Abstract
An exact second-order theory is formulated for predicting the slow drift excitation forces on moored vessels in random seas. It is based upon direct integration of the hydrodynamic pressure on the submerged body surface in conjunction with the consistent perturbation expansion to second order in wave steepness. Green's second identity and Haskind's reciprocal relations are used to derive a formula for the second-order exciting forces due to the second-order waves. This permits the evaluation of the slow drift forces only from the solution to the first-order diffraction problem. As application of the theory, results for the slow drift forces on the semi-submersible are presented, which are evaluated by means of the source-distribution numerical technique. The results based on the present exact theory are compared with the solutions from different simplified approaches. It is concluded that Newman's method using data of mean drift forces in regular waves gives accurate results for the slow drift forces in short to moderate seas, but tends to underestimate the forces in extreme sea states with longer mean wave period.
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