Baroclinic instability and large-scale wave propagation in a planetary-scale atmosphere

Midlatitude atmospheric variability is dominated by the dynamics of the baroclinically unstable jet stream, which meanders and sheds eddies at the scale of the Rossby deformation radius. The eddies interact with each other and with the jet, affecting the variability on a wide range of scales, but the mechanisms of planetary-scale fluctuations of the jet are not well understood. Here, we develop a theoretical framework to explore the stability of planetary-scale motions in an idealized two-layer model of the atmosphere. The model is based on a combination of vertical shear and the Sverdrup relation, providing the dynamic link between the two layers, with meridional eddy heat fluxes parameterized as a diffusive process with the memory of past baroclinicity of the jet. We find that a planetary-scale instability exists if the vertical shear of the jet does not exceed a particular threshold. The inclusion of the eddy-memory effect enables westward or eastward propagation of planetary waves relative to the barotropic mean flow. Importantly, we find growing planetary waves that propagate slowly westward or are stationary, which could have important implications for the formation of atmospheric blocking events. Our theoretical results suggest that, with ongoing polar amplification due to global warming and the corresponding reduction of the vertical shear of the mean wind, the background conditions for the growth of planetary-scale waves via planetary-scale baroclinic instability are becoming more favorable.