A parabolic equation based on a rational quadratic approximation for surface gravity wave propagation

Abstract

In this work, we are interested in the parabolic formulation of the propagation equation of surface gravity waves in terms of angular capability with respect to the privileged propagation direction. This parabolic formulation is obtained by splitting the Berkhoff equation operator into two parabolic operators representing progressive and reflected wave propagation. The use of the quadratic rational approximation permits to derive simultaneously parabolic equations for transmitted and reflected waves. Two well-known reference examples, which represent the propagation of surface gravity waves when a caustic occurs, will be studied numerically and results will be compared with those of the literature.