A dynamically consistent closure for zonally averaged ocean models

Abstract

Simple idealized layered models and primitive equation models show that the meridional gradient of the zonally averaged pressure has no direct relation with the meridional flow. This demonstrates a contradiction in an often-used parameterization in zonally averaged models. The failure of this parameterization reflects the inconsistency between the model of Stommel and Arons and the box model of Stommel, as previously pointed out by Straub. A new closure is proposed. The ocean is divided in two dynamically different regimes: a narrow western boundary layer and an interior ocean; zonally averaged quantities over these regions are considered. In the averaged equations three unknowns appear: the interior zonal pressure difference Δp i, the zonal pressure difference Δp b of the boundary layer, and the zonal velocity u δ at the interface between the two regions. Here Dpi is parameterized using a frictionless vorticity balance, Δp b by the difference of the mean pressure in the interior and western boundary, and ud by the mean zonal velocity of the western boundary layer. Zonally resolved models, a layer model, and a primitive equation model validate the new parameterization by comparing with the respective zonally averaged counterparts. It turns out that the zonally averaged models reproduce well the buoyancy distribution and the meridional flow in the zonally resolved model versions with respect to the mean and time changes. © 2011 American Meteorological Society.