This paper studies water wave diffraction and radiation by a submerged sphere in front of a vertical wall. Based on the image principle, the physical problem is transformed into an imaginary problem of two spheres, which are symmetric with respect to the original vertical wall, in a horizontally open water domain. Then, an analytical solution for the imaginary problem is developed in the context of linear wave theory. The velocity potential of fluid motion is obtained by adopting the method of multipole expansions combined with the shift of local spherical coordinate systems. The wave exciting forces in surge, sway and heave directions, and added mass and radiation damping due to the sphere oscillation are calculated. The convergence of the series solution is very rapid, and the results of analytical solution and numerical solution based on boundary element method are highly consistent. Calculation examples are presented to examine the effects of wave/oscillation frequency, spacing between sphere and wall, submergence depth and wave incident angle on various hydrodynamic quantities of the sphere. Results show that because the submerged sphere is subjected to not only incident/radiated waves but also reflected waves from the wall, the hydrodynamic quantities noticeably differ from those in an open water domain.

本文研究了垂直墙前的水下球体的水波衍射和辐射。基于图像原理，将物理问题转化为水平开放水域中相对于原垂直壁对称的两个球体的假想问题。然后，在线性波理论的背景下开发了该假想问题的解析解。流体运动的速度势是采用多极展开结合局部球坐标系位移的方法得到的。计算了由于球体振荡引起的涌浪、摇摆和垂荡方向的波浪激振力，以及附加质量和辐射阻尼。级数解的收敛速度非常快，基于边界元法的解析解与数值解的结果高度一致。计算示例用于检查波浪/振荡频率、球体与壁之间的间距、淹没深度和波浪入射角对球体的各种流体动力学量的影响。结果表明，由于水下球体不仅受到入射/辐射波的影响，还受到壁面反射波的影响，因此水动力量与开放水域中的水动力量明显不同。