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Viscous rotational stagnation-point flow

Published online by Cambridge University Press:  29 March 2006

Alan S. Hersh
Alan S. Hersh*
Affiliation:
University of California, Los Angeles
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Abstract

The investigation by Hayes (1964a) of the behaviour of a constant-density inviscid rotational flow in the neighbourhood of a stagnation point on a plane wall has been extended to include the effects of viscosity. The principal effect is the manner in which the singularity in vorticity discovered by Hayes is removed. A solution of only the boundary-layer equatiosn indicates the vorticity decays algebraically from the wall. Application of the method of matched asymptotic expansions, however, shows that the difference between boundary layer and outer vorticity, when carried out to second order in the outer flow, does not contribute to an algebraic decay. These results suggest that an infinite number of higher-order outer terms are generated which match the algebraic terms thereby yielding the conventional exponential decay. Numerical results are presented which also support this conclusion. The main contribution of the wall shear stress in the immediate neighbourhood of the stagnation point is shown to come from the external lateral vorticity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 45 , Issue 1 , 15 January 1971 , pp. 1 - 11
Copyright
Copyright © Cambridge University Press 1971

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Footnotes

Present address: Bolt Beranek and Newman Inc., Canoga Park, California.

References

Boger, R. C. 1966 General stagnation-point flow in OHD and MHD. Ph.D. Thesis, Cornell University.Google Scholar
Boger, R. C. & Ludford, G. S. S. 1967 Rotational stagnation-point flow J. Math. Mech. 16, 13391359.Google Scholar
Conti, R. & Van Dyke, M. 1969 Reacting flow as an example of a boundary layer under singular external conditions J. Fluid Mech. 38, 513535.Google Scholar
Davey, A. 1961 Boundary-layer flow at a saddle point of attachment J. Fluid Mech. 10, 593610.Google Scholar
Hayes, W. D. 1964a Rotational stagnation point flow J. Fluid Mech. 19, 366374.Google Scholar
Hayes, W. D. 1964b Inviscid rotational stagnation point flow PMM J. Appl. Math. Mech. 28, 684687.Google Scholar
Slater, L. J. 1964 Confluent Hypergeometric Functions. Handbook of Math. Functions, 503514. U.S. Dept. of Commerce, Washington, D.C.Google Scholar
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. New York: Academic.Google Scholar