This article studies water wave interaction with a submerged quarter-circular breakwater based on potential theory and multipole expansion method. The obliquely and normally incident waves are independently considered. The series solution of velocity potential in the external fluid domain is expressed through the multipole expansions, while the series solution of velocity potential in the quarter-circular internal fluid domain is obtained through the separation of variables. Then, the unknown coefficients in the series solutions are determined by matching the boundary conditions between external and internal fluid domains. The calculation methods for the reflection and transmission coefficients of the submerged quarter-circular breakwater as well as the horizontal and vertical wave forces on the breakwater are presented. The wave forces acting on the submerged breakwater with a seaside quarter-circular-arc and that with a leeside quarter-circular-arc are compared. The hydrodynamic quantities of the submerged quarter-circular breakwater are also compared with those of the submerged semi-circular breakwater. In addition, the effects of breakwater radius, incident frequency, and incident angle on the hydrodynamic quantities of the quarter-circular breakwater are clarified. Valuable results for practical engineering application are drawn.

中文翻译：

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用多极法分析水波与淹没式四分之一圆形防波堤的相互作用

本文基于势理论和多极展开方法研究了水波与淹没式四分之一圆形防波堤的相互作用。斜入射波和垂直入射波是独立考虑的。外部流体域中速度势的级数解通过多极展开表示，而四分之一圆内部流体域中的速度势级数通过变量分离得到。然后，通过匹配外部和内部流体域之间的边界条件来确定级数解中的未知系数。介绍了水下四分之一圆形防波堤反射系数和透射系数的计算方法，以及作用在防波堤上的水平和垂直波浪力的计算方法。比较了作用在海边四分之一圆弧和背风四分之一圆弧淹没式防波堤上的波浪力。水下四分之一圆形防波堤的水动力量也与水下半圆形防波堤的水动力量进行了比较。此外，阐明了防波堤半径、入射频率和入射角对四分之一圆防波堤水动力量的影响。为实际工程应用得出了有价值的结果。阐明了四分之一圆防波堤水动力量的入射角和入射角。为实际工程应用得出了有价值的结果。阐明了四分之一圆防波堤水动力量的入射角和入射角。为实际工程应用得出了有价值的结果。