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.