An unstructured grid, nonhydrostatic, generalized vertical coordinate ocean model

TL;DR

This paper introduces a flexible unstructured grid ocean model with a generalized vertical coordinate system that can adaptively represent various vertical coordinate types, improving simulation accuracy and efficiency for nonhydrostatic flows.

Contribution

It develops a novel GVC framework integrated into the SUNTANS model, enabling flexible vertical coordinate choices and adaptive layering for nonhydrostatic ocean simulations.

Findings

Successfully simulates nonhydrostatic internal solitary waves with isopycnal coordinates.

Demonstrates improved accuracy using adaptive vertical coordinates in lock-exchange tests.

Maintains conservation of mass, heat, and volume in the numerical scheme.

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.