The classical Green function and a related simpler Green function associated with the linearized free-surface boundary condition for 3D diffraction-radiation by a ship advancing in regular waves are considered for the special case of steady flows. The classical Green function also satisfies the linear free-surface condition in the nearfield (where this linear condition is only an approximation, due to nearfield effects), whereas the simple Green function satisfies the linear free-surface condition only approximately in the nearfield. Numerical differences between these alternative free-surface Green functions are shown to vanish in the farfield, as expected, and to be relatively moderate in the nearfield.
Theoretical prediction of the behavior of ships and offshore structures in time-harmonic ambient waves is one of the most important core issues in free-surface hydrodynamics. For offshore structures, robust and highly-efficient panel methods have been developed, and are routinely used, to solve the canonical wave diffraction-radiation problems associated with the definition of added-mass and wave-damping coefficients, and wave-exciting forces and moments. These potential-flow methods are based on numerical solution of a boundary-integral equation formulated using the Green function that satisfies the linear free-surface boundary condition for diffraction-radiation of time-harmonic waves without forward speed. Applications of this classical approach, often identified as the free-surface Green-function method, to wave diffraction-radiation by ships (i.e. with forward speed) have also led to useful methods—see e.g. Diebold (2003), Boin et al. (2002,2000), Chen et al. (2000), Guilbaud et al. (2000), Fang (2000), Wang et al. (1999), Du et al. (2000,1999), Iwashita and Ito (1998), Iwashita (1997)—although not to a comparable degree of practicality because forward speed introduces major difficulties (not present for wave diffraction-radiation at zero forward speed).
