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Long waves induced by short-wave groups over an uneven bottom

Published online by Cambridge University Press:  20 April 2006

Chiang C. Mei  and
Chakib Benmoussa
Chiang C. Mei
Affiliation:
Parsons Laboratory, Department of Civil Engineering, Massachusetts Institute of Technology
Chakib Benmoussa
Affiliation:
Parsons Laboratory, Department of Civil Engineering, Massachusetts Institute of Technology
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Abstract

Unidirectional and periodically modulated short waves on a horizontal or very nearly horizontal bottom are known to be accompanied by long waves which propagate together with the envelope of the short waves at their group velocity. However, for variable depth with a horizontal lengthscale which is not too great compared with the group length, long waves of another kind are further induced. If the variation of depth is only one-dimensional and localized in a finite region, then the additional long waves can radiate away from this region, in directions which differ from those of the short waves and their envelopes. There are also critical depths which define caustics for these new long waves but not for the short waves. Thus, while obliquely incident short waves can pass over a topography, these second-order long waves may be trapped on a ridge or away from a canyon.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 139 , February 1984 , pp. 219 - 235
Copyright
© 1984 Cambridge University Press

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