Convergence studies with the Sandia Ocean modeling system

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Abstract
Five numerical schemes are compared using convergence studies in the framework of the hydrostatic Sandia Ocean Modeling System (SOMS). Three resolutions are used, 40, 20 and 10 km, with respectively three, seven and 15 layers and time steps of 60, 30 and 15 min, so 15 convergence calculations are performed. The same geophysical prototype problem (exhibiting baroclinic instability in a statically stable environment) is used for all calculations.All five schemes are second‐order‐accurate in space, but those using four‐point interpolations for the Coriolis and pressure gradient terms are shown to produce much more accurate results, with relatively little extra computation, than schemes using two‐point interpolations.Convergence is also indicated with decreasing horizontal diffusivities of 107, 106, and 105 cm2s−1. Using 107 cm2s−1 diffusivities causes substantial damping of the dominant instabilities during the 30‐day integrations performed, but using 106 cm2 s−1 results in little damping and yields results very close to those using 105 cm2 s−1.A barotropic (vertically averaged flow) cyclonic northern basin gyre is explained as a weakly forced circulation. Its equilibrium amplitude is determined by a balance between dissipation effects due to horizontal mixing and diffusion, and weak second‐order driving associated with thermodynamic forcing and vorticity dissipation at the basin bottom. It is thus quite sensitive to model dissipation but can be well described by SOMS owing to SOMS' low numerical dissipation.