A unified coupled-mode method for wave scattering by rectangular-shaped objects

This paper presents a general solution for wave scattering by stationary objects, which consist of a submerged rectangular plate and a floating rectangular dock. These objects have the same width and their centerlines are aligned. The objects can be either permeable or solid. Within the framework of linear potential flow theory, the method of eigenfunction expansion is adopted to solve the wave scattering problem. Two auxiliary potentials are introduced in each flow regions to facilitate the eigenfunction expansions. This approach avoids solving a complex dispersion relation. A computing program has been developed based on the present general solutions. The numerical model is checked with existing solutions for single rectangular object, such as a surface-piercing permeable breakwater, a bottom mounted submerged permeable or solid breakwater and a submerged permeable plate. Perfect agreements between the present solutions for the general model and the existing solutions are observed. The general model can also yield new solutions for different combinations of objects, e.g.,a single floating permeable breakwater, and a combination of a floating and a bottom mounted permeable or solid breakwater.