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On boundary layers in two-dimensional flow with vorticity

Published online by Cambridge University Press:  28 March 2006

J. F. Harper
J. F. Harper
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Free School Lane, Cambridge
Now at the Department of Mathematics, University of Bristol.
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Abstract

The starting-point for this paper is the suggestion (Batchelor 1956b) that the wake behind a bluff body in a uniform stream may consist principally of two eddies rotating in opposite directions. The fluid is assumed to be incompressible and in two-dimensional steady motion at a very high Reynolds number. Along the boundary between the eddies, a viscous layer must form. This layer is unusual in that merely the vorticity, and not the velocity itself, varies appreciably across it. It will be shown that such layers can be treated theoretically much more simply than the general case, because it is possible to linearize the equation of motion. They may, of course, exist in flows other than that past a bluff body.

A discussion is also given of the flow near the rear stagnation point, where this boundary layer meets the body. It had been suggested that a large number of small eddies would have to exist there, but this seems not to be so.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 17 , Issue 1 , September 1963 , pp. 141 - 153
Copyright
© 1963 Cambridge University Press

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References

Batchelor, G. K. 1956a J. Fluid Mech., 1, 177.
Batchelor, G. K. 1956b J. Fluid Mech., 1, 388.
Carslaw, H. S. & Jaeger, J. C. 1947 Conduction of Heat in Solids. Oxford University Press.
Falkner, V. M. & Skan, S. W. 1930 Aero. Res. Counc., Lond., Rep. and Mem. no. 1314.
Fraenkel, L. E. 1961 J. Fluid Mech. 11, 400.
Goldstein, S. (ed.) 1938 Modern Developments in Fluid Dynamics, vol. I. Oxford University Press.
Hiemenz, K. 1911 Dingl. Polytech. J. 326, 321.
Kármán, Th. Von & Millikan, C. B. 1934 N.A.C.A. Rep. no. 504.
Moore, D. W. 1959 J. Fluid Mech. 6, 113.
Moore, D. W. 1963 J. Fluid Mech. 16, 161.
Proudman, I. 1960 J. Fluid Mech. 9, 593.
Schlichting, H. 1960 Boundary Layer Theory, 4th ed. New York: McGraw-Hill.