Linear baroclinic instability of an eddy-free reference state atmosphere

Normal-mode stability analysis of parallel flows is one of most thoroughly studied subjects in geophysical fluid dynamics, yet its application to the atmosphere has some fundamental conceptual difficulties. One such difficulty is that the zonal-mean time-mean flow is already modified by finite-amplitude eddies so its linear (small-amplitude) stability has to be interpreted with care: if anything, the flow is likely close to neutral at the scale of most energetic eddies, assuming that ‘baroclinic adjustment' has already taken place. This can lead to a conclusion that (normal-mode) baroclinic instability is of little relevance to the atmosphere. However, it is our opinion that linear stability analysis should be applied to an eddy-free state to truly gauge the importance of baroclinic instability. For this reason, we construct an eddy-free reference atmosphere by ‘unwrapping' the observed potential vorticity contours adiabatically, rather than taking the zonal average, and apply stability analysis to this reference state and compare the results with conventional analysis. (We focus on the Southern Hemisphere where the effects of orography are small.) The difference between the two analyses helps us understand the nature of baroclinic adjustment by the observed eddies.