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On the spatial instability of piecewise linear free shear layers

Published online by Cambridge University Press:  21 April 2006

T. F. Balsa
T. F. Balsa
Affiliation:
Aerospace and Mechanical Engineering Department, University of Arizona, Tucson, AZ 85721, USA
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Abstract

The main goal of this paper is to clarify the spatial instability of a piecewise linear free shear flow. We do this by obtaining numerical solutions to the Orr–Sommerfeld equation at high Reynolds numbers. The velocity profile chosen is very much like a piecewise linear one, with the exception that the corners have been rounded so that the entire profile is infinitely differentiable. We find that the (viscous) spatial instability of this modified profile is virtually identical to the inviscid spatial instability of the piecewise linear profile and agrees qualitatively with the inviscid results for the tanh profile when the shear layers are convectively unstable. The unphysical features, previously identified for the piecewise linear velocity profile, arise only when the flow is absolutely unstable. In a nutshell, we see nothing wrong with the inviscid spatial instability of piecewise linear shear flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 174 , January 1987 , pp. 553 - 563
Copyright
© 1987 Cambridge University Press

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References

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