The behavior of an offshore structure in regular waves – and the related (linear and nonlinear) wave loads, added-mass and wave-damping coefficients, and body-motions – are commonly analyzed via the Green-function and boundary-integral method associated with potential-flow theory. This realistic, widely-used method requires accurate and efficient numerical evaluation of flows created by distributions of singularities (source, dipole) over (flat or curved) panels of various shapes (triangle, quadrilateral) that are used to approximate the surface of an offshore structure. This basic core element of the theory of diffraction–radiation of regular waves by an offshore structure is considered for water of uniform finite depth. The special case of deep water is also considered. An analytical representation of the flow created by a general distribution of singularities over a hull-surface panel is given. This flow-representation is based on the Fourier–Kochin (FK) approach, in which space-integration over the panel is performed first and Fourier-integration is performed subsequently, unlike the common approach in which the Green function (defined via a Fourier integration) is evaluated first and subsequently integrated over the panel. The analytical and numerical complexities associated with the numerical evaluation and subsequent panel integration of the singular Green function for wave diffraction–radiation by offshore structures are then avoided in the FK approach. In this approach, panel integration merely amounts to integrating an elementary (exponential–trigonometric) function, a trivial task that can be performed accurately and efficiently. The analytical flow-representation given in the study provides a mathematically-exact smooth decomposition of free-surface effects into a non-oscillatory local flow and waves. The waves in this flow decomposition are defined by a regular single Fourier integral, and the local flow is given by a double Fourier integral with a smooth integrand that only involves ordinary functions and is dominant within a compact region near the origin of the Fourier plane. Illustrative numerical applications for typical distributions of sources and dipoles over a panel show that the flow-representation given in the study is well suited for practical numerical evaluations.

通常通过格林函数和边界积分法分析常规波浪中海上结构的行为，以及相关的（线性和非线性）波浪载荷，附加质量和波浪阻尼系数以及人体运动。势流理论。这种现实的，广泛使用的方法要求对流量进行精确，高效的数值评估，该流量是由用于近似海上表面的各种形状（三角形，四边形）的（平面或弯曲）面板上的奇异点（源或偶极子）分布所产生的结构体。对于均匀有限深度的水，考虑了海上结构对规则波的衍射-辐射理论的这一基本核心要素。还考虑了深水的特殊情况。给出了船体表面面板上奇异点的一般分布所产生的流动的解析表示。该流表示法基于傅立叶–柯钦（FK）方法，在该方法中，首先在面板上进行空间积分，然后执行傅立叶积分，这与通常的Green函数（通过傅立叶积分定义）不同。 ）首先进行评估，然后整合到面板上。在FK方法中，避免了与数值评估相关的分析和数值复杂性，以及随后的奇异Green函数对海上结构波衍射-辐射的面板整合。在这种方法中，面板集成仅相当于集成基本（指数-三角）函数，可以准确而有效地执行的琐碎任务。研究中给出的解析流动表示法将自由表面效应数学精确地平滑分解为非振荡的局部流动和波动。该流动分解中的波由规则的单个傅立叶积分定义，局部流量由带有光滑被积的双傅立叶积分给出，该积分仅涉及普通函数，并且在靠近傅立叶平面原点的紧凑区域内占主导地位。在面板上典型的源和偶极子分布的说明性数值应用表明，研究中给出的流量表示非常适合于实际数值评估。研究中给出的解析流动表示法将自由表面效应数学精确地平滑分解为非振荡的局部流动和波动。该流动分解中的波由规则的单个傅立叶积分定义，局部流量由带有光滑被积的双傅立叶积分给出，该积分仅涉及普通函数，并且在靠近傅立叶平面原点的紧凑区域内占主导地位。在面板上典型的源和偶极子分布的说明性数值应用表明，研究中给出的流量表示非常适合于实际数值评估。研究中给出的解析流动表示法将自由表面效应数学精确地平滑分解为非振荡的局部流动和波动。该流动分解中的波由规则的单个傅立叶积分定义，局部流量由带有光滑被积的双傅立叶积分给出，该积分仅涉及普通函数，并且在靠近傅立叶平面原点的紧凑区域内占主导地位。在面板上典型的源和偶极子分布的说明性数值应用表明，研究中给出的流量表示非常适合于实际数值评估。局部流动由带有光滑被积的双傅立叶积分给出，该积分仅涉及普通函数，并且在靠近傅立叶平面原点的紧凑区域内占优势。在面板上典型的源和偶极子分布的说明性数值应用表明，研究中给出的流量表示非常适合于实际数值评估。局部流动由具有光滑被积的双傅立叶积分给出，该积分仅涉及普通函数，并且在靠近傅立叶平面原点的紧凑区域内占主导地位。在面板上典型的源和偶极子分布的说明性数值应用表明，研究中给出的流量表示非常适合于实际数值评估。