An idealized model for the spatial structure of the eddy-driven Ferrel cell in mid-latitudes

Conceptual models of the midlatitude atmospheric circulation have added greatly to understanding its behavior. Here,  we present a new conceptual model for the spatial structure of the Ferrel cell. The poleward heat flux resulting from the baroclinic growth of eddies leads to a decrease in the meridional temperature gradient, which is parameterized through a down-gradient eddy diffusion coefficient D. Similarly, the eddy momentum flux, influenced by barotropic wave breaking, is assumed to be proportional to a factor M>0 to the horizontal shear of the zonal mean zonal wind, 
thereby enhancing the intensity of the zonal mean zonal wind at upper levels. By incorporating the parameterization of turbulent eddies into the zonal-mean quasi-geostrophic potential vorticity equation, a balance is achieved, resulting in eddy-driven circulations in mid-latitudes akin to the Ferrel cell. 
The meridional structure of the temperature exhibits two primary features. The first feature is a linear decline in anomalous potential temperature, 
inducing westerly winds in mid-latitudes. The second feature corresponds to jet streams generated by eddy momentum fluxes. Along with the jet streams, the eddy driven circulations exhibit the downward (upward) motion at the southern (northern) flank of the jets. The meridional structure of the circulation is influenced by three key factors. The first factor is a structural number denoted as D/SM, where S is the dry static stability affecting the life cycle of synoptic eddies in mid-latitudes. The second factor relates to the planetary size and the third factor is the vertical structure of the atmosphere, associated with eigenvalues of the vertical mode in the heat equation. The combination of these three factors within the characteristic equation also
determines the location and number of eddy-driven jets in mid-latitudes.