Wave component in the Green function for diffraction radiation of regular water waves

摘要

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