On the reflection of a solitary wave at a sloping beach: Analytical results
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.
scientific article; zbMATH DE number 4083180
scientific article