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

Abstract. As global warming intensifies, mid-latitude regions increasingly experience unusual and disruptive weather phenomena, such as extreme heatwaves and devastating floods, posing significant threats to societies. The dynamics of the jet stream largely govern mid-latitude weather patterns, with fluid dynamical instabilities generating baroclinic waves that propagate through the atmosphere before breaking. These waves play a critical role in shaping regional weather by influencing the jet stream’s maintenance and inducing an indirect meridional circulation. Understanding how the life cycle of baroclinic waves maintains the zonal-mean zonal wind and the indirect circulation is essential for improving predictions of mid-latitude weather under global warming. This study introduces a simplified theoretical framework that provides analytic solutions for the steady-state zonal-mean zonal wind and the indirect circulation. By incorporating a parameterization of turbulent eddies into the zonal-mean quasi-geostrophic potential vorticity equation, the model establishes a balance that drives eddy-induced circulations in mid-latitudes, analogous to the Ferrel cell. The meridional temperature structure reveals two key features: (1) a linear decrease in anomalous potential temperature, producing westerly winds, and (2) jet streams generated by eddy momentum fluxes. These jet streams are accompanied by downward (upward) motions on their southern (northern) flanks, further characterizing the eddy-driven circulations. The intensity and extent of the Ferrel cell are found to be governed by the baroclinic wave life cycle, constrained by the meridional temperature gradient, static stability, and boundary conditions influenced by tropical forcing. Under global warming, projected changes in these factors will alter mid-latitude circulation patterns. The theoretical framework proposed in this study offers a robust basis for analyzing and predicting the evolving dynamics of mid-latitude circulations in a warming climate.