16 - Dynamic stability

Summary

Disturbances in the rotating cylindrical annulus are a laboratory analogue of synoptic weather systems, which prevail outside the tropics. Each develops through instability of the zonal-mean circulation. Instability was considered earlier in relation to the vertical stratification of mass (Chap. 7). If distributions of temperature and humidity violate the conditions for static stability, then small displacements lead to parcels accelerating away from their undisturbed positions. Unlike the response under stable stratification, this reaction leads to finite displacements of air. Fully developed convection then rearranges air, driving the stratification toward neutral stability.

Two classes of instability are possible. Parcel instability follows from reinforcement of air displacements by a negative restoring force, as occurs in the development of convection. Wave instability occurs in the presence of a positive restoring force, but one that amplifies parcel oscillations inside wave motions. Unstable waves amplify by extracting energy from the mean circulation, for example, from available potential energy that accompanies baroclinic stratification and vertical shear (Chap. 15). Strong zonal wind that follows from the nonuniform distribution of atmospheric heating, in concert with geostrophic balance, makes this class of instability the one most relevant to the large-scale circulation. Like parcel instability, it develops to neutralize instability in the mean flow. This objective is achieved through the rearrangement of air.