Formulation of an unstructured grid model for global ocean dynamics

A conservative discretization of the ocean primitive equations for global ocean dynamics is formulated on an unstructured grid. The grid consists of triangular cells with a C-type staggering of variables, where scalar variables are located at centers of grid cells and normal components of velocity are placed at cell boundaries. Reconstructions, necessitated by the staggering of variables, are chosen from a set of admissible reconstructions such that the discrete equations obey a weighted weak form, which guarantees discrete conservation properties. At the same time a spurious mode, specific to the triangular C-grid, is controlled in a way that is compatible with conservation properties. The conservation properties of the discrete model are verified. Numerical simulations are presented, ranging from idealized geophysical flows to an ocean simulation at eddy-permitting resolution, in order to substantiate the statement that global ocean dynamics can be formulated on triangular C-grids.