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An exact solution for progressive capillary waves of arbitrary amplitude

Published online by Cambridge University Press:  28 March 2006

G. D. Crapper
G. D. Crapper
Affiliation:
Department of Mathematics, University of Manchester
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Abstract

An exact solution is found in a fairly simple form for two-dimensional progressive waves of arbitrary amplitude on a fluid of unlimited depth, when only surface tension and not gravity is taken into account as the restoring force. The calculated wave forms are exhibited graphically for various amplitudes, and the relation between wave velocity and amplitude is plotted. The wave of greatest height occurs when the vertical distance between trough and crest is 0·730 wavelengths (compared with 0·142 for gravity waves). Higher waves are prevented from appearing by the enclosing of air bubbles in the troughs.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 2 , Issue 6 , August 1957 , pp. 532 - 540
Copyright
© 1957 Cambridge University Press

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References

Lamb, H. 1932 Hydrodynamics, 6th Ed. Cambridge University Press.
Michell, J. H. 1893 Phil. Mag. (5), 36, 430.
Stokes, G. G. 1847 Trans. Camb. Phil. Soc. 8, 441.
Stokes, G. G. 1880 Mathematical and Physical Papers, Vol. 1. Cambridge University Press.