A Numerical Model for Refraction of Linear and Cnoidal Waves

Abstract

A numerical model for refraction of linear and cnoidal waves over an arbitrary bottom is presented. The model, which is based on the ray theory of refraction (11), utilizes linear theory in deep and intermediate water and cnoidal theory in shallow water. The model permits one to determine nearshore wave properties using a nonlinear wave theory. Nearshore wave properties such as wave height, celerity, and wave angle determined using the linear-cnoidal refraction model may vary considerably from those determined using a linear refraction model. In general, cnoidal waves refract less, travel faster, and shoal higher than linear waves. This result can have a considerable effect on coastal engineering design, particularly in the areas of coastal structure design and longshore transport computations.