Mean meridional circulation driven by eddy forcings of different timescales

In this paper, the mean meridional circulation (MMC) forced by eddy fluxes of heat and momentum is examined using a simple quasigeostrophic, two-level model of the zonal-mean atmosphere. Analytic solutions have been obtained, which show that analyses of the eddy-induced MMC using the Kuo-Eliassen equation are most appropriate for high-frequency fluctuations. For steady-state or low-frequency fluctuations, the eddy fluxes will lead to changes in the zonal-mean zonal wind and temperature. These changes in the zonal-mean state will induce changes in frictional dissipation and diabatic heating, which (together with the eddy fluxes) are constrained to satisfy a generalization of the Eliassen-Palm theorem and will also act as source terms to the Kuo-Eliassen equation. The inclusion of these induced terms usually leads to a significant enhancement in the diagnosed intensity of the MMC. This can explain why previous studies of the MMC found a much weaker eddy-induced Ferrel cell than that observed when the induced frictional and diabatic heating terms were left out and the eddy fluxes only were used as source terms. The relevant timescale separating the high- and low-frequency limits is found to be the radiative timescale in the model.