Adopting a recently developed theoretical framework of finite-amplitude wave activity (FAWA), we found a marked periodicity in the vertically integrated FAWA around 20-30 days in the reanalysis products and in a hierarchy of climate models. With the assumption that the interaction between eddies and the mean flow plays an important role in this periodic behavior, we develop a new theoretical framework of the eddy - mean flow interaction. It consists of three coupled equations for the interior and surface finite- amplitude wave activity (FAWA) and the barotropic zonal-mean zonal flow. The theory provides an accurate latitude-by-latitude description of atmospheric angular momentum - wave activity budget that captures the storm track dynamics.
In the mid-latitude austral summer, the wave activity budget reveals a largely adiabatic, antiphase covariation of FAWA and the mean flow. A marked periodicity is found for FAWA, but not for the mean flow. The former is primarily driven by the low-level meridional eddy heat flux, which also exhibits a sharp spectral peak around 25 days, whereas the latter is primarily driven by the meridional eddy momentum flux. The observed eddy heat flux cospectra in summer contain a few dominant frequencies for each of the energy-containing zonal wavenumbers (4-6). As these modes travel at different phase speeds they interfere with each other and produce an amplitude modulation to the eddy heat flux with a periodicity consistent with the BAM. The meridionally confined baroclinic zone in the mean state of the austral summer provides a waveguide that directs the mode propagation and interference along the latitude circle.
We demonstrates that the essence of the periodicity is reproduced in a hierarchy of numerical models including Community Earth System Model, an idealized dry GCM, and a two-layer quasigeostrophic model. A dry GCM reproduces qualitatively BAM-like eddy heat flux spectra if the zonal-mean state resembles that of the austral summer and if the surface thermal damping is sufficiently strong. As a baseline model, the two-layer quasigeostrophic model captures the gist of oscillation when baroclinicity is weak and the bottom layer is chosen sufficiently thinner than the top layer, which is physically equivalent to a strong low-level thermal damping. This is consistent with the observed strong thermal damping in the Southern Hemisphere storm track. Based on insights from the two-layer quasigeostrophic model, we show that several key parameters control the robustness of the periodicity in observations, and further we discuss how the robustness changes in a warming climate.