Efficient Nonhydrostatic Modeling of Surface Waves from Deep to Shallow Water

Abstract

An efficient nonhydrostatic model with the embedded Boussinesq-type like equations at the free surface is presented to simulate surface waves from shallow to deep water. The new free-surface treatment yields an accurate expression of vertical distribution of nonhydrostatic pressure. This approach is free of the irrotational flow assumption. Two locations of reference velocities obtained through interpolations of nonhydrostatic velocities are used to optimize frequency dispersion for a wide range of wave conditions. Accuracy and efficiency of the model is critically tested against analytical solutions and experimental data. Overall, the present nonhydrostatic model using a small number of vertical layers (i.e., 2–4) is capable of resolving dispersive wave motions with various effects.