Overview
A methodology has been developed for simulating nonhydrostatic ocean flows, employing a horizontally-unstructured grid alongside a moving generalized vertical coordinate (GVC). This GVC system is designed to encompass established coordinate types such as z-level, terrain-following, and isopycnal coordinates, while also integrating a vertically-adaptive coordinate utilizing r-adaptivity. The framework implements the nonhydrostatic governing equations, transformed into the GVC system.
Research Context
Ocean modeling frequently requires the simulation of complex flow dynamics, including nonhydrostatic phenomena, across varied spatial scales and bathymetries. The choice of vertical coordinate system can significantly influence both the accuracy and computational efficiency of these simulations. Traditional methods often rely on fixed vertical coordinates or struggle with adaptive capabilities in nonhydrostatic contexts.
Approach
The core of the methodology involves transforming the nonhydrostatic governing equations into a GVC system. This system allows for the representation of different vertical coordinates through an arbitrary Lagrangian-Eulerian (ALE) approach. Within this ALE framework, vertical coordinate lines undergo vertical translation, and layer heights are synchronized with vertical grid velocities via a discrete layer-height equation. Vertical grid velocities are also incorporated into the discrete momentum and scalar transport equations.
Key conservation properties are maintained:
- Momentum is approximately conserved.
- Mass, heat, and volume are conserved both locally and globally.
The nonhydrostatic pressure component is managed using a pressure-correction method. This method enforces the transformed continuity equation within the model. The developed GVC framework has been integrated into the SUNTANS ocean model (Fringer et al., 2006).
Findings
Two primary simulations were conducted to demonstrate the capabilities of the model:
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Nonhydrostatic Internal Solitary-like Waves Simulation
Simulations of nonhydrostatic internal solitary-like waves indicated that isopycnal coordinates are capable of representing dynamics similar to those captured by z-level coordinates. A notable finding from this simulation was that the use of isopycnal coordinates achieved this representation at a fraction of the computational cost associated with z-level coordinates.
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Nonhydrostatic Lock-Exchange Simulation
A nonhydrostatic lock-exchange simulation was performed. This demonstrated that adaptive vertical coordinates can enhance the accuracy of the model. This improvement was attributed to the ability of adaptive coordinates to concentrate a greater number of grid layers in regions characterized by higher vertical density gradients.
Why This Matters
The described methodology offers a flexible and potentially efficient approach to simulating nonhydrostatic ocean flows. Its ability to utilize various vertical coordinates, including adaptive ones, along with demonstrating computational efficiency for specific wave phenomena and improved accuracy in density-stratified regions, could impact the precision and resource demands of oceanographic modeling efforts.