Cyclonic vortices on the tropopause are characterized by compact structure and larger pressure, wind and temperature perturbations when compared to broader and weaker anticyclones. Neither the origin of these vortices nor the reasons for the preferred asymmetries are completely understood; quasigeostrophic theory, in particular, is dynamically unbiased.

In order to explore these and related problems, we introduce a novel small Rossby-number approximation to the primitive equations applied to a simple model of the tropopause in continuously stratified fluid. This model resolves the dynamics that give rise to vortical asymmetries, while retaining both the conceptual simplicity of quasigeostrophic dynamics and the computational economy of two-dimensional flows. The model contains no depth-independent (barotropic) flow, and thus may provide a useful comparison to \twod\ flows dominated by this flow component.

Solutions for random initial conditions (i.e., freely decaying turbulence) exhibit vortical asymmetries typical of tropopause observations, with strong localized cyclones, and weaker diffuse anticyclones. Cyclones cluster around a distinct length scale at a given time whereas anticyclones do not. These results differ significantly from previous studies of cyclone--anticyclone asymmetry in the shallow-water primitive equations and the periodic balance equations. An important source of asymmetry in the present solutions is divergent flow associated with frontogenesis and the forward cascade of tropopause potential-temperature variance. This thermally direct flow changes the mean potential temperature of the tropopause, selectively maintains anticyclonic filaments relative to cyclonic filaments, and appears to promote merger of anticyclones relative to cyclones.

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