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

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 M2M2 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 M2M2 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 M2M2 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.