Feldstein, S. B., 1994: A weakly nonlinear primitive equation baroclinic life cycle. J. Atmos. Sci., 51, 23-34.
A weakly nonlinear baroclinic life cycle is examined with a spherical, multilevel, primitive equation model. The structure of the initial zonal jet is chosen so that the disturbance grows very slowly, that is, linear growth rate less than 0.1 per day, and the life cycles of the disturbance are characterized by baroclinic growth and followed by barotropic decay. It is found that if the disturbance grows sufficiently slowly, the decay is baroclinic. As a result, the procedure for determining this weakly nonlinear jet is rather delicate.
The evolution of the disturbance is examined with Eliassen-Palm flux diagrams, which illustrate that the disturbance is bounded at all times by its critical surface in the model's middle and upper troposphere. The disturbance undergoes two large baroclinic growth/barotropic decay life cycles, after which it decays by horizontal diffusion. At the end of the first cycle, the zonally averaged zonal flow is linearly stable, suggesting that the disturbance growth during the second cycle may have arisen through nonmodal instability. This stabilization of the disturbance is due to an increase in the horizontal shear of the zonal wind, that is, the barotropic governor mechanism. It is argued that this stabilization is due to the large number of model levels.
A quasigeostrophic refractive index is used to interpret the result that as the linear growth rate of the disturbance is lowered, the ratio of equatorward to poleward wave activity propagation decreases. A parameter is defined as the ratio of the horizontal zonal wind shear to the Eady growth rate. It is found that the growing disturbance tends to be confined to regions of local minima of this parameter.