Linear hydrodynamic modelling of arrays of submerged oscillating cylinders

The radiation and diffraction problems for an array of submerged circular cylinders with vertical axes of revolution are formulated exactly to first order in the frequency domain. Matched eigenfunction expansions and a transform matrix method are used to solve the scattering problem for an arbitrary array using a truncated system of matrix equations. For a single shallowly submerged cylinder, the model is used to characterise the occurrence of resonances in the region of fluid above the cylinder moving in heave and surge motion. The method is then applied to a square array of four cylinders, and the effect of array interactions demonstrated. It is found that fluid resonances above the cylinder are still important, but are modified by multiple scattering. Finally, the mean vertical drift force is calculated from the first order solution by direct pressure integration over the body surface.