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On the generation of viscous toroidal eddies in a cylinder

Published online by Cambridge University Press:  19 April 2006

J. R. Blake
J. R. Blake
Affiliation:
CSIRO Division of Mathematics and Statistics, PO Box 1965, Canberra City, ACT, 2601, Australia Present address: Department of Mathematics, University of Wollongong, P.O. Box 1144, NSW, 2500, Australia.
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Abstract

The streamlines due to a stokeslet on the axis in a finite, semi-infinite and infinite cylinder are obtained together with the case of a Stokes-doublet and source-doublet in an infinite cylinder. In the infinite and semi-infinite cylinder examples an infinite set of toroidal eddies are obtained. The eddies alternate in sign and the magnitude of the stream function decays exponentially with distance from the driving singularity. In the finite cylinder a primary interior eddy adjacent to the singularity is always obtained and, depending on location of the singularity within the cylinder and the ratio of cylinder length to radius, a finite number of secondary interior eddies. In the case of long cylinders, the eddies are generated along the axis, whereas, for squat cylinders, secondary eddies occur in the radial direction. The interior eddies emerge from the corner as the length of the cylinder is increased. Moffatt corner eddies exist but they are very much smaller than the interior eddies.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 95 , Issue 2 , 28 November 1979 , pp. 209 - 222
Copyright
© 1979 Cambridge University Press

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