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The Quarterly Journal of Mechanics and Applied Mathematics 1976 29(4):381-397; doi:10.1093/qjmam/29.4.381
© 1976 by Oxford University Press
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A CLOSED TORUS IN STOKES FLOW

J. M. DORREPAAL, S. R. MAJUMDAR, M. E. O'NEILL and K. B. RANGER

( Department of Mathematics, University of British Columbia Vancouver, Canada
Department of Mathematics, University of Calgary Calgary, Canada
Department of Mathematics, University College London, England
Department of Mathematics, University of Toronto Toronto, Canada )

Axisymmetrical Stokes flows about a closed torus, formed from the rotation of two equal touching circles about their common tangent, are studied for the cases when the torus rotates steadily about its axis of symmetry in a quiescent fluid or is at rest in a uniform axial stream. The resistance coefficients for the body are determined and compared with those of a sphere, disk and hemispherical cup. For streaming motion past the torus, the flow is shown to separate from the body and a dividing streamline in each cusp separates fluid which flows past the body from fluid which is trapped in closed eddy-type motion. Within these regions of flow, the fluid rotates in an infinite set of toroidal vortices.


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