Newman’s Manuscript and His Impact on Offshore Hydrodynamics

Abstract

Prof. Nick Newman has spent an important part of his career researching the mathematical and numerical aspects of the radiation/diffraction Green’s function, i.e. the linearized potential of an oscillatory source submerged below the free surface [1–4]. The first part of the paper pays tribute to Newman’s accomplishments by presenting three thus far unpublished expansions of the oscillatory source potential. The first one is based on an unpublished manuscript by Newman himself [5] and in essence amounts to the backward recursive computation of a one-dimensional Taylor series expansion. The second expansion assumes the form of a remarkably simple Bessel series expansion and was inspired by a paper by Bessho [6]. The third expansion is another remarkably simple asymptotic series expansion in terms of incomplete Gamma functions and Legendre polynomials. The second part of the paper addresses the practical significance of some of Newman’s key accomplishments for the field of offshore hydrodynamics. Attention is focused on his ‘slow drift approximation’ [7], which has proved to be invaluable for the practical estimation of slow wave drift responses of floating structures. The diffraction program WAMIT [8] has by now matured into a de facto industry standard. The combined effectiveness of Newman’s slow-drift approximation and the WAMIT program will be illustrated by comparing some full-scaled measured and numerically hindcasted responses of Shell’s Mars Tension Leg Platform during hurricane Katrina [9].