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The Quarterly Journal of Mechanics and Applied Mathematics 1996 49(4):621-633; doi:10.1093/qjmam/49.4.621
© 1996 by Oxford University Press
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TIME-DEPENDENT DECAY OF THE MOTION OF A SPHERE TRANSLATING AND ROTATING IN A VISCOUS LIQUID

K. B. RANGER

( Department of Mathematics, University of Toronto Toronto, Ontario, Canada M5S 1A1 )

An exact solution of the Navier-Stokes equations is found for the (axisymmetric) motion (with swirl) representing exponentially time-dependent decay of a solid sphere translating and rotating in a viscous fluid relative to a uniform stream whose speed also decays exponentially with time. A similar solution is also described for the two-dimensional analogue where the sphere is replaced by a circular cylinder of infinite length.


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