The Stability Properties and Energy Transformations of the Two-layer Model of Variable Static Stability

The design and performance of simple atmospheric models is briefly reviewed as an introduction to the question of energetic consistency. The two-layer model of Lorenz appears to be the simplest fully-consistent formulation, and the freedom of this model from the constraints upon the Coriolis parameter and static stability characteristic of the usual quasi-geostrophic models is felt to be particularly important. As a prelude to actual numerical integration, the baroclinic stability properties and the energy transformations of this two-layer model are examined. It is found that the perturbations are here significantly more unstable than when the static stability is constrained in the usual manner. For the finite-amplitude disturbances, it is found that some of their available potential energy is transferred to the mean state through the stabilizing action of the systematic rising of the warmer air. These results suggest that the variation of the static stability both promotes the growth of new disturbances and limits the growth of the mature disturbances-effects which would appear to remedy some of the conspicuous performance errors of the conventional two-level models.