Balanced and Unbalanced Upper-Level Frontogenesis

Abstract

The dynamics of frontogenesis at upper levels are investigated using a hierarchy of three numerical models. They are, in order of decreasing sophistication, the anelastic (AN), the geostrophic momentum (GM), and the quasi-geostrophic (QG) approximations to the full equations of motion. Each model is two-dimensional and assumes the same basic-state, which incorporates the frontogenetical mechanisms of confluence and horizontal shear. The dependence of the numerical solutions on the initial vertical shear of the cross-front component of the geostrophic wind, ?, and its associated along-front temperature gradient is examined in detail. For the values of ? chosen, the along-front temperature gradient is either zero (? = 0) or such that cold air is advected along the upper front (? < 0). Intercomparison of the broad-scale structure of the upper-level jet?fronts as described by the AN and GM models shows close agreement. For zero or weak shears (? = 0 s?1 or ? = ?2 ? 10?3 s?1), the solutions are essentially identical. Vertical shear in the cross-front geostrophic wind serves to increase the amplitude of the cross-front circulation and displace the subsiding branch toward the warmer air. In the cases of weak or zero shear, the dominant mechanism for generating vertical vorticity at upper levels is the stretching of preexisting vertical vorticity, whereas for stronger shear (? = ?5.741 ? 10?3 s?1) the key process becomes the tilting of horizontal vorticity into the vertical by differential vertical motion. In contrast, the QG model exhibits marked differences with its AN and GM counterparts, which become even more pronounced as |?| is increased. These differences are related largely to the neglect of vortex tilting in generating vertical vorticity in the OG model. The GM and QG models assume cross-front thermal wind balance at all time. A posteriors examination of the numerical solutions shows this to be an excellent approximation when the vertical shear in the cross-front geostrophic wind is weak. For strong vertical shear of the cross-front geostrophic wind, the unbalanced along-front ageostrophic wind is proportional to the vertical advection of the cross-front velocity. Diagnoses of these simulations reveal thermal wind balance to be less well satisfied. It is shown that in contrast to the GM and QG models, wherein the along-front ageostrophic velocity is passive and thus cannot contribute to the evolution of the jet?front system, the unbalanced along-front flow contributes significantly to the dynamics as described by the AN model.