The classical problem of time-harmonic diffraction and radiation of free-surface flows due to wave–body interaction is revisited based on the Fourier–Kochin theory for zero forward speed. The key idea of the Fourier–Kochin theory is reversing the order of the two fundamental tasks of the Green function based direct solutions of free-surface flows, i.e., evaluation of the Green function and its gradient, and their subsequent integration over the boundary surface. By implementing a higher-order numerical approximation along with the use of extended boundary integral equation method to suppress the irregular frequencies, three different bodies – a hemisphere, a vertical cylinder, and a frigate model – are studied. The Fourier–Kochin framework accurately captures the radiated and diffracted flow about oscillating bodies, in general, but slight irregularities are also observed at high frequencies for complicated body forms. Since the floating body is stationary here, the problem has a standard, unambiguous solution and the indirect approach introduced by the Fourier–Kochin theory may not seem worthwhile to adopt; however, its perspective becomes rewarding when the forward speed effects are considered. As a premise of this idea, the main goals here are to assess the practical application of the theory, to identify the challenges, and to investigate how to surmount them.

基于傅里叶-科钦理论将零波前移速度归因于由波体相互作用引起的时谐衍射和自由表面流辐射的经典问题。傅里叶-科钦理论的关键思想是逆转基于格林函数的自由表面流直接解的两个基本任务的顺序，即对格林函数及其梯度的求值，以及它们随后在边界面上的积分。通过执行高阶数值近似以及使用扩展边界积分方程法来抑制不规则频率，研究了三个不同的物体-半球，垂直圆柱体和护卫舰模型-。傅里叶-科钦（Fourier-Kochin）框架可以准确地捕获围绕振荡体的辐射流和衍射流，通常，但是对于复杂的身体形态，在高频下也会观察到轻微的不规则性。由于浮动物体在这里是静止的，因此问题具有标准的，明确的解决方案，傅里叶-科钦理论引入的间接方法似乎不值得采用。但是，当考虑前进速度的影响时，它的观点就变得很有用。作为该思想的前提，此处的主要目标是评估该理论的实际应用，确定挑战并研究如何克服这些挑战。当考虑到前进速度的影响时，它的观点就变得有意义。作为该思想的前提，此处的主要目标是评估该理论的实际应用，确定挑战并研究如何克服这些挑战。当考虑到前进速度的影响时，它的观点就变得有意义。作为该思想的前提，此处的主要目标是评估该理论的实际应用，确定挑战并研究如何克服这些挑战。