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

The dynamics of the mid-latitude jet stream and the associated Ferrel cell are fundamentally governed by the life cycle of synoptic-scale baroclinic waves. While numerical simulations and reanalysis have long highlighted the role of turbulent eddy fluxes in regulating the zonal-mean flow, a closed analytical theory that captures the interplay between eddy parameterisation, diabatic forcing, and the resulting circulation remains a challenge. In this study, we derive analytic solutions for a steady-state mid-latitude circulation within a quasi-geostrophic framework on a β-plane. We employ two complementary parameterisation schemes to capture the diverse regimes of eddy-mean flow interaction. First, a downgradient potential vorticity (PV) flux framework demonstrates that the jet's morphology is highly sensitive to the spatial distribution of eddy diffusivity, Kq. We find that a “dual-regime” of mixing – characterised by high-diffusivity transfer zones adjacent to low-diffusivity “deposition” zones – is essential for generating a sharp, intense jet core and the characteristic PV staircase. Second, we investigate the self-maintenance of the jet by separately parameterising downgradient heat and upgradient momentum fluxes. This approach reveals that the jet can be sustained through an internal dynamical balance where Rossby wave breaking on the equatorward flank converges momentum to counteract the broadening effect of baroclinic heat transport. This study provides a physically transparent framework for scaling the Ferrel cell and understanding the emergence of jet structures from eddy-mean flow interactions.