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Hydromechanics of low-Reynolds-number flow. Part 5. Motion of a slender torus

Published online by Cambridge University Press:  19 April 2006

Robert E. Johnson  and
Theodore Y. Wu
Robert E. Johnson
Affiliation:
Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, Urbana
Theodore Y. Wu
Affiliation:
Engineering Science Department, California Institute of Technology, Pasadena
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Abstract

In order to elucidate the general Stokes flow characteristics present for slender bodies of finite centre-line curvature the singularity method for Stokes flow has been employed to construct solutions to the flow past a slender torus. The symmetry of the geometry and absence of ends has made a highly accurate analysis possible. The no-slip boundary condition on the body surface is satisfied up to an error term of O(ε2 In ε), where ε is the slenderness parameter (ratio of cross-sectional radius to centre-line radius). This degree of accuracy makes it possible to determine the force per unit length experienced by the torus up to a term of O(ε2). A comparison is made between the force coefficients of the slender torus to those of a straight slender body to illustrate the large differences that may occur as a result of the finite centre-line curvature.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 95 , Issue 2 , 28 November 1979 , pp. 263 - 277
Copyright
© 1979 Cambridge University Press

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