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Free-surface breakdown in a rapidly rotating liquid

Published online by Cambridge University Press:  12 April 2006

W. E. Scott
W. E. Scott
Affiliation:
Ballistic Research Laboratories and Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, Maryland 21218
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Abstract

It is shown that the wavelets which appear on the inertial wave form of the inner free surface of a fully spun-up cylindrical mass of liquid contained in a vertical, rapidly rotating and gyrating gyrostat are capillary waves. It is further shown that the interaction between these capillary waves and the excited inertial waves is not the mechanism which effects an observed two-period collapse (‘breakdown’) and reappearance of the free-surface inertial wave form. Rather, the two-period breakdown can be explained by the conjecture that it is a beat phenomenon arising from the interaction of two differently structured inertial wave modes, which have the same frequency at small amplitudes of oscillation of the gyrostat but which, owing to the dependence of the inertial mode frequency on the amplitude of the gyrostatic motion, have slightly different frequencies at larger amplitudes of oscillation of the gyrostat.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 86 , Issue 3 , 14 June 1978 , pp. 457 - 463
Copyright
© 1978 Cambridge University Press

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References

Karpov, B. G. 1965 Liquid filled gyroscope: the effect of Reynolds number on resonance. U.S. Army Ballistic Res. Lab. Rep. no. 1302.Google Scholar
Lamb, H. 1932 Hydrodynamics. Dover.
Scott, W. E. 1975 J. Fluid Mech. 72, 649.
Stewartson, K. 1959 J. Fluid Mech. 5, 577.