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The Cauchy–Poisson problem for a viscous liquid

Published online by Cambridge University Press:  28 March 2006

John W. Miles
John W. Miles
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, La Jolla Also Department of Aerospace and Mechanical Engineering Sciences.
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Abstract

The axisymmetric, free-surface response of a semi-infinite viscous liquid to either a point impulse or an initial displacement of zero net volume is calculated. The asymptotic disturbance is resolved into three components: (i) a damped gravity wave, which represents a primary balance between gravitational and inertial forces with secondary, but cumulative, modification by viscous forces; (ii) a diffusive motion, which represents a balance between viscous and inertial forces; (iii) a creep wave, which represents a balance between gravitational and viscous forces. Van Dorn has suggested that the results may be relevant to the concentric circular ridges that surround the crater Orientale on the Moon.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 34 , Issue 2 , 12 November 1968 , pp. 359 - 370
Copyright
© 1968 Cambridge University Press

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References

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ERDÉLYI, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. 1953 Tables of Integral Transforms, vol. 2. New York: McGraw-Hill.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Sretenskii, L. 1941 Concerning waves on the surface of a viscous fluid (in Russian). Trudy Tsentral. Aèro-Gidrodinam. Inst. No. 541, 1–34.Google Scholar
VAN DORN, W. G. 1968 Nature (in the Press).