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Shoaling of finite-amplitude surface waves on water of slowly-varying depth

Published online by Cambridge University Press:  19 April 2006

M. Stiassnie  and
D. H. Peregrine
M. Stiassnie
Affiliation:
Department of Mathematics, University of Bristol, England Permanent address: Faculty of Civil Engineering, Technion-Israel Institute of Technology, Haifa, Israel.
D. H. Peregrine
Affiliation:
Department of Mathematics, University of Bristol, England
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Abstract

Periodic wave trains propagating over water which varies in depth in the direction of wave propagation are studied by using accurate solutions for wave trains in constant depth of water. The accurate solutions are (i) Cokelet's (1977) extension of Stokes’ approximation and, for the longer waves, (ii) a solution for trains of solitary waves using the solitary-wave solution of Longuet-Higgins & Fenton (1974).

A representative selection of results is shown in diagrams. A feature which arises from the use of these accurate solutions is that near the highest wave two solutions are possible for a given incoming wave. Although the solutions cannot describe waves that break, it is shown that as depth is decreased a point is reached beyond which no solution can be found. This is taken to indicate the region in which waves break.

The limitations of the theory are discussed and analysed. Comparisons with experimental measurements of Hansen & Svendsen (1979) are included.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 97 , Issue 4 , 29 April 1980 , pp. 783 - 805
Copyright
© 1980 Cambridge University Press

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