Abstract In this work, formulas for the reflection and transmission coefficients of one-dimensional linear water waves propagating over a submerged structure with a cycloidal cross section in presence of a sloping beach are determined. In the specialized literature, the previous coefficients are obtained mainly for the limit of linear water waves, considering that the water depth upstream and downstream of the structure is flat. For the analysis, we have obtained an approximate analytical solution to the dimensionless Modified Mild-Slope Equation, which models the interactions of a wide range of water waves, from short waves to long waves. The results shown that the presence of small breakwaters not always generate increments on the reflection coefficients, but on the contrary case they contribute to the reflection of the waves decreasing, which is due to the interference of energy that exists between the inclined beach and the structure. To validate the approximate analytical solution, we present a comparison against analytical solutions reported in the specialized literature, obtained with the aid of linear long wave theory, and a numerical solution, all the solutions adjust properly. Results of this study are expected to be used by coastal engineers for preliminary feasibility and desk design of submerged cycloidal breakwaters.

中文翻译：

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存在不同深度剖面的海滩时，水下摆线防波堤的波浪反射

摘要 在这项工作中，确定了一维线性水波在存在倾斜海滩的情况下在具有摆线横截面的水下结构上传播的反射系数和透射系数的公式。在专业文献中，前面的系数主要是针对线性水波的极限得到的，考虑到结构上下游的水深是平坦的。为了进行分析，我们获得了无量纲修正缓坡方程的近似解析解，该方程模拟了从短波到长波的各种水波的相互作用。结果表明，小防波堤的存在并不总是会增加反射系数，但相反，它们会导致波浪的反射减少，这是由于倾斜海滩和结构之间存在能量干扰。为了验证近似解析解，我们与专业文献中报道的解析解进行了比较，借助线性长波理论和数值解获得，所有解都适当调整。这项研究的结果预计将被沿海工程师用于水下摆线防波堤的初步可行性和桌面设计。