Wave-structure interactions in harbors of arbitrary geometry

Multi-dimensional boundary element methods were developed to investigate the hydrodynamic responses of free floating and moored offshore structures in open-sea and in harbors of arbitrary geometry. The diffraction and radiation boundary value problems are presented with a distribution of singularities on the submerged surface of the offshore structure and on the harbor boundary. John's Green's function is used to represent the singularities at a field point due to an oscillating source of unit strength at a source point. The strengths of the singularities are determined by the boundary conditions.; The domain of interest is divided into three regions: the semi-infinite ocean (Region I), the basin excluding the vicinity of the floating body (Region II), and the region around the floating body (Region III). Potential functions in Regions I and II are calculated with line integrals, and that in Region III are computed with surface integrals. Final solutions are obtained by matching potential functions and their normal derivatives at two matching boundaries: one is the imaginary harbor entrance, and the other one is the boarder of Regions II and III. The deformed incoming wave potential and its normal derivative in the harbor are calculated by the Weber's solution of the Helmholtz equation to reflect the genuine incident wave potential.; It is found that: (1) the hydrodynamic responses of an offshore structure in a harbor are considerably different from that in open-sea; (2) the shape of the matching boundary between Regions II and III does not contribute a significant difference in hydrodynamic loading on offshore structures; (3) larger Region III generates more accurate hydrodynamic forces; (4) the accuracy of the calculated hydrodynamic responses increases as the offshore structure is moored farther away from the harbor boundary; (5) the mooring does not necessary reduce the hydrodynamic responses of a floating body in a harbor; (6) the hydrodynamic responses of a moored floating body in a rectangular basin are greatest near the harbor entrance: oscillations are reduced as the floating body is moored away from the harbor entrance; and (7) the mesh size with one-eighth of shortest wavelength is adequate in the numerical computation.