  The baroclinic annular mode (BAM) is a leading-order mode of the eddy-kinetic
energy in the Southern Hemisphere exhibiting. oscillatory behavior at
intra-seasonal time scales. The oscillation mechanism has been linked to
transient eddy-mean flow interactions that remain poorly understood. Here we
demonstrate that the finite memory effect in eddy-heat flux dependence on the
large-scale flow can explain the origin of the BAM's oscillatory behavior. We
represent the eddy memory effect by a delayed integral kernel that leads to a
generalized Langevin equation for the planetary-scale heat equation. Using a
mathematical framework for the interactions between planetary and
synoptic-scale motions, we derive a reduced dynamical model of the BAM - a
stochastically-forced oscillator with a period proportional to the geometric
mean between the eddy-memory time scale and the diffusive eddy equilibration
timescale. Our model provides a formal justification for the previously
proposed phenomenological model of the BAM and could be used to explicitly
diagnose the memory kernel and improve our understanding of transient eddy-mean
flow interactions in the atmosphere.

Atmospheric and Oceanic Physics