  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.

Atmospheric and Oceanic Physics;Fluid Dynamics