Analytical and numerical modelling of jet streaks: Barotropic dynamics

Abstract

Abstract Observations suggest that vortex dipoles of mesoscale dimensions may provide a simple yet realistic representation of the structure and dynamics of jet streaks in the extratropical upper troposphere. Moreover, the effects of horizontal divergence in the vicinity of jet streaks often may be of secondary dynamical importance, suggesting that a nondivergent barotropic framework may provide a logical starting point for an idealized investigation of jet streaks. Analytical solutions of barotropic vortex dipoles are shown to exhibit characteristic signatures similar to those identified in observational case‐studies of jet streaks. In addition to the dipole of relative vorticity, these signatures include: (i) a localized maximum in fluid speed (i.e. a jet streak), (ii) ageostrophic flow that is directed towards lower pressure in the entrance region and towards higher pressure in the exit region of the jet streak, (iii) a four‐cell pattern of ageostrophic vorticity that is cyclonic in the entrance and exit regions and anticyclonic on the flanks of the streak, and (iv) a translation speed that is significantly slower than the maximum fluid speed. On the basis of these similarities, it is suggested that vortex dipoles provide a plausible dynamical representation of the structure and motion of jet streaks. Nevertheless, vortex dipoles in isolation are unable to account for certain observed features of jet streaks, such as the anisotropy of the wind field in the along‐stream direction and the asymmetry in 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 be zonally varying or wavelike. Analytical and numerical solutions of barotropic vortex dipoles in the presence of a variety of non‐uniform background flows characteristic of the large‐scale extratropical circulation are shown to account for the above features absent from dipoles in isolation. These solutions are also shown to provide idealized depictions of the life cycles of jet streaks in the extratropical upper troposphere.