Effect of wave-directionality on second-order loads induced by the set-down |
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Authors: | B. Molin V. Fauveau |
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Affiliation: | Institut Français du Pétrole, B.P. 311, 92506 Rueil-Malmaison, France |
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Abstract: | At first-order of approximation a sea-state may be considered as an infinite sum of Airy components with angular frequencies ωi and wave-number vectors ki. A second-order analysis shows the co-existence of long waves appearing at the difference frequencies ωi—ωj with wave-number vectors ki—kj. In shallow water they become appreciable in amplitudes and may induce slow-drift motion of moored structures.For small values of ωi—ωj,ki—kj may take all kinds of directions for an angular-spread wave system. Then it may be questioned how the in-line and transverse second-order accelerations compare to those obtained for a mono-directional wave-system.This analysis is carried out here by relating the spectra of the second-order horizontal accelerations to the directional wave-spectrum. Numerical applications are first performed for deep water. They show that at low frequencies, even for very narrowly spread wave systems, the transverse component is larger than the in-line component. In shallow water both components are dratically reduced as compared to the mono-directional case. As a consequence one may question the validity of model-testings or numerical models which take no account of the directionality of the wave-system. |
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Keywords: | wave directionality slow drift motion set-down |
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