AI 中文总结
本文针对线性单色波下水下垂直透浪防波堤的波散射，采用二维势波理论，通过摄动法推导解析解并验证，分析了相关参数对反射、透射系数的影响，给出了解的应用。
AI 中文摘要
针对线性单色波作用下水下垂直板式透浪防波堤散射的波速场，本文得到了解析解并给出了该解的应用。研究设定水域为无限深度，假设水流不可压缩、无粘性且无旋，由此采用二维势波理论。该透浪防波堤垂直占据水面下方的有限区间，水流可穿过防波堤。通过摄动法求解所得的非线性边界条件，其中小参数代表透浪性；解被展开至一阶项，使得主导阶项可代表不透浪防波堤产生的散射波，一阶项则给出考虑透浪防波堤散射波的解的修正项。各阶波速势通过约化法确定，这使得主导阶问题对应齐次黎曼-希尔伯特问题，一阶问题对应非齐次黎曼-希尔伯特问题。作为该解应用的示例，本文详细讨论了波长、防波堤长度及防波堤透浪性条件对反射系数和透射系数的影响；还推导了精确能量恒等式，该恒等式验证了一阶解，并给出了展开有效性范围的闭式边界ε_max(kb)。
英文摘要
An analytical solution for a wave velocity field scattered by a submerged permeable vertical plate-type breakwater under the linear monochromatic wave is obtained and the applications of the solution are presented. The water has an infinite depth, and the flow is assumed to be incompressible, inviscid, and irrotational, which leads to the two-dimensional potential wave theory. The permeable breakwater vertically occupies a finite interval beneath the water surface and the water flows through the breakwater. The resulting nonlinear boundary condition is resolved by the perturbation method with a small parameter representing the permeability. The solution was expanded up to the first order so that the leading-order term can represent the wave scattered by the impermeable breakwater and the first-order term can give the correction to the solution considering the wave scattered by the permeable breakwater. Each order of the wave velocity potential is determined by a reduction method and this leads to the homogeneous Riemann-Hilbert problem for the leading-order problem and the nonhomogeneous Riemann-Hilbert problem for the first-order problem. \rev{The effects} of wavelength, breakwater length, and breakwater permeability conditions on the reflection and transmission coefficients are discussed in detail as an illustrative example of the application of the solution. \rev{An exact energy identity is also derived; it verifies the first-order solution and yields a closed-form boundary $\varepsilon_{\max}(kb)$ of the validity range of the expansion.
Comments23 pages, 8 figures. Under consideration for publication in Wave Motion
