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Long waves on a rotating earth in the presence of a semi-infinite barrier

Published online by Cambridge University Press:  28 March 2006

J. Crease
J. Crease
Affiliation:
National Institute of Oceanography, Wormley, Surrey
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Abstract

In this paper the problem is considered of long gravity waves approaching a semi-infinite barrier which extends parallel to the wave crests, the whole system being in rotation. It is well known that, when the rotation is zero, there is a ‘shadow region’ behind the barrier in which the disturbance diminishes rapidly with distance from the edge. However, it is shown that the rotation gives rise to an additional wave in the shadow region. The crests of this wave are at right-angles to the incident wave, and it travels along the barrier without attenuation in that direction. The amplitude falls off exponentially with distance from the barrier, as in a Kelvin wave. The amplitude at the barrier may exceed that of the incident waves.

The problem arises in connexion with the propagation of tides and storm surges in the ocean.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 1 , Issue 1 , May 1956 , pp. 86 - 96
Copyright
© 1956 Cambridge University Press

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References

Baker, B. B. & Copson, E. T. 1950 The Mathematical Theory of Huygen's Principle, 2nd Ed. Oxford University Press.
Clemmow, P. C. & Mumford, C. M. 1952 Phil. Trans. A, 245, 189.
Copson, E. T. 1946 Quart. J. Math. 17, 19.
Corkan, R. H. 1948 Storm surges in the North Sea. Hydr. Office Misc. no 15072.
Erdely, I. A. et al. 1955 Tables of Integral Transforms, Vols. 1 & 2. New York: McGraw-Hill.
Karp, S. N. 1950 Commun. Pure Appl. Math. 3, 411.
Lamb, H. 1932 Hydrodynamics, 6th Ed. Cambridge University Press.
Peters, A. S. & Stoker, J. J. 1954 Commun. Pure Appl. Math. 7, 565.
Proudman, J. 1953 Dynamical Oceanography London: Methuen.
Rossiter, J. R. 1954 Phil. Trans. A, 246, 371.
Titchmarsh, E. C. 1948 Theory of Fourier Integrals, 2nd Ed. Oxford University Press.
Watson, G. N. 1944 Theory of Bessel Functions, 2nd Ed. Cambridge University Press.