An investigation of two-dimensional wave propagation problems

The methods used in practice for computing wave-propagation are mainly based on two theories. The first one describes the refraction of waves in case of variable depth. The determination of this effect is based on the assumption that a wave locally behaves as a straight-crested wave of constant amplitude. Because of this the celerity is dependent on the depth only, which leads to the Snell's law for a medium of variable density. This theory finds its application in the ray-method. This in fact is the practical adaption of Fermat's principle. The second theory treats the diffraction-effect and describes the two-dimensional wave propagation in case of constant depth. The result of this theory is e.g. described by Sommerfeld's solution for the case of a semi-infinite break-water. It is well-known that both theories cannot be applied simultaneously. So using the ray-method, one evidently neglects the diffraction-effect. As a result of this, errors may be introduced, e.g. singularities may occur behind submarine canyons and shoals, where neighbouring rays intersect. This problem of course is not restricted to waterwaves only (7,13). Schönfeld has recently developed a theory in which both the refraction- and diffraction-effects are included. In order to use this theory in the investigation of crossing rays the result of this theory will be approximated numerically and the issue will be checked in a laboratory model. To be able to make comparison. Numerals in parentheses refer to items in reference list with the ray-method-singularities, a model has been chosen in such a way that these singularities do occur.VloeistofmechanicaHydraulic EngineeringCivil Engineering and Geoscience