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Existence of viscous eddies near boundaries

Published online by Cambridge University Press:  20 April 2006

N. Liron  and
J. R. Blake
N. Liron
Affiliation:
Department of Mathematics, I.I.T. The Technion, Haifa, Israel
J. R. Blake
Affiliation:
Department of Mathematics, The University of Wollongong, P.O. Box 1144, Wollongong, N.S.W. 2500, Australia
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Abstract

Kinematic and dynamic conditions for the existence, or otherwise, of viscous eddies due to point, ring or a line distribution of stokeslets near no-slip boundaries are investigated. Boundaries considered are (i) a single plane boundary, (ii) two parallel plane boundaries, (iii) an infinite cylinder, and (iv) a finite cylinder. It is found that the following constraints on the fluid lead to the existence of eddies (i) a zero flux condition, (ii) confinement due to boundaries, (iii) streamline convergence near the singularity, and (iv) the interaction of flow fields due to adjacent stokeslets. The existence or non-existence of various viscous eddies is illustrated and discussed in detail for the case of infinite line distributions of stokeslets (i.e. a two-dimensional stokeslet). The paper suggests that flow fields produced by sessile micro-organisms are determined primarily by the container geometry in which they are located.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 107 , June 1981 , pp. 109 - 129
Copyright
© 1981 Cambridge University Press

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