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The stability of viscous flow between rotating cylinders

Published online by Cambridge University Press:  26 February 2010

S. Chandrasekhar
S. Chandrasekhar
Affiliation:
Yerkes Observatory and Institute for Nuclear Studies, University of Chicago.
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Extract

As is well known the stability of viscous flow between two concentric rotating cylinders was first successfully treated both experimentally and theoretically by G. I. Taylor [1]. The mathematical problem underlying this classical investigation in hydrodynamic stability is the following:

The hydrodynamical equations allow the stationary solution

for the rotational velocity at a distance r from the axis of rotation, where A and B are constants related to the angular velocities Ω1 and Ω2 with which the inner and outer cylinders (of radii R1 and R2, R2 > R1) are rotated. Thus

where

Type
Research Article
Information
Mathematika , Volume 1 , Issue 1 , June 1954 , pp. 5 - 13
Copyright
Copyright © University College London 1954

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References

1.Taylor, G. I., Phil. Trans. Roy. Soc., A 223 (1923), 289–343.Google Scholar
2.Jeffreys, H., Proc. Roy. Soc. A, 118 (1928), 195–208.Google Scholar
3.Meksyn, D., Proc. Roy. Soc. A, 187 (1946), 115–128.Google Scholar
4.Meksyn, D., Proc. Roy. Soc. A, 187 (1946), 480–491.Google Scholar
5.Meksyn, D., Proc. Roy. Soc. A, 187 (1946), 492–504.Google Scholar
6.Pellew, A. and Southwell, R. V., Proc. Roy. Soc. A, 176 (1940), 312–343.Google Scholar