  Eddy saturation describes the nonlinear mechanism in geophysical flows
whereby, when average conditions are considered, direct forcing of the zonal
flow increases the eddy kinetic energy, while the energy associated with the
zonal flow does not increase. Here we present a minimal baroclinic model that
exhibits complete eddy saturation. Starting from Phillips' classical
quasi-geostrophic two-level model on the beta channel of the mid-latitudes, we
derive a reduced order model comprising of six ordinary differential equations
including parameterised eddies. This model features two physically realisable
steady state solutions, one a purely zonal flow and one where, additionally,
finite eddy motions are present. As the baroclinic forcing in the form of
diabatic heating is increased, the zonal solution loses stability and the eddy
solution becomes attracting. After this bifurcation, the zonal components of
the solution are independent of the baroclinic forcing, and the excess of heat
in the low latitudes is efficiently transported northwards by finite eddies, in
the spirit of baroclinic adjustment.
