A σ‐coordinate non‐hydrostatic model with embedded Boussinesq‐type‐like equations for modeling deep‐water waves

Abstract

AbstractA σ‐coordinate non‐hydrostatic model, combined with the embedded Boussinesq‐type‐like equations, a reference velocity, and an adapted top‐layer control, is developed to study the evolution of deep‐water waves. The advantage of using the Boussinesq‐type‐like equations with the reference velocity is to provide an analytical‐based non‐hydrostatic pressure distribution at the top‐layer and to optimize wave dispersion property. The σ‐based non‐hydrostatic model naturally tackles the so‐called overshooting issue in the case of non‐linear steep waves. Efficiency and accuracy of this non‐hydrostatic model in terms of wave dispersion and nonlinearity are critically examined. Overall results show that the newly developed model using a few layers is capable of resolving the evolution of non‐linear deep‐water wave groups. Copyright © 2009 John Wiley & Sons, Ltd.