Why do baroclinic eddies increase the temperature gradient?

In Earth's atmosphere, the full effect of baroclinic eddies is to increase the equatorward temperature gradient across the latitude of strongest eddy activity. This has significant implications for, among other things, how the extratropical atmosphere responds to ENSO.

In steady state and in the zonal mean, deviations of the temperature from radiative equilibrium are determined by the distribution of equatorward eddy fluxes of potential vorticity (Eliassen-Palm flux convergence). If the strongest EP-flux convergences are displaced sufficiently far poleward or equatorward from the strongest near-surface eddy generation, the transformed Eulerian mean circulation, which is poleward across the region of eddy absorption, features rising motion poleward, or sinking motion equatorward, of where the eddies are generated. This adiabatic cooling or warming is necessarily balanced by radiative heating or cooling, and the result is a strengthened temperature gradient across the latitudes of strongest eddy generation.

This arrangement is found in Earth's atmosphere and, over a wide range of parameters, in two very idealized representations of Earth's atmosphere: a two-level primitive equation model on the sphere and Panetta and Held's doubly periodic two-level quasigeostrophic model with a single zonal wave. In these systems, the enhanced-temperature-gradient state does not arise in the limit of very weak baroclinic instability, but occurs only when some threshold for the strength of baroclinic instability has been exceeded. There is a marked rearrangement of the circulation as this threshold is crossed that includes mutually reinforcing changes in the strengths and phase speeds of eddies, the strengths of the potential vorticity gradients, and the locations of critical lines.