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The viscous secondary flow ahead of an infinite cylinder in a uniform parallel shear flow

Published online by Cambridge University Press:  28 March 2006

Alar Toomre
Alar Toomre
Affiliation:
Mechanics of Fluids Department, University of Manchester
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Abstract

A simple method is presented in this paper for calculating

  1. the secondary velocities, and

  2. the lateral displacement of total pressure surfaces (i.e. the ‘displacement effect’)

in the plane of symmetry ahead of an infinitely long cylinder situated normal to a steady, incompressible, slightly viscous shear flow; the cylinder is also perpendicular to the vorticity, which is assumed uniform but small. The method is based on lateral gradients of pressure, these being calculated from the primary flow alone. Profiles of the secondary velocities are obtained at several Reynolds numbers ahead of two specific cylindrical shapes: a circular cylinder, and a flat plate normal to the flow. The displacement effect is derived and, rathe surprisingly, is found to be virtually independent of the Reynolds number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 7 , Issue 1 , January 1960 , pp. 145 - 155
Copyright
© 1960 Cambridge University Press

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References

Goldstein, S. (ed.) 1938 Modern Developments in Fluid Dynamics, vol. 1. Oxford University Press.Google Scholar
Lighthill, M. J. 1956 J. Fluid Mech. 1, 31.Google Scholar
Lighthill, M. J. 1957 J. Fluid Mech. 3, 113.Google Scholar
Livesey, J. L. 1956 J. Aero. Sci. 23, 949.Google Scholar
Milne-Thomson, L. M. 1955 Theoretical Hydrodynamics, 3rd ed. New York: Macmillan.Google Scholar