Abstract This study develops analytical solutions for Bragg scattering of water waves propagating over a series of submerged perforated semi-circular breakwaters (bars) based on potential theory. The series solutions for velocity potentials in the external common fluid domain of the bars are expressed through multipole expansions, whilst those in the internal fluid domains are given using the separation of variables. The continuous condition of fluid velocity and a quadratic pressure drop condition on the perforated semi-circular arcs are applied to determine the unknowns in the series solutions. In the analytical solutions, obliquely and normally incident waves are independently considered. The calculation methods of the reflection, transmission and energy loss coefficients are given. Experimental tests are performed to measure the reflection and transmission coefficients of the breakwaters at different wave periods and water depths. The analytical solutions are in excellent agreement with the independently developed multi-domain BEM (boundary element method) solutions, and are also compared with the wide-spacing approximations and the experimental results. Calculation examples are presented to check the effects of various parameters (e.g., bar number, bar radius, bar spacing and incident wave angle) on the hydrodynamic quantities of the breakwaters. Main valuable results for engineering application are draw.

中文翻译：

---

多个水下穿孔半圆形防波堤对水波布拉格散射的分析与实验研究

摘要 本研究基于势理论，开发了在一系列水下穿孔半圆形防波堤（条）上传播的水波的布拉格散射的解析解。杆的外部公共流体域中速度势的级数解通过多极展开表示，而内部流体域中的速度势的级数通过变量分离给出。应用流体速度的连续条件和穿孔半圆弧上的二次压降条件来确定级联解中的未知数。在解析解中，斜入射波和垂直入射波是独立考虑的。给出了反射系数、透射系数和能量损失系数的计算方法。进行了实验测试，以测量不同波浪周期和水深下防波堤的反射和透射系数。解析解与自主开发的多域 BEM（边界元法）解非常吻合，并与宽间距近似和实验结果进行了比较。计算示例用于检查各种参数（例如，钢筋数量、钢筋半径、钢筋间距和入射波角）对防波堤水动力量的影响。主要有工程应用价值的成果被绘制出来。解析解与自主开发的多域 BEM（边界元法）解非常吻合，并与宽间距近似和实验结果进行了比较。计算示例用于检查各种参数（例如，钢筋数量、钢筋半径、钢筋间距和入射波角）对防波堤水动力量的影响。主要有工程应用价值的成果被绘制出来。解析解与自主开发的多域 BEM（边界元法）解非常吻合，并与宽间距近似和实验结果进行了比较。计算示例用于检查各种参数（例如，钢筋数量、钢筋半径、钢筋间距和入射波角）对防波堤水动力量的影响。主要有工程应用价值的成果被绘制出来。