A global approximation to the Green function for diffraction radiation of water waves

The Green function of the theory of diffraction radiation of time-harmonic (regular) waves by an offshore structure, or a ship at low speed, in deep water is considered. The Green function G and its gradient ∇G are expressed in the usual manner as the sum of three components that correspond to the fundamental free-space singularity, a non-oscillatory local flow, and waves. Simple approximations that only involve elementary continuous functions (algebraic, exponential, logarithmic) of real arguments are given for the local flow components in G and ∇G. These approximations are global approximations valid within the entire flow region, rather than within complementary contiguous regions as can be found in the literature. The analysis of the errors associated with the approximations to the local flow components given in the study shows that the approximations are sufficiently accurate for practical purposes. These global approximations provide a particularly simple and highly efficient way of numerically evaluating the Green function and its gradient for diffraction radiation of time-harmonic waves in deep water.