On the reflection of a solitary wave at a sloping beach: Analytical results

This paper modifies the edge layer theory introduced by Sugimoto and Kakutani in [1] by including terms up to the order of O(ε{lunate} ^{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 ω = μ^-1 B(z), in Appendix A. Comparisons are made with available experimental and numerical results. © 1988.