A global approximation to the green function for diffraction-radiation of regular water waves in deep water

Abstract

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 com- ponents 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

regions as can be found in the literature.