A numerical model was developed in this study to simulate the wave diffraction caused by an arbitrarily shaped structure in the presence of bi-directional incident waves based on a higher-order boundary element method (HOBEM). Based on the developed model, the wave elevation quadratic transfer function (QTF) in bi-directional waves, which is defined as the second-order wave elevation caused by two incident waves of unit amplitude from two directions, can be determined. The developed model was subsequently used to investigate the wave interaction with a cylinder situated near a vertical wall. The image principle was applied to transform the original problem into an equivalent one of wave diffraction caused by two symmetrical cylinders in open seas exposed to bi-directional incident waves. The second-order wave run-up on the cylinder can then be determined using the wave elevation QTF obtained from an analysis of the equivalent problem. A detailed numerical analysis was then conducted. Numerical results revealed that the presence of the vertical wall can apparently disturb the wave diffraction process from the cylinder, and lead to significantly amplified second-order wave elevation within the region between the wall and cylinder. In addition, the respective contribution from the first- and second-order components to the overall wave elevation around the cylinder was discussed.

本研究中建立了一个数值模型，以基于高阶边界元法（HOBEM）来模拟在双向入射波存在下任意形状的结构引起的波衍射。基于所开发的模型，可以确定双向波中的波高二次传递函数（QTF），其定义为由两个方向上单位振幅的两个入射波引起的二阶波高。随后将开发的模型用于研究与垂直壁附近的圆柱体的波浪相互作用。应用图像原理将原始问题转换为等效的波衍射，该波衍射是由暴露于双向入射波的公海中的两个对称圆柱体引起的。然后可以使用从等效问题分析中获得的波高QTF来确定圆柱上的二阶波上升。然后进行了详细的数值分析。数值结果表明，垂直壁的存在显然会干扰圆柱体的波衍射过程，并导致壁和圆柱体之间区域内的二阶波高程显着放大。此外，还讨论了从一阶和二阶分量到圆柱周围总波高的各自贡献。数值结果表明，垂直壁的存在显然会干扰圆柱体的波衍射过程，并导致壁和圆柱体之间区域内的二阶波高程显着放大。此外，还讨论了从一阶和二阶分量到圆柱周围总波高的各自贡献。数值结果表明，垂直壁的存在显然会干扰圆柱体的波衍射过程，并导致壁和圆柱体之间区域内的二阶波高程显着放大。此外，还讨论了从一阶和二阶分量到圆柱周围整个波高的各自贡献。