Hostname: page-component-77c89778f8-vpsfw Total loading time: 0 Render date: 2024-07-17T04:52:29.735Z Has data issue: false hasContentIssue false
  • English
  • Français

On determination of the characteristic equations for the stability of parallel flows

Published online by Cambridge University Press:  28 March 2006

W. P. Graebel
W. P. Graebel
Affiliation:
Department of Engineering Mechanics, The University of Michigan
Get access Rights & Permissions [Opens in a new window]

Abstract

The Orr-Sommerfeld equation is solved for large Reynolds number by use of inner and outer expansion theory. The method is shown to have distinct computational advantages over the method of solution due to Sommerfeld and Lin and to be applicable to a wider class of boundary conditions. The method can be simply extended to other characteristic problems in fluids involving viscous effects concentrated in narrow regions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 24 , Issue 3 , March 1966 , pp. 497 - 508
Copyright
© 1966 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

Duty, R. L. & Reid, W. H. 1964 J. Fluid Mech. 20, 8.
Heisenberg, W. 1924 Ann. Phys., Lpz. 74, 57.
Lin, C. C. 1945a Quart. Appl. Math. 3, 11.
Lin, C. C. 1945b Quart. Appl. Math. 3, 21.
Lin, C. C. 1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Luke, Y. L. 1962 Integrals of Bessel Functions. New York: McGraw-Hill.
Orr, W. M. 1906–7 Proc. Roy. Irish Acad., A 27, 69.
Sommerfeld, A. 1908 Proc. 4th Int. Cong. Math., Rome, p. 116.
Tollmien, W. 1935 Nachr. Ges. Wiss. Göttingen, Math.-phys. Klasse, 50, 79. (English translation in NACA TM no. 792 1936.)
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. New York: Academic Press.