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On the stability of two-dimensional stagnation flow

Published online by Cambridge University Press:  29 March 2006

J. Kestin  and
R. T. Wood
J. Kestin
Affiliation:
Brown University
R. T. Wood
Affiliation:
Brown University
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Abstract

The paper examines the stability of the uniform flow which approaches a two-dimensional stagnation region formed when a cylinder or a two-dimensional blunt body of finite curvature is immersed in a crossflow. It is shown that such a flow is unstable with respect to three-dimensional disturbances. This conclusion is reached on the basis of a mathematical analysis of a simplified form of the disturbance equation for the stream-wise component of the vorticity vector. The ultimate, or stable, flow pattern is governed by a singular Sturm–Liouville problem whose solution possesses a single eigenvalue. The resulting flow is one in which a regularly distributed system of counter-rotating vortices is super-imposed on the basic, Hiemenz-like pattern of streamlines. The spacing of the vortices is a unique function of the characteristics of the flow, and a theoretical estimate for it agrees well with experimental results. The analysis is extended heuristically to include the effect of free-stream turbulence on the spacing.

The problem is similar to the classical Görtler–Hämmerlin study of the stability of stagnation flow against an infinite flat plate, which revealed the existence of a spectrum of eigenvalues for the disturbance equation. The present analysis yields the same result when an infinite radius of curvature is assumed for the blunt body.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 44 , Issue 3 , 26 November 1970 , pp. 461 - 479
Copyright
© 1970 Cambridge University Press

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References

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Note added in proof. Additional information regarding the experimental work mentioned in this paper can be found in the following two references:
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