I summarize a series of works in which, together with a number of colleagues, I have tried to understand how the eddy fluxes of heat and potential vorticity are constrained in this statistically steady state. Central to this work is the relationship between inhomogeneous jet-like flows of atmospheric interest and homogeneous geostrophic turbulence, and the related question of whether theories for the eddy fluxes are fundamentally local or global. I argue that the homogeneous turbulence limit is very relevant to this problem. In the homogeneous limit, eddy length scales are typically determined by the Rhine's scale, rather than the radius of deformation, and this provides a central ingredient in a scaling theory for the eddy fluxes that closely mimics the results of numerical simulations.
The two-layer model is easily criticized for distorting linear baroclinic instability, as compared to that in models with continuous stratification, in particular by artificially creating a critical shear for instability that is proportional to the depth of the lower layer. An argument will be presented that the two-layer model may be a better model of strongly nonlinear statistically steady flows than of linear instability.