Comparison of Thermally Driven Circulations from a Depth-Coordinate Model and an Isopycnal-Layer Model. Part I: Scaling-Law Sensitivity to Vertical Diffusivity
Two different types of numerical ocean circulation models are used in a classical idealized problem, the thermally induced circulation in an ocean basin bounded by two meridians to the east and west and by the equator and a line of constant latitude. A simple scaling theory exists for predicting poleward heat transport and the strength of meridional overturning as a function of vertical diffusivity and other external factors. However, previous studies have indicated conflicting results, and other scaling laws have been proposed. Experiments with two widely used types of numerical models, one based on depth coordinates and the other based on isopycnal layers, provide insight into the discrepancies of previous studies. In the numerical experiments vertical diffusivity is varied over a range of 200. The source of the difficulty in previous studies is in part traced to applying a fixed restoring coefficient at the upper boundary and considering the buoyancy forcing at the surface fixed irrespective of vertical diffusivity κ. Globally or zonally averaged results show a robust agreement between the two models and support the simple scaling law in a flat-bottom basin and a bowl-shaped basin, as long as the meridional circulation is estimated along isopycnal surfaces and in situ rather than externally imposed restoring density differences are used to estimate the geostrophic-scale velocity. Over the thermocline the vertical mean of the zonally averaged zonal baroclinic pressure gradient has constant ratio to the vertical mean of the zonally averaged meridional baroclinic pressure gradient, consistent with the scaling assumptions for a diffusive thermocline.