Rankine and Fourier-Kochin Representation of Near-Field Ship Waves

Abstract

New fundamental analytical representations of the near-held potential how that corresponds to a given how at a surface bounding a potential-how region are given for three classes of free-surface hows in deep water: diffraction-radiation of regular water waves by an offshore structure, steady ship waves, and time-harmonic ship waves (diffraction-radiation with forward speed). These near-held how representations, called Rankine and Fourier-Kochin representations, define the how in terms of distributions of Rankine singularities and Fourier-Kochin distributions of elementary waves over the boundary surface and its intersection with the mean free surface. The Rankine and Fourier-Kochin near-held how representations involve only simple ordinary functions. These how representations extend the previously given Fourier-Kochin representations of waves.