A Simple Green Function for Diffraction-Radiation of Time-Harmonic Waves with Forward Speed

Abstract

Green functions that satisfy the radiation condition and the linearized free- surface boundary condition in the farfield – but only approximately in the nearfield – are given for diffraction-radiation of time-harmonic waves with forward speed and the special cases corresponding to zero forward speed and zero wave frequency. These Green functions are considerably simpler than the related Green functions employed in the literature, which satisfy the linearized free-surface boundary condition everywhere, i.e. in both the farfield (where the linear free-surface condition is valid) and the nearfield (where the linear free-surface condition is only an approximation, due to nearfield effects).