Internal waves are a prominent coastal process. They often appear as a rank-ordered train of solitary waves whose shape is a balance between nonlinearity and dispersion. The major challenge to numerical simulation of internal waves is resolving dispersion, which requires both a nonhydrostatic model and high horizontal grid resolution. These challenges suggest that a nonhydrostatic isopycnal coordinate model may provide an excellent framework to the problem at hand. Here we present the formulation and testing of a nonhydrostatic isopycnal coordinate model that is designed specifically for simulations of internal waves. The numerical method still requires the solution of an elliptic equation for the dynamic pressure (as traditional nonhydrostatic models do) which increases the computational effort. However, the isopycnal approach gains efficiency by reducing the required number of vertical grid points from O(100) grid points in traditional ocean models to O(1) grid points. Ideally, in locations where the internal wave structure is predominantly mode-1, an isopycnal model with only two layers may suffice. We demonstrate that the new model is capable of resolving nonhydrostatic dispersion and internal solitary waves in idealized cases.
