The response of the atmospheric circulation to greenhouse gas-induced SST warming is investigated using large ensemble experiments with two AGCMs, with a focus on the robust feature of the poleward shift of the eddy driven jet. In these experiments, large ensembles of simulations are conducted by abruptly switching the SST forcing on from January 1st to focus on the wintertime circulation adjustment. A hybrid, finite amplitude wave activity budget analysis is performed to elucidate the nonlinear and irreversible aspects of the eddy-mean flow interaction during the adjustment of the zonal wind towards a poleward shifted state. The results confirm the results from earlier more idealized studies, particularly the importance of reduced dissipation of wave activity, in which the midlatitude decrease of effective diffusivity appears to be dominant. This reduction in dissipation increases the survival of midlatitude waves. These surviving waves, when reaching the upper propagation level in the upper troposphere, are subject to the influence of the increase of reflection phase speed at the poleward side of the mean jet, and thus more waves are reflected equatorward across the jet, giving rise to a poleward transport of momentum and thus an eddy momentum flux convergence for the poleward shift. The relative importance of wave breaking-induced PV mixing versus diabatic PV source in the evolution of the Lagrangian PV gradient is also investigated. The former plays the dominant role in the PV gradient formation during the initial phase of the jet shift, while the latter actually opposes the evolution of the Lagrangian PV gradient at times.