An unstructured C-grid based method for 3-D global ocean dynamics: Free-surface formulations and tidal test cases

Abstract

In an earlier work, we described how an unstructured grid numerical framework based on an energy-conserving Arakawa C-grid discretization could be applied to ocean general circulation models (OGCMs). We discuss herein how we adapted our previously published rigid-lid, hydrostatic, Boussinesq OGCM techniques to shallow-water and baroclinic free-surface dynamics. The simulation of the global M 2 tide is proposed as a useful benchmark for testing unstructured grid ocean models. Tidal simulations are much more manageable that full-fledged OGCM climate simulations, being based on simpler physical assumptions and parameterizations, and requiring less computation time per test. We demonstrate that the results of unstructured Arakawa C-grid simulations of the M 2 tide reproduce those of an equivalent regular grid discretization. Because unstructured grid methods carry a computational overhead, however, their use can only be justified where resolution must be concentrated in localized regions. The tides around Hudson’s Bay are well-described in a multi-scale context, and we show that strong discontinuities in mesh resolution do not appreciably distort the shallow-water tidal solution. Progressing to fully 3-D models, it is demonstrated that the barotropic M 2 tidal structure is consistently represented between models. Efforts to resolve the generation of baroclinic waves by the barotropic tide were, however, frustrated by the existence of a numerical mode that has been independently verified by other investigators working on similar methods. This presents a challenge for future work.