An unstructured grid, nonhydrostatic, generalized vertical coordinate ocean model

Abstract

We present a method to simulate nonhydrostatic ocean flows on a horizontally-unstructured grid with a moving generalized vertical coordinate (GVC). The nonhydrostatic governing equations are transformed to a GVC system that can represent the well-known z-level, terrain-following, or isopycnal coordinates while also being able to employ a vertically-adaptive coordinate using r-adaptivity. Different vertical coordinates are accommodated with the arbitrary Lagrangian-Eulerian (ALE) approach in which the vertical coordinate lines translate vertically, and the layer heights are made consistent with the vertical grid velocities through a discrete layer-height equation. Vertical grid velocities are also accounted for in the discrete momentum and scalar trans-port equations. While momentum is approximately conserved, the mass, heat, and volume are conserved both locally and globally. The nonhydrostatic pressure is implemented using a pressure-correction method that enforces the transformed continuity equation. The proposed GVC framework is implemented in the SUNTANS (Fringer et al., 2006) ocean model. Non-hydrostatic internal solitary-like waves are simulated to demonstrate that isopycnal coordinates can represent similar dynamics as z-levels at a fraction of the computational cost. The nonhydrostatic lock-exchange is then simulated to demonstrate that adaptive vertical coordinates can improve the accuracy of the model by concentrating more grid layers in regions of higher vertical density gradients.