–380.Google Scholar
Gallagher, A. P. & Mercer, A. McD. 1962 On the behaviour of small disturbances in plane Couette flow J. Fluid Mech. 13, 91–100.Google Scholar
Gallagher, A. P. & Mercer, A. McD. 1964 On the behaviour of small disturbances in plane Couette flow. Part 2. The higher eigenvalues J. Fluid Mech. 18, 350–352.Google Scholar
Grohne, D. 1954 Z. angew. Math. Mech. 34, 344. (See also Nat. Adv. Comm. Aero. (Wash.) Tech. Mem. no. 1417.)
Reid, W. H. 1974 Uniform asymptotic approximations to the solutions of the Orr-Sommerfeld equation. Part 1. Plane Couette flow. Studies in Appl. Math. To be published.Google Scholar
Southwell, R. V. & Chitty, L. 1930 On the problem of hydrodynamic stability. I. Uniform shearing motion in a viscous fluid. Phil. Trans A 229, 205–53.Google Scholar