Affiliation: College of Arts and Sciences, Department of Physics and Astronomy
A computational framework for the evolution of non-hydrostatic, baroclinic flows encountered in regional and coastal ocean simulations is presented, which combines the flexibility of Adaptive Mesh Refinement (AMR) with a suite of numerical tools specifically developed to deal with the high degree of anisotropy of oceanic flows and their attendant numerical challenges. This framework introduces a semi-implicit update of the terms that give rise to buoyancy oscillations, which permits a stable integration of the Navier-Stokes equations when a background density stratification is present. The lepticity of each grid in the AMR hierarchy, which serves as a useful metric for anisotropy, is used to select one of several different efficient Poisson-solving techniques. In this way, we compute the pressure over the entire set of AMR grids without resorting to the hydrostatic approximation, which can degrade the structure of internal waves whose dynamics may have large-scale significance. We apply the modeling framework to three test cases, for which numerical or analytical solutions are known that can be used to benchmark the results. In all the cases considered, the model achieves an excellent degree of congruence with the benchmark, while at the same time achieving a substantial reduction of the computational resources needed.