Parameterization of Directional Spectra and Its Influence on Ship Motion Predictions

Abstract

An approach to parameterizing directional spectra proposed by Hogben & Cobb based on a combination of the Ochi & Hubble 6-parameter spectrum and the Longuet-Higgins et al cos2p model is adopted for a study of directional parameterizations and their influence on ship motion predictions. Two schemes for evaluating the directional spreading parameters are assessed in terms of their ability to reproduce highly resolved measured directional spectra, and the best approach, termed the 10-parameter spectrum, is adopted. The applicability of the 10-parameter spectrum to hindcast spectra is investigated, and acceptable fits obtained for 93% of the spectra considered. An evaluation of the ability of the hindcast model to reproduce the measured spectral data is also made. In general, it is found that the differences between the hindcast spectra and associated 10-parameter fits are significantly smaller than the differences between the hindcast spectra and the field data, and it is concluded that the 10-parameter spectrum is a suitable basis for developing statistical descriptions of directional wave climates. The effects of directional parameterization on ship motion predictions are investigated by computing the ship responses as a function of heading for sample hindcast spectra, and the associated 10-parameter and Bretschneider 2-parameter spectra. The responses calculated using the 10-parameter spectrum are found to be in better agreement with the hindcast results than those obtained with the Bretschneider 2-parameter spectrum, with a significant improvement in modeling accuracy in the case of bi-modal spectra. The potential advantages of incorporating the 10-parameter spectrum in future operability analyses of flight operations is examined by comparing the head-to-wind roll response computed using hindcast spectra with that predicted using 10-parameter and Bretschneider spectra.