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Edge Waves on a Sloping Beach

F. Ursell
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 214, No. 1116 (Aug. 7, 1952), pp. 79-97
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/99161
Page Count: 19
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Edge Waves on a Sloping Beach
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Abstract

The set of eigenfrequencies of a mechanical system forms its spectrum. A discussion is given of systems with discrete, continuous and mixed spectra. It is shown that resonance occurs at discrete points of the spectrum, and at cut-off frequencies (end-points of the continuous spectrum). The motion in a semi-infinite canal of finite width closed by a sloping beach has a mixed spectrum. The inviscid theory predicts that at a discrete frequency the resonance is confined to the neighbourhood of the beach (inviscid edge wave), while at a cutoff frequency the resonance extends a long way down the canal. The latter resonance is confined to the neighbourhood of the beach (viscous edge wave) by viscosity which is important near a cut-off frequency. Especially large resonances are predicted for a series of critical angles, of which the largest is 30 °. The theory is verified experimentally in the frequency range 100 to 17 c/min for the angles 37· 6 and 29· 5°.

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