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Trapping and resonance of long shelf waves due to groups of short waves

Published online by Cambridge University Press:  21 April 2006

Yehuda Agnon  and
Chiang C. Mei
Yehuda Agnon
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Chiang C. Mei
Affiliation:
Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

Groups of short waves within a narrow frequency band are known to be accompanied by second-order long waves travelling at the group velocity of the predominant short waves. When the short waves are refracted by bottom topography, new long waves can be further radiated and propagated away from the topography at the shallow-water speed. Since over a long submarine ridge there can be trapped modes of long-period waves, incident groups of short waves can excite the trapped waves through a second-order mechanism. In this paper we study such excitations over a rectangular shelf which scatters the first-order short waves. By employing asymptotic methods we examine the transient excitation of the trapped long wave by both sinusoidal wave groups and wave packets. The effects of a small angular spread of the incident waves are also included.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 195 , October 1988 , pp. 201 - 221
Copyright
© 1988 Cambridge University Press

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References

Agnon, Y. & Mei C. C. 1985 Slow drift motion of a two-dimensional block in beam seas. J. Fluid Mech. 151, 279–294.Google Scholar
Carrier G. F. 1970 The dynamics of tsunamis. Mathematical Problems in Geophysical Fluid Dynamics, pp. 157–181. American Mathematical Society, Providence, RI.Google Scholar
Foda, M. A. & Mei C. C. 1981 Nonlinear excitation of long trapped waves by a group of short swells. J. Fluid Mech. 111, 319–345.Google Scholar
Garrett C. J. R. 1971 Wave forces on a circular dock. J. Fluid Mech. 46, 129–139.Google Scholar
Longuet-Higgins M. S. 1967 On the trapping of wave energy round islands. J. Fluid Mech. 29, 781–821.Google Scholar
Mei C. C. 1983 Applied Dynamics of Ocean Surface Waves. Wiley Interscience.
Mei, C. C. & Benmoussa C. 1984 Long waves induces by short-wave groups over an uneven bottom. J. Fluid Mech. 139, 219–235.Google Scholar
Mei, C. C. & Black J. L. 1969 Scattering of surface waves by rectangular obstacles in waters of finite depth. J. Fluid Mech. 38, 499–511.Google Scholar
Miles J. W. 1967 Surface wave scattering matrix for a shelf. J. Fluid Mech. 28, 755–767.Google Scholar
Newman J. N. 1965 Propagation of water waves past long two dimensional obstacles. J. Fluid Mech. 23, 23–29.Google Scholar