A dynamically consistent closure for zonally averaged ocean models
Simple idealized layered and primitive equation models are used to show that the meridional gradient of the zonally averaged pressure has no direct relation with the meridional flow and therefore contradicts an often used parametrization in zonally averaged models. The failure of these parametrizations reflects the inconsistency between the model of Stommel and
Arons (1960) and the box-model of Stommel (1961), which was previously pointed out by Straub (1996).
We have closed the system of the zonally averaged equations by dividing the
ocean into two dynamically different regimes, a narrow western boundary layer
and an interior ocean, and zonally averaged over these regions. Both, zonally resolved layer and a primitive equation model are used to validate
our parametrizations and to compare with the results of the zonally averaged
model. It turns out that the zonally averaged model produces well the
buoyancy distribution and meridional overturning stream functions in all
cases considered here, including time dependency.