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The stability of a rigidly rotating column of liquid

Published online by Cambridge University Press:  26 February 2010

L. M. Hocking
L. M. Hocking
Affiliation:
University College, London, W.C.I.
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Extract

The stability of a non-rotating column of liquid was discussed by Rayleigh [1] who showed that axisymmetric disturbances of wave-lengths greater than the circumference of the column decreased the surface area and the consequent release of surface energy enabled the disturbance to grow. Rayleigh [2] also considered the effect of viscosity on the same problem and found that for high viscosity the range of stability was unaltered. For disturbances which are the same in all planes perpendicular to the axis of the column, it is clear that any disturbance increases the length of the boundary of a plane section of the column and hence increases the surface energy. Thus the column is stable for these disturbances.

Type
Research Article
Information
Mathematika , Volume 7 , Issue 1 , June 1960 , pp. 1 - 9
Copyright
Copyright © University College London 1960

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References

1.Rayleigh, Lord, Proc. London Math. Soc., 10 (1878), 4–13.CrossRefGoogle Scholar
2.Rayleigh, Lord, Phil. Mag., 34 (1892), 145–164.CrossRefGoogle Scholar
3.Hooking, L. M. and Michael, D. H., Mathematika, 6 (1959), 25–32.CrossRefGoogle Scholar
4.Goldstein, S. (ed.), Modern developments in fluid dynamics (Oxford, 1938), 115.Google Scholar