Approximation of Second-Order Low-Frequency Wave Loading in Multi-Directional Waves

Further to the studies by Chen & Rezende (OMAE2009) on the quadratic transfer function (QTF) of low-frequency wave loading in which the QTF is developed by the series expansion associated with the difference-frequency up to the order-Δω², new formulations have been developed in order to take into account the effect of interactions between waves of different headings. It provides a novel method to evaluate the low-frequency second-order wave loads in a more accurate than usual order-Δω approximation (often called Newman approximation) and more efficient way comparing to the computation of complete QTF in multi-directional waves. New developments including numerical results of different components of QTF are presented here. Furthermore, the time-series reconstruction of excitation loads by quadruple sums in the motion simulation of mooring systems is analyzed and a new efficient and accurate scheme using only a triple sum is demonstrated.