Flow around a ship that advances at a constant speed in calm water of finite depth is considered within the usual framework of the Green-function and boundary-integral method associated with potential-flow theory. This method requires accurate and efficient evaluation of flows created by distributions of singularities over panels used to approximate the ship hull surface. This basic element of the Green-function method is considered for steady motion of ships in the subcritical and supercritical flow regimes. 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 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 Green function are then avoided in the Fourier-Kochin approach. The analytical flow-representation provides a smooth decomposition of free-surface effects into waves and a non-oscillatory local flow. Illustrative numerical applications to the flow potentials and velocities associated with a typical distribution of sources over a panel show that the flow-representation given in the study is well suited for accurate and efficient numerical evaluation.


Flow around a ship that advances at a constant speed in calm water of uniform finite depth is considered within the classical framework of linear potential-flow theory and the related Green-function and boundary-integral method in which the Green function satisfies the linearized Kelvin-Michell free-surface boundary condition. This theoretical frame-work is realistic and suited for routine practical applications.

Indeed, in deep water, this theory has been shown to yield predictions of the wave drag, the hydrodynamic lift and pitch-moment (and the resulting sinkage and trim), as well as the wave profile along a ship hull, that are sufficiently accurate for practical purposes within a broad range of Froude numbers (Noblesse et al., 2013; Huang et al., 2013; Zhang et al., 2014; Ma et al., 2017, 2018). In addition, numerical methods based on potential-flow theory are well suited for ship design and hull-form optimization, as is largely demonstrated in e.g. (Yang et al., 2014; Huang et al., 2016; Huang & Yang, 2016; Yang & Huang, 2016; Zha et al., 2021).

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