Mean and low frequency wave drifting forces on floating structures

A recently developed method, based on three-dimensional potential theory, to compute the mean wave drifting forces on a free floating structure in regular waves, is extended to include low frequency oscillatory components which arise when the structure is floating in regular wave groups consisting of two regular waves with small difference frequency. This completes the information necessary for the determination of the wave drifting forces under arbitrary irregular wave conditions.In regular wave groups the drifting forces not only depend on the first order velocity potential and the first body motions, but also on the wave exciting forces due to the low frequency part of the second order potential. For the general three-dimensional case the latter contribution can only be determined numerically and at the expense of long computation times. Since this contribution is generally not large compared to components which may be determined using linear potential theory it is included using a simple approximation. Results of the method of approximation are compared with some two-dimensional cases for which exact solutions are known.Results of computations of the total mean and low frequency surge forces on a rectangular barge and a column stabilized semi-submersible platform are presented. For both structures, the computed mean surge drifting forces in regular head waves are compared with results of model tests.The computed components of the total mean drifting forces are presented. It appears that for both the barge and the semi-submersible the same components are of importance.For the semi-submersible, the computed low frequency second order surge forces in head waves are compared with results obtained from a test in irregular head waves using cross-bispectral analysis methods.