Propagation of short gravity waves in shoaling waters: Refraction and diffraction

In this report,a description is given of some approximation methods, to solve the problem of short wave propagation in shoaling water. The problem is stated as an elliptic initial value problem, which is in general not properly posed. After reduction of the wave equation to the Helmholtz equation, the transition to amplitude and phase is investigated, in particular at singular points. Perturbation theory is applied, by introducing expansions in powers of a small parameter. Three approximation methods have been compared : 1) the phase-integral method, including the geometrical optics approximation as a special case, 2) Rytov's method, 3) a modification of Rytov's method