LAUSR

Abstract The Green function for diffraction radiation of regular waves in deep water is considered. The Green function G and its gradient ∇G involve non-oscillatory local-flow components L and ∇L, for which simple global approximations valid within the entire flow region exist, and wave components W and ∇W. The waves W and ∇W in this basic decomposition involve the intrinsic Fortran Bessel functions J0(h) and J1(h), where h denotes the horizontal distance between the source and flow-field points in the Green function, and the Struve functions H ˜ 0 ( h ) and H ˜ 1 ( h ) for which complementary approximations valid within the nearfield or farfield ranges 0 ≤ h ≤ 3 or 3  H ˜ 0 ( h ) and H ˜ 1 ( h ) defeat the global nature of the approximations to the local-flow components L and ∇L. This issue, however, is readily remedied if practical approximations, given by Aarts and Janssen in 2016, that relate the Struve functions H ˜ 0 ( h ) and H ˜ 1 ( h ) to the Bessel functions J0(h) and J1(h) are used. The resulting approximations to the waves W and ∇W given here, and the global approximations to the local-flow components L and ∇L given previously, yield practical and particularly simple approximations to G and ∇G that are valid within the entire flow region, can be evaluated simply and efficiently, and are sufficiently accurate for practical applications.