Abstract

The dynamics of tropopause-based jet streaks are examined both analytically and numerically using idealised models (nondivergent barotropic and shallow-water) on both f and beta planes. Motivated by observations linking positive-negative couplets of relative vorticity (i.e., `vortex dipoles') to jet streaks, we investigate the possibility that the theory of coherent structures, and in particular that of vortex dipoles, may provide insight into jet-streak dynamics. Comparison of vortex-dipole solutions between the two models allows for examination of the extent to which divergent circulations are necessary for a first-order dynamical description of jet streaks, as is the case for conceptual models of jet streaks prevalent in synoptic meteorology.

Characteristic signatures of analytical and numerical solutions of vortex dipoles in isolation are examined in both models, and are shown to exhibit structure similar to that seen in observational studies of jet streaks. In addition to a dipole of relative vorticity, these signatures are: (i) a localised maximum in fluid speed; (ii) an ageostrophic flow that is directed towards lower geopotential height in the entrance region of the streak and towards higher geopotential height in the exit region; (iii) a four-cell pattern of ageostrophic vorticity that is cyclonic in the entrance and exit regions and anticyclonic on the flanks of the jet streak; and (iv) a four-cell pattern of divergence (in the shallow-water model only) that conforms to that seen in conceptual models of jet streaks but that is at least an order of magnitude smaller than the ageostrophic vorticity. The technique of piecewise PV inversion is employed to diagnose the velocity field induced by each component vortex of the dipole, and hence the speed at which the dipole translates due to self- and mutual advection of these vortices. It is shown that this translation speed is considerably slower than the maximum fluid speed in the core of the jet streak, a common property of jet streaks in the atmosphere. In light of these foregoing properties, it is suggested that vortex-dipole solutions to the nondivergent barotropic model provide a dynamically reasonable representation of the structure and motion of jet streaks.

Nevertheless, vortex-dipole solutions in isolation are unable to explain certain characteristic features of jet streaks in the atmosphere, in particular the along-stream anisotropy of the wind field and the asymmetry of the relative vorticity field, in which the cyclonic vortex typically is stronger than the anticyclonic vortex. Moreover, jet streaks generally are not isolated, but are embedded in a larger-scale jet stream, which may have a zonally varying or wavelike character. A numerically derived steady solution to the nondivergent barotropic model for a vortex dipole in a jet-like zonal flow is presented that exhibits significant along-stream anisotropy in comparison to a vortex dipole in isolation. Furthermore, the interaction between a symmetric vortex dipole and a large-scale wavelike background flow is shown to exhibit transient asymmetry that is associated with a superposition of the respective relative vorticity fields as the dipole travels through the wave. This interaction is shown to depict idealised jet-streak life cycles that appear to exhibit similarities to the evolution of jet streaks in the atmosphere. Further numerical simulations are presented that describe the evolution of symmetric and asymmetric dipoles in a jet-like zonal flow that itself is asymmetric (i.e., that exhibits stronger cyclonic than anticyclonic shear). Although these simulations display complex evolutions, they appear to have observational support in atmospheric water vapour imagery.