This lecture series describes how the combination of rotation and stratification affects the large-scale flow in the atmosphere and the oceans. The key idea is that on time scales of two to three days or more the evolution of three-dimensional rotating stratified flow may be viewed as controlled by the distribution of potential vorticity in a similar way that two-dimensional incompressible flow is controlled by the distribution of vorticity. The similarity is such that the whole subject of two- dimensional vortex dynamics introduced in M.E. McIntyre's lectures has immediate relevance to the three-dimensional rotating stratified case. Quasi-geostrophic theory is introduced as a convenient mathematical expression of the similarity.
Some of the types of flow possible in the atmosphere and ocean are examined in detail. Waves known as Rossby waves, which propagate along potential vorticity gradients, allow the effects of external forcing to propagate over large distances, e.g. downward from the ocean surface, upward from the lowest levels of the atmosphere into the stratosphere, and in latitudinal and longitudinal directions from geographically localized forcing regions. Some features of observed flows, e.g. eddies on ocean current systems and the day to day variation of the winds, may be understood in terms of disturbances growing on an unstable basic flow. Potential vorticity gradients are of fundamental relevance to the stability properties of the flow. Waves and eddies do not simply propagate or grow on a fixed basic flow, but lead to systematic changes in the flow. Such wave, mean-flow interactions are important in many aspects of the observed atmosphere and ocean, perhaps most impressively in the generation of reversal in the direction of the wind in the equatorial lower stratosphere every 14 months or so; the so-called quasi-biennial oscillation. But similar effects are thought to be important in for example the generation of a deep region of recirculating flow below wind-forced western boundary currents, such as the Gulf Stream. Again, considering the potential vorticity transfer properties of the eddies is one illuminating way of trying to understand such phenomena. Application of these ideas to the larger-scale circulation of the atmosphere will be discussed.