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Convergence studies with the Sandia Ocean modeling system
Author(s) -
Dietrich David E.,
Roache Patrick J.,
Marietta Mel G.
Publication year - 1990
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650110202
Subject(s) - baroclinity , barotropic fluid , dissipation , hydrostatic equilibrium , convergence (economics) , geophysical fluid dynamics , mechanics , computation , vorticity , ocean gyre , instability , physics , geology , mathematics , vortex , thermodynamics , algorithm , subtropics , quantum mechanics , fishery , biology , economics , economic growth
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 10 7 , 10 6 , and 10 5 cm 2 s −1 . Using 10 7 cm 2 s −1 diffusivities causes substantial damping of the dominant instabilities during the 30‐day integrations performed, but using 10 6 cm 2 s −1 results in little damping and yields results very close to those using 10 5 cm 2 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.