A nonhydrostatic, isopycnal-coordinate ocean model for internal waves

Abstract

We present a nonhydrostatic ocean model with an isopycnal (density-following) vertical coordinate system. The primary motivation for the model is the proper treatment of nonhydrostatic dispersion and the formation of nonlinear internal solitary waves. The nonhydrostatic, isopycnal-coordinate formulation may be preferable to nonhydrostatic formulations in z- and σ-coordinates because it improves computational efficiency by reducing the number of vertical grid points and eliminates spurious diapycnal mixing and solitary-wave amplitude loss due to numerical diffusion of scalars. The model equations invoke a mild isopycnal-slope approximation to remove small metric terms associated with diffusion and nonhydrostatic pressure from the momentum equations and to reduce the pressure Poisson equation to a symmetric linear system. Avoiding this approximation requires a costlier inversion of a non-symmetric linear system. We demonstrate that the model is capable of simulating nonlinear internal solitary waves for simplified and physically-realistic ocean-scale problems with a reduced number of layers.