Water-wave diffraction and radiation by multiple three-dimensional bodies over a mild-slope bottom

In this article, a method to model wave diffraction and radiation by bodies of arbitrary shape over a variable bathymetry is developed. The effect of the bottom on the waves is modelled through the elliptic mild-slope equation, while the effect of the bodies through so-called diffraction transfer matrices. The numerical treatment proposed to solve the mild-slope equation is based on a finite-element discretisation of the fluid domain outside the bodies, while these are replaced by vertical surfaces over which analytical solutions exist. The solutions are then combined with diffraction transfer matrices to develop the required boundary conditions at the bodies. Full reflection and Sommerfeld's radiation condition at sea, where the water depth is assumed constant, are taken into account to fully determine the numerical solution. The method is further verified against exact solutions to the problem of tsunami response of a cylindrical island over a parabolic shoal, and the problem of wave diffraction by an array of truncated vertical cylinders over a flat bottom. Comparison between exact and present method wave amplitude solutions for the two problems show good agreement. Finally, the effects of a submarine plateau and a fully reflective coast on the wave diffraction and radiation by an array of surging barges are discussed.