| Abstract: | In the present paper, limited to the discussion of weak non-linear shallow water waves, the transmission and reflection of a planar soliton on a two-dimensional structure are considered. The whole flow field is divided mainly into two subfields. One is in the vicinity of the structure, called the inner field; the other is far from the structure, called the outer field. In the outer field, according to its definition, the influence of the structure on the flow is negligible; to the order O(α, β) the governing equation for the flow is replaced by the Boussinesq equation. In the inner field the effect of the structure on the flow is significant, so the full Laplace equation is adopted as the governing equation for the flow field. Then the matched asymptotic expansion method is employed to connect smoothly the inner and outer solutions. Owing to the irregularity of the bottom of the structure, the boundary element method is incorporated. As an example, the case in which the incoming wave is a solitary wave is calculated and the time histories of transmitted and reflected waves are plotted. |
