Model for Refraction of Water Waves

A simple explicit numerical model suitable for a personal computer is discussed that provides for the refraction and shoaling of linear and nonlinear water waves over irregular bathymetry, including wave‐current interaction. Finite‐differenced forms of the conservation of wave action and the irrotationality of the wave number equations are used in the model. Applications of the model to a planar shoreline, where Snell's law is valid, show that the model results are independent of the step size. Two other bathymetries are examined: one, an idealized coastline with a rip channel; and the other, a section of the New Jersey coastline. The model output is displayed in terms of wave height and direction vectors.