DIFFRACTION OF GRAVITY WAVES BY LARGE ISLANDS

Abstract

The combined refraction and diffraction of long gravity water waves for certain depth variations around large islands is investigated analytically in a circular-symmetric geometry. Creeping waves are shown to exist for bottom profiles less convex than required by the trapping criterion due to Longuet-Higgins and Shen et al. From an asymptotic representation of the solution to the scattering problem the decay exponent and the diffraction coefficient is extracted. These "canonical" quantities may then be used for the construction of diffracted fields around smooth islands of more complex shape in accordance with J.B. Keller's Geometrical Theory of Diffraction.