Water wave scattering by an array of rectangular breakwaters on a step bottom topography

Water wave scattering by an array of identical rectangular breakwaters is investigated in the presence of a heterogenous bottom boundary in the cases of both infinite and semi-infinite fluid domains. Boundary value problem is formulated by employing small amplitude water wave theory and is reduced to a system of linear algebraic equations using matching eigenfunction expansion method. These equations are solved numerically to perceive the complete solution of the problems under present interest. The reflection and transmission coefficients are computed in different modes, and the energy relation is used to check the accuracy of computed results. Effects of different parameters on the total reflected and transmitted wave energy are computed and analyzed. Further, the surface motion is computed to see the wave phenomena in the vicinity of the breakwaters. The unknown coefficients appearing in velocity potentials are estimated, the frequency of resonance mode is resolved, and resonance surface modes are plotted in the case of the semi infinite fluid domain. This study is useful for the breakwater designer to install breakwaters near an uneven bottom topography.