Approximation of the Green Function for Diffraction Radiation of Water Waves

摘要

The Green function, and its gradient, of the theory of diffraction radiationof time-harmonic water waves by an offshore structure in deep water areconsidered. This Green function G and its gradient ∇G are expressedin the usual manner as the sum of three components that correspond tothe fundamental free-space singularity, a non-oscillatory local flow, andwaves. Simple approximations to the local flow components in G and∇G are given. These approximations only involve elementary continuousfunctions (algebraic, exponential and logarithmic) of real arguments andare valid within the entire flow region, and are then particularly simpleand well suited for practical purposes.