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The slow motion of a sphere in a rotating, viscous fluid

Published online by Cambridge University Press:  28 March 2006

Stephen Childress
Stephen Childress
Affiliation:
Jet Propulsion Laboratory, California Institute of Technology
Now at Courant Institute of Mathematical Sciences, New York University
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Abstract

The uniform, slow motion of a sphere in a viscous fluid is examined in the case where the undisturbed fluid rotates with constant angular velocity Ω and the axis of rotation is taken to coincide with the line of motion. The various modifications of the classical problem for small Reynolds numbers are discussed. The main analytical result is a correction to Stokes's drag formula, valid for small values of the Reynolds number and Taylor number and tending to the classical Oseen correction as the last parameter tends to zero. The rotation of a free sphere relative to the fluid at infinity is also deduced.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 20 , Issue 2 , October 1964 , pp. 305 - 314
Copyright
© 1964 Cambridge University Press

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References

Chang, I-dee 1960 J. Fluid Mech. 9, 473.
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Kaplun, S. & Lagerstrom, P. A. 1957 J. Math. Mech. 6, 585.
Maxworthy, T. 1962 Jet Prop. Lab. Space Prog. Summary no. 37–16, 22.
Saffman, P. G. 1963 Jet Prop. Lab. Space Prog. Summary no. 37–21, 259.