Comparison of Classical And Simple Free-surface Green Functions

Abstract

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. Both the classical Green function and the simpler Green function satisfy the radiation condition and the linearized free-surface condition in the farfield (where the linear free-surface condition is valid). 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.