Water-wave scattering by a semi-infinite periodic array of arbitrary bodies

Abstract

We consider the scattering by a semi-infinite array of bodies of arbitrary geometry excited by an incident wave in the linear water-wave formulation (which reduces to the simpler case of Helmholtz scattering if the depth dependence can be removed). The theory presented here is extremely general, and we present example calculations for an array of floating elastic plates (a highly non-trivial scatterer). The solution method follows closely from the solution for point scatterers in a medium governed by Helmholtz's equation. We have made several extensions to this theory, considering water-wave scattering, allowing for bodies of arbitrary scattering geometry and showing how to include the effects of bound waves (called Rayleigh–Bloch waves in the water-wave context) in the formulation. We present results for scattering by arrays of cylinders that show the convergence of our methods and also some results for the case of scattering by floating elastic plates and fixed docks.