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On angles of separation in Stokes flows

Published online by Cambridge University Press:  20 April 2006

M. E. O'Neill
M. E. O'Neill
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1K 6BT
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Abstract

A two-dimensional Stokes flow close to the line of contact of two touching cylinders or three-dimensional axisymmetric Stokes flow close to the point of contact of two touching bodies is shown in general to separate into infinite sets of eddies with angles of separation from the bodies which tend to 58.61° as the line or point of contact is approached. The flow near the vertex of a conical cusp is shown to be a system of nested toroidal vortices and the separation angles tend to 45.25° as the vertex is approached. Stokes flow between parallel planes or within a circular cylinder is shown in general to separate far from the generating disturbances with cellular eddy structure and separation angles which tend to 58.61° and 45.25° respectively. The mathematical equivalence of the various problems is established.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 133 , August 1983 , pp. 427 - 442
Copyright
© 1983 Cambridge University Press

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