The 3D frequency-domain analysis of the flow around a ship advancing in regular waves, in deep water, via the Green-function and boundary-integral method requires a practical and reliable way of evaluating the flow due to an arbitrary distribution of singularities (sources and dipoles) over the (flat or curved, quadrilateral or triangular) panels that are commonly used to approximate a ship hull-surface. This crucial element of the Green-function method, also widely called panel method, in a 3D analysis of ship motions is classically performed via a two-step procedure that involves evaluation of the Green function $G$ and its gradient $\nabla G$ as a first step, and their subsequent integration over hull-surface panels. This usual direct method, widely studied and applied in the literature, involves notorious well-documented mathematical and numerical complexities. A novel alternative method, based on the Fourier–Kochin approach, is expounded in the study. In this method, evaluation of $G$ and $\nabla G$ is bypassed, i.e. $G$ and $\nabla G$ are not evaluated, and the flow due to a distribution of singularities is evaluated directly, in the manner already expounded for the particular cases of steady flow around a ship advancing in calm water and diffraction-radiation of regular waves by an offshore structure or a ship at zero forward speed. The method expounded in these previous studies and extended here is based on an analytical representation of the flow due to a distribution of singularities (including the special case of a Green function and its gradient) that yields a formal decomposition into a wave component, given by single Fourier integrals along the dispersion curves associated with the dispersion relation, and a non-oscillatory local-flow component given by a double integral that has a smooth integrand mostly dominant within a compact region of the Fourier plane. An important aspect of this analytical flow decomposition is that the wave and local-flow components are smooth, unlike the wave and local-flow components in the expressions for $G$ and $\nabla G$ given in the literature. Moreover, the analytical representation of the flow due to a distribution of singularities given in the study provides a practical mathematical basis that is well suited for accurate and efficient numerical evaluation, as is demonstrated via the illustrative applications reported previously for steady flow around a ship advancing in calm deep water and diffraction-radiation of regular waves by an offshore structure in deep water, and reported here for the more general case of a ship advancing in deep water at a constant speed $V$ through regular waves of frequency $\omega$ in the regime $\tau \equiv V\omega ∕g<1∕4$ where $g$ denotes the acceleration of gravity.

通过Green函数和边界积分方法对深水中规则波前进的船舶周围流进行3D频域分析，需要一种实用且可靠的方法来评估由于奇异点的任意分布而引起的流（源（偶极子和偶极子）在通常用于近似船体表面的（平坦或弯曲，四边形或三角形）面板上。在船舶运动的3D分析中，格林函数方法（也广泛称为面板方法）的这一关键要素通常通过两步过程来执行，该过程涉及对格林函数的评估$G$ 及其梯度 $\nabla G$作为第一步，以及它们随后在船体表面板上的整合。这种通常使用的直接方法在文献中得到了广泛的研究和应用，其中涉及到臭名昭著的数学和数值复杂性。在研究中阐述了一种基于傅立叶-科钦方法的新颖替代方法。在这种方法中，评估$G$ 和 $\nabla G$ 被绕过，即 $G$ 和 $\nabla G$不进行评估，而是直接评估奇异性分布引起的流动，具体方式已针对在平静水中前进的船舶周围稳定流动以及海上结构或船舶对规则波的衍射辐射的特殊情况进行了阐述。前进速度为零 这些先前研究中阐述并在此处扩展的方法是基于流动的解析表示，这是由于奇异性（包括格林函数及其梯度的特殊情况）的分布而产生的，形式上分解为波分量，由沿与色散关系相关的色散曲线的单个傅立叶积分，以及由双重积分给出的非振荡局部流分量，该双重积分在傅立叶平面的紧缩区域内具有主要占优势的光滑被积体。$G$ 和 $\nabla G$在文献中给出。此外，由于研究中给出的奇异性分布而对流量的解析表示提供了一个非常实用的数学基础，非常适合准确而有效的数值评估，如先前报道的用于船舶前进的稳定流量的说明性应用所证明的那样在平静的深水中以及深海中的近海结构产生的规则波的衍射辐射，在此报告了更普遍的情况，即船舶以恒定速度在深水中前进$V$ 通过频率的规律波 $\omega$ 在政权中 $\tau \equiv V\omega ∕G<\mathrm{1个}∕4$ 哪里 $G$ 表示重力加速度。