On the reflection of a solitary wave at a sloping beach: Analytical results
type: Item
instance of: scholarly article
title: On the reflection of a solitary wave at a sloping beach: Analytical results
zbMATH Open document ID: 0662.76027
DOI: 10.1016/0165-2125(88)90034-0
published in: Wave Motion
publication date: 1988-01-01T00:00:00Z
review text: This paper modifies the edge layer theory introduced by \textit{N. Sugimoto} and \textit{I. Kakutani} [J. Fluid Mech. 146, 369-382 (1984; Zbl 0565.76022)] by including terms up to the order of \(O(\epsilon^{3/2})\) in the boundary condition for the exterior problem to take account in the edge layer of the surging movement at the shoreline. A perturbation procedure involving strained coordinates combined with the inner and outer expansions is then developed to solve such an exterior problem. The analytical results obtained make clear the long-time evolution of a solitary wave after its reflection at the beach. Analytical expressions for the maximum run-up at the beach and the time when it is attained are presented. Analytical results are also given for a beach of the form \(\xi =\mu^{-1}B(z)\), in Appendix A. Comparisons are made with available experimental and numerical results.
Mathematics Subject Classification ID: 76B25
zbMATH DE Number: 4083180
zbMATH Keywords: edge layer theory
zbMATH Keywords: exterior problem
zbMATH Keywords: perturbation procedure
zbMATH Keywords: strained coordinates
zbMATH Keywords: inner and outer expansions
author: Alan Jeffrey
author: Hui-Hui Dai
MaRDI profile type: Publication
full work available at URL: 0165-2125(88)90034-0
OpenAlex ID: W1995854306
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description: scientific article; zbMATH DE number 4083180