Application of the Fourier–Kochin theory for the diffraction and radiation of free-surface waves about stationary floating bodies

Abstract

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.