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The continuous spectrum of the Orr-Sommerfeld equation: note on a paper of Grosch & Salwen

Published online by Cambridge University Press:  26 April 2006

A. D. D. Craik
A. D. D. Craik
Affiliation:
Department of Mathematical and Computational Sciences, University of St. Andrews, St. Andrews, Fife, KY16 9LN, UK
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Abstract

Grosch & Salwen (1978) discuss the continuous-spectrum contribution in both temporal and spatial stability problems that are governed by the linear Orr–Sommerfeld equation. Their computed temporal continuum eigenfunctions for the Blasius boundary layer and for a laminar jet profile show surprising differences. This note provides an improved physical understanding of the results through a simple model, and shows that these differences are more apparent than real.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 226 , May 1991 , pp. 565 - 571
Copyright
© 1991 Cambridge University Press

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References

Craik, A. D. D.: 1985 Wave Interactions and Fluid Flows. Cambridge University Press.
Criminale, W. O. & Drazin, P. G., 1990 The evolution of linearized perturbations of parallel flows. Stud. Appl. Maths 83, 123–157.Google Scholar
Drazin, P. G. & Reid, W. H., 1981 Hydrodynamic Stability. Cambridge University Press.
Grosch, C. E. & Salwen, H., 1978 The continuous spectrum of the Orr-Sommerfeld equation. Part 1. The spectrum and the eigenfunctions. J. Fluid Mech. 87, 33–54 (referred to herein as I).Google Scholar
Kelvin, Lord 1887 Stability of fluid motion: rectilinear motion of viscous fluid between two parallel plates. Phil. Mag. 24 (5), 188–196.Google Scholar