Multiple scattering of surface water-waves and wave forces on cylinder arrays

The interactions between water waves and arrays of three-dimensional bodies are studied in the context of linearized potential flow. The bodies are vertical cylinders with an arbitrary cross section. These cylinders could be fully submerged, semi-submerged or fully extended throughout the water. Using the eigenfunction expansion method, the three-dimensional diffraction problem is reduced to a set of two-dimensional boundary value problems corresponding to propagation and evanescent models. An integral equation for each boundary value problem is found and solved numerically with appropriate boundary conditions. This method is, therefore, exact since the diffraction of evanescent modes are included. Numerical results for wave forces and moments are obtained for several examples. Good agreement between the exact three-dimensional numerical solutions and the present numerical results is achieved if two or more evanescernt modes are kept in the computations.