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The rotation of two circular cylinders in a viscous fluid

Part of: Incompressible viscous fluids

Published online by Cambridge University Press:  26 February 2010

S. H. Smith
S. H. Smith
Affiliation:
Professor S. H. Smith, Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 1A1, Canada.
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Extract

Almost seventy years ago Jeffery [1] showed that a finite velocity can result at infinity when the biharmonic equation is solved for the titled problem. Here, we extend his calculations to show that finite vorticity is the more general conclusion, and then indicate a resolution of the apparent paradox.

MSC classification

Secondary: 76D05: Navier-Stokes equations
Type
Research Article
Information
Mathematika , Volume 38 , Issue 1 , June 1991 , pp. 63 - 66
Copyright
Copyright © University College London 1991

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References

1 Jeffery, G. B.. The rotation of two circular cylinders in a viscous fluid. Proc. Roy. Soc. (A), 101 (1922), 169–174.Google Scholar
2 Dorrepaal, J. M., O'Neill, M. E. and Ranger, K. B.. Two dimensional Stokes flows with cylinders and line singularities. Mathematika, 31 (1984), 65–75.CrossRefGoogle Scholar
3 Proudman, I. and Pearson, J. R. A.. Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder. J. Fluid Meek, 2 (1957), 237–262.CrossRefGoogle Scholar
4 Kaplun, S. and Lagerstrom, P. A.. Asymptotic expansions of Navier-Stokes solutions for small Reynolds numbers. J. Math. Mech., 6 (1957), 585–593.Google Scholar