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The instability of a shear layer between two parallel streams

Published online by Cambridge University Press:  28 March 2006

Robin E. Esch
Robin E. Esch
Affiliation:
Pierce Hall, Harvard University
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Abstract

An unbounded parallel flow, consisting of a linear shear layer between uniform streams, is investigated for stability. A conventional eigenvalue problem is formulated, and solved by both analytical and numerical methods. The region of instability in the plane of Reynolds number R and disturbance wave number α is determined, and typical growth rates in the unstable region are computed.

Unstable disturbances are found at all values of R. Results for αR > 100 are found to agree closely with inviscid theory results. An analytic method useful for αR < 1 is developed.

The extent to which the present results can be applied to the laminar boundary layer between free streams is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 3 , Issue 3 , December 1957 , pp. 289 - 303
Copyright
© 1957 Cambridge University Press

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References

Carrier, G. 1954 Interface stability of the Helmholtz type, Los Alamos Internal Report.Google Scholar
Lamb, H. 1945 Hydrodynamics. New York: Dover.
Lessen, M. 1950 On stability of free laminar boundary layer between parallel streams, Nat. Adv. Comm. Aero., Wash., no. 979.Google Scholar
Lin, C. C. 1955 Theory of Hydrodynamic Stability. Cambridge University Press.
Rayleigh, Lord 1945 Theory of Sound. New York: Dover.
Watson, G. N. 1944 Theory of Bessel Functions. Cambridge University Press.