Equations are presented for the evolution of isobaric shear and curvature vorticity and for isentropic shear and curvature potential vorticity in natural (streamline-following) coordinates, in the case of adiabatic, frictionless flow. In isobaric coordinates, two terms of equal magnitude and opposite sign arise in the respective tendency equations for shear and curvature vorticity; these terms represent conversions between shear and curvature vorticity in the sense that their sum does not alter the total tendency of absolute vorticity. In isentropic coordinates, only the conversion terms remain in the tendency equations for shear and curvature potential vorticity, consistent with potential-vorticity conservation. The vorticity and potential-vorticity conversions arise from (i) along-stream variations in wind speed in the presence of Lagrangian changes in wind direction and (ii) flow-normal gradients of Lagrangian changes in wind speed. The assumption of horizontal nondivergence simplifies the interpretation of the vorticity-interchange process by relating the conversion terms directly to flow curvature. Schematics are developed in order to illustrate the conversion terms in idealized representations of jet-entrance and jet-exit regions and curved flow patterns; these schematics provide the basis for understanding vorticity interchanges in realistic flow regimes.
The evolution of the midtropospheric shear- and curvature-potential-vorticity fields is described for a jet- trough interaction event in northwesterly flow, leading to the formation of a well-defined midtropospheric cutoff cyclone over the eastern United States between [8 and 20 January 1986. This time period coincides with the first intensive observing period of the Genesis of Atlantic Lows Experiment. Major midtropospheric cyclogenesis begins as a jet embedded in northwesterly flow, identified as a maximum of cyclonic shear potential vorticity, propagates toward the base of a diffluent trough, identified as a maximum of cyclonic curvature potential vorticity. The potential-vorticity tendency equations reveal that for this particular stage, the interchange terms contribute both to the amplification of the trough and to the formation of a maximum of cyclonic shear potential vorticity on the downstream side of the trough. The potential-vorticity interchange process is shown to play a key role in transforming the asymmetric configuration of shear and curvature potential vorticity characteristic of the diffluent trough stage, where the cyclonic shear maximum lags the cyclonic curvature maximum, to the relatively symmetric configuration characteristic of the cutoff stage. At the culmination of the cutoff stage, the shear- and curvature-potential-vorticity maxima overlap substantially. This overlap is a consequence of the presence of a single, cyclonically curved jet within the base of the cutoff cyclone.
A second important structural change occurring during midtropospheric cyclogenesis is the transformation of the potential-vorticity anomaly corresponding to the cutoff cyclone into a circularly symmetric configuration, which is accomplished by the contraction of the northwestern extension of the potential-vorticity anomaly toward the cyclone center. This contraction process, which is shown to involve significant interchanges between shear and curvature potential vorticity, results in the detachment of the potential-vorticity anomaly from the “stratospheric reservoir” of potential vorticity located north of the cyclone.