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Exact solutions for Stokes flow in and around a sphere and between concentric spheres

Published online by Cambridge University Press:  17 July 2009

P. N. SHANKAR
P. N. SHANKAR*
Affiliation:
Computational & Theoretical Fluid Dynamics Division, National Aerospace Laboratories, Bangalore 560 017, India
*
†Email address for correspondence: [email protected]
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Abstract

A general method is suggested for deriving exact solutions to the Stokes equations in spherical geometries. The method is applied to derive exact solutions for a class of flows in and around a sphere or between concentric spheres, which are generated by meridional driving on the spherical boundaries. The resulting flow fields consist of toroidal eddies or pairs of counter-rotating toroidal eddies. For the concentric sphere case the exact solution when the inner sphere is in instantaneous translation is also derived. Although these solutions are axisymmetric, they can be combined with swirl about a different axis to generate fully three-dimensional fields described exactly by simple formulae. Examples of such complex fields are given. The solutions given here should be useful for, among other things, studying the mixing properties of three-dimensional flows.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 631 , 25 July 2009 , pp. 363 - 373
Copyright
Copyright © Cambridge University Press 2009

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References

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