The motions of (LNG) vessels moored offshore at depths ranging from about 20 to 100 m may depend significantly on the presence of (bound) low-frequency waves with periods in the order of 100 s. This is because these moored vessels show a large motion response in this frequency range and because the energy contents of low-frequency waves at these 'intermediate' depths is relatively large. As part of the Joint Industry Project Hawal, the operational Boussinesq-type wave model of Deltares, TRITON, was used to investigate whether this type of wave models could predict bound low-frequency waves (setdown waves) at intermediate depths. Comparison to measured and theoretical data, however, showed an underestimation of the computed levels of bound low-frequency wave heights for this depth range by a factor 2 to 4. Recently, additional tests were made with TRITON in situations for which the model has been designed: coastal engineering applications in shallow water (depths up to at most 20 m). These also showed an underestimation of the bound low-frequency wave heights, albeit smaller, up to a factor 2. In view of the importance of the energy contained in the low-frequency range for certain nearshore and shoreline processes, such as morphological processes, this underestimation is also of concern in coastal engineering. This triggered the development of a higher-order extension of the TRITON model equations (Borsboom, 2008, Wellens, 2010), with the aim to improve the accuracy of the model for long waves while still keeping computational times within acceptable (operational) limits. This paper reports on the usefulness of the extended model for the field of application considered in JIP Hawal/II: providing wave data for calculating the motions of vessels moored in intermediate depths. The results show a significant improvement of the modeling of nonlinear wave dynamics, including the prediction of bound low-frequency waves. This means that the model extension is an important step towards an operational Boussinesq-type wave model with sufficient accuracy in both the wave-frequency (sea, swell) and the low-frequency range for applications in intermediate depths.
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