Split‐Step Fourier Algorithm for Water Waves

Abstract

A parabolic model for propagation of water waves, implemented with an efficient split‐step Fourier transform algorithm, is presented. The split‐step Fourier transform algorithm, widely used in acoustics to solve the parabolic form of the Helmholtz equation and modified to approximately account for wave number dependency in the direction of propagation, has been successfully applied to model refraction and diffraction of water waves. The solution algorithm is exact for a constant depth ocean and gives a good approximation for a wave spectrum on a uniform slope. The results of the model for an elliptical shoal on a uniform slope are presented for both linear and nonlinear wave dispersion relationships and show good agreement with experimental results. The wide‐angle capabilities of the model are also examined for a circular shoal of elliptical cross section on a flat bottom. The algorithm is very efficient and stable, permitting large computational step sizes in the direction of propagation.