Eigenvalue bounds for the Orr-Sommerfeld equation-Reference-Cited by-同舟云学术

Eigenvalue bounds for the Orr-Sommerfeld equation

Published:1968-09-02 Issue:3 Volume:33 Page:617-621
ISSN:0022-1120
Container-title:Journal of Fluid Mechanics
language:en
Short-container-title:J. Fluid Mech.

Author:

Joseph Daniel D.

Abstract

Estimates of the eigenvalues C belonging to the manifold of solutions of the Orr-Sommerfeld equation are constructed by application of elementary isoperimetric inequalities. The inequalities also lead to a considerable improvement on the estimate of (αR) regions of linear stability given by Synge.

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Reference8 articles.

1. Eagles, P. M. 1966 The stability of a family of Jeffery-Hamel solutions for divergent channel flow J. Fluid Mech. 24,191–207.

2. Drazin, P. G. & Howard, L. N. 1966 Hydrodynamic stability of parallel flow of an inviscid fluid Adv. Appl. Mech. 9,1–85.

3. Lin, C. C. 1955 The Theory of Hydrodynamic Stability .Cambridge University Press.

4. HØILAND, E. 1953 On two-dimensional perturbation of linear flow.Geofys. Publ. 18, J. Fluid Mech. 16, 333–42. See also Drazin & Howard (1966).

5. Pai, S. I. 1954 On a generalization of Synge's criterion for sufficient stability of plane parallel flows Quart. Appl. Math. 12,203–6.

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