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Reflection of a shallow-water soliton. Part 1. Edge layer for shallow-water waves

Published online by Cambridge University Press:  20 April 2006

N. Sugimoto  and
T. Kakutani
N. Sugimoto
Affiliation:
Department of Mechanical Engineering, Faculty of Engineering Science. Osaka University, Toyonaka, Osaka 560, Japan
T. Kakutani
Affiliation:
Department of Mechanical Engineering, Faculty of Engineering Science. Osaka University, Toyonaka, Osaka 560, Japan
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Abstract

To investigate reflection of a shallow-water soliton at a sloping beach, the edge-layer theory is developed to obtain a ‘reduced’ boundary condition relevant to the simplified shallow-water equation describing the weakly dispersive waves of small but finite amplitude. An edge layer is introduced to take account of the essentially two-dimensional motion that appears in the narrow region adjacent to the beach. By using the matched-asymptotic-expansion method, the edge-layer theory is formulated to cope with the shallow-water theory in the offshore region and the boundary condition at the beach. The ‘reduced’ boundary condition is derived as a result of the matching condition between the two regions. An explicit edge-layer solution is obtained on assuming a plane beach.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 146 , September 1984 , pp. 369 - 382
Copyright
© 1984 Cambridge University Press

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