Diffraction and refraction calculations for waves incident on an island

An island of circular cylindrical shape, situated on a paraboloidal shoal (Fig. 1 and Table 1) in an infinite ocean of constant depth is attacked by small regular waves of long period and of plane incidence. The wave field around the island is calculated according to two different approaches, viz. a diffraction theory and a refraction theory (i.e. geometrical optics). The solutions are compared for those (tsunami) periods, where the Coriolis force can be neglected