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Variational properties of steady fall in Stokes flow

Published online by Cambridge University Press:  29 March 2006

H. F. Weinberger
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Abstract

It is shown that for a given body and a given orientation g there is always a position of the centre of mass which produces a stable falling motion in a very viscous fluid with g vertical and, in general, with a spin about the vertical axis. The corresponding terminal settling speed is bounded by means of several variational principles.

Relations between the terminal speeds for falls with different downward directions and between the terminal speed and the geometry of the body are deduced. In particular, it is proved that for a large class of slender bodies the first approximation to the drag obtained from the slender-body theory of Burgers (1938) is correct. It follows that the ratio of the terminal speeds for falls with the long axis vertical and horizontal is near two.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 52 , Issue 2 , 28 March 1972 , pp. 321 - 344
Copyright
© 1972 Cambridge University Press

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