Dynamics of jet streaks in a stratified quasi-geostrophic atmosphere: Steady-state representations

The structure and dynamics of jet streaks in the extratropical upper troposphere are examined in the context of a continuously stratified quasi-geostrophic (QG) framework. It is hypothesized that jet streaks may result from the superposition of monopolar or dipolar vortices of mesoscale dimensions with the enhanced potential-vorticity gradients constituting the tropopause. Based on this hypothesis, steady-state monopolar and dipolar vortices in a uniform zonal background flow on an f-plane are investigated for their applicability as idealized dynamical representations of jet streaks. The representations of jet streaks satisfy the nonlinear governing equations of the continuously stratified QG framework: the monopolar vortex is specified in terms of axisymmetric distributions of QG potential vorticity in the interior of the domain and perturbation potential temperature on upper (tropopause) and lower (surface) boundaries, whereas the dipolar vortex is adapted from a closed-form analytical solution for the geostrophic stream function. Through the incorporation of vertical structure and divergent circulations, these representations of jet streaks extend those presented previously by the authors using a non-divergent barotropic model. It is shown that these vortex representations display characteristic signatures similar to those observed in atmospheric jet streaks. In particular, both the monopole and the dipole exhibit an ageostrophic wind directed towards lower geopotential height in the entrance region of the streak and towards higher geopotential height in the exit region. For the monopole, this ageostrophic wind is entirely rotational and there is no vertical motion. For the dipole. the rotational part of the ageostrophic wind dominates the divergent part; the latter is associated with a four-cell pattern of vertical velocity similar to that described in conceptual models of straight jet streaks. For both the monopole and the dipole, the jet streak is induced by the vortex structure such that the wind speed maximum translates at the same speed as the individual vortices; this translation speed is slower than the maximum wind speed in the core of the speed maximum, consistent with observations of jet streaks. It is proposed that the above representations provide a formal theoretical foundation for the conceptual models of jet streaks prevalent in the literature; these conceptual models typically are based on heuristic kinematic or parcel arguments and not on consistent solutions to a physically plausible set of equations. The representations also provide a foundation upon which to explore the unsteady behaviour of jet streaks in terms of the superposition of monopolar and dipolar vortices with non-uniform zonal background flows.