Investigation of second-order low-frequency wave forces approximations for moored floating structures

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Floating structures are widely used in both shallow and deep waters in industries such as offshore oil, gas, and wind. However, the safety of floating structures subject to long-crested irregular waves is threatened by slowly varying wave drift forces. In this study, the mesh-convergence laws for a panel model, which is used to calculate second-order potentials using a near-field approach, are investigated using a semi-submersible platform as an example. The effect of the relative-wave-height component of low-frequency (LF) wave forces is sensitive to the mesh near the waterline; therefore, it should be fully refined. The key difference-frequency band of the quadratic transfer function (QTF) matrix is investigated using time-domain-coupled dynamic analysis with a truncated QTF matrix. The results show that a difference-frequency limit of 0.4 rad/s is sufficient to calculate the slow drift and mooring tension. Based on prior approximations of the second-order LF wave force, a new hybrid approximation method is proposed. The discrepancies between the approximations and the full-QTF method are investigated in the time domain. This shows that the approximations are greatly affected by the water depth and the spectral peak period. This is because shallow-water mooring systems are more rigid than deep-water mooring systems; thus, the structural response is strongly dependent on a wider difference frequency and the off-diagonal elements in the QTF matrix (with a bigger difference frequency), which contain more errors. In approximations, the mooring-tension error is more sensitive to the water depth than the slow drift owing to the effects of heave and pitch. If the maximum values of the drift offset and mooring tension are considered, the approximation without the free-surface integral and the proposed “WN + Newman” hybrid approximation are recommended for use in shallow water.