Hydrodynamic loads on offshore structures in bichromatic bidirectional seas

A complete second-order solution is given for the hydrodynamic loads on ocean structures in bichromatic, bidirectional waves. The solution to the first-order problem is obtained utilizing a Green's function approach using higher order boundary elements. The second-order hydrodynamic loads explicitly due to the second-order potential components are computed using the indirect, assisting radiation potential approach. An efficient numerical technique, that accounts for the directionality of the waves, is presented to treat the free-surface integral which appears in the second-order load formulation. Numerical results are presented which illustrate the sensitivity to wave directionality of the second-order sum- and difference-frequency hydrodynamic loads on example structures. In particular, arrays of bottom-mounted, surface piercing cylinders and tension-leg platforms are considered. It is found that wave directionality may have a significant influence on the second-order hydrodynamic loads on these structures at both sum- and difference-frequencies and that the assumption of unidirectional waves does not always lead to conservative estimates of the second-order loading.