In this paper we discuss the atmospheric dynamics of the North Atlantic Oscillation (NAO), the zonal index, and annular patterns of variability (also known as annular modes). Our goal is to give a unified treatment of these related phenomena, to make explicit how they are connected and how they differ, and to illustrate their dynamics with the aid of an idealized primitive equation model. Our focus is on tropospheric dynamics.
We first show that the structure of the empirical orthogonal functions (EOFs) of the NAO and annular modes follows, at least in part, from the structure of the baroclinic zone. Given a single baroclinic zone, and concomitantly a single eddy-driven jet, the meridional structure of the EOFs follows from the nature of the jet variability, and if the jet variability is constrained to conserve zonal momentum then the observed structure of the EOF can be explained with a simple model. In the zonal direction, if the baroclinic zone is statistically uniform then so is the first EOF, even though there may be little correlation of any dynamical fields in that direction. If the baroclinic activity is zonally concentrated, then so is the first EOF. Thus, at the simplest order of description, the NAO is a consequence of the presence of an Atlantic storm track; the strong statement of this would be that the NAO is the variability of the Atlantic storm track. The positive phase of the NAO corresponds to eddy momentum fluxes (themselves a consequence of wave breaking) that push the eddy-driven jet polewards, separating it distinctly from the subtropical jet. The negative phase of the NAO is characterized by an equatorial shift and, sometimes, a weakening of the eddy fluxes and no separation between sub-tropical and eddy-driven jets. Variations in the zonal index (a measure of the zonally averaged zonal flow) also occur as a consequence of such activity, although the changes occurring are not necessarily synchronous at different longitudes, and the presence of annular modes (i.e., the associated patterns of variability) does not necessarily indicate zonally symmetric dynamics.
The NAO, is not, however, a consequence of purely local dynamics, for the storm tracks depend for their existence on patterns of topographic and thermal forcing of near hemispheric extent. The Atlantic storm track in particular is a consequence of the presence of the Rocky mountains, the temperature contrast between the cold continent and warm ocean, and the lingering presence of the Pacific storm track. The precise relationship between the NAO and the storm tracks remains to be determined, as do a number of aspects of storm track dynamics, including their precise relation to the stationary eddies and to the regions of largest baroclinicity. Similarly, the influences of the stratosphere and of sea-surface temperature anomalies, and the causes and predictability of the inter-annual variability of the NAO remain open problems.