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On an invariant property of water waves

Published online by Cambridge University Press:  29 March 2006

T. Brooke Benjamin  and
J. J. Mahony
T. Brooke Benjamin
Affiliation:
Fluid Mechanics Research Institute, University of Essex, Colchester, Essex
J. J. Mahony
Affiliation:
Fluid Mechanics Research Institute, University of Essex, Colchester, Essex
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Abstract

The discussion concerns free wave motions generated from rest in a finite region of an ocean of heavy liquid lying on a horizontal plane. It is shown that the horizontal fist moment of the free-surface displacement varies linearly with time. Hence, if the total volume displaced is not zero and therefore the centroid of the displacement is definable, the centroid travels with a constant horizontal velocity as the wave motion evolves. This conclusion holds exactly for waves of any amplitude and even remains applicable subsequent to the breaking of waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 49 , Issue 2 , 29 September 1971 , pp. 385 - 389
Copyright
© 1971 Cambridge University Press

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References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Keulegan, G. C. & Patterson, G. W. 1940 Mathematical theory of irrotational translation waves. J. Res. Natn. Bur. Stand., 24, 47.Google Scholar
Wehausen, J. V. & Laitone, E. V. 1960 Surface waves. In Handbuch der Physik, vol. 9. Berlin: Springer.