Numerical studies of eddy transport properties in eddy‐resolving and parametrized models

This paper is a study of the transport properties of large‐scale quasi‐geostrophic flow, when it is forced by an unstable shear of much greater horizontal scale than the scale of the resultant eddies. One of the purposes is thereby to test certain phenomenological parametrization schemes which predict the transport of potential vorticity or heat, or which predict the time‐mean state of the zonally averaged atmosphere. Models used are highly nonlinear spectral quasi‐geostrophic models, with sufficient resolution to resolve the energy‐containing scales and partially resolve an enstrophy inertial range. A scale separation is enforced between the mean and eddy flow, this being a necessary condition for transfer theories to work. An expression is derived for the rate of change of the mean flow in such cases. As a quantitative predictor of the time‐mean state of the zonal flow, baroclinic adjustment is found to work only when nonlinear wave‐wave interaction between eddies is small. In such cases, the amplitude of the eddy flow is determined by the forcing on the zonal flow, which itself equilibrates close to the critical value for linear instability. In fully nonlinear models if the zonal flow is strongly forced the mean flow can be highly supercritical. The flux of potential vorticity is found to depend strongly and monotonically on the mean shear, although no obvious simple relationship is found relating it to potential vorticity gradient. In part because potential vorticity is not a passive scalar, using phenomenological transfer coefficients is by no means straightforward. Such transfer relationships are seen to be in some ways unsatisfactory.