Diffusivity, Kinetic Energy Dissipation, and Closure Theories for the Poleward Eddy Heat Flux

Diffusive eddy closure theory for estimating the poleward heat flux is reexamined and tested in the context of a two-layer homogeneous model. Consideration of the inverse energy cascade induced by baroclinic turbulence on the b plane leads to an expression for diffusivity in terms of the kinetic energy dissipation and the b effect. A key step in the closure is the identification of this diffusivity with that for potential vorticity in the lower of the two layers in the model. This assumption is then combined with an exact expression relating the diffusivity to the baroclinic energy generation and the mean vertical shear. The theory is closed by identifying the kinetic energy dissipation entering the inverse cascade argument with the baroclinic energy production. It is found that the first constraint in isolation based on inverse cascade arguments between the diffusivity of lower-layer potential vorticity and the kinetic energy dissipation is robust and accurate, whereas the final theory relating diffusivity to vertical shear remains useful but has somewhat degraded accuracy and is more sensitive to model parameters, such as numerical resolution and small-scale dissipation. In the limit of large supercriticality, this theory reduces to that of Held and Larichev. However, it is much more accurate in reproducing numerical results from a twolayer homogeneous model on a b plane for the moderate supercriticalities that are typical of model atmospheres. The problems involved in generalizing this result to models with more layers on the vertical or with a continuous stratification are discussed.