On quasigeostrophic dynamics near the tropopause
Under quasigeostrophic (QG) dynamics, the presence of a sharp transition in the stratification profile leads to the formation of comparably sharp vertical gradients of buoyancy. When the QG potential vorticity is assumed to be confined to the jump region, as in surface quasigeostrophy (SQG), the sharp gradients are present initially in the buoyancy field. If smoothly-varying initial conditions are considered instead, numerical simulations reveal that jump-scale features nevertheless emerge after a few turnover times. The introduction of this small scale, h, characterizing the tropopause implies a larger Froude number, thereby undermining the validity of the quasigeostrophic approximation. For fixed h, scale analysis gives a characteristic horizontal velocity, U, above which not only does QG break down, but statically unstable conditions also develop. Using typical atmospheric values for the Brunt-Vaisala frequency, N=0.01 s^-1 and the jump width, h=100 m, we argue that U must be less than about 1 m/s for static stability to hold (and smaller still for quasigeostrophy to be formally valid). Therefore, quasigeostrophic dynamics are consistent only with very weak near-tropopause flows, and thus can hardly account for the observed wind profiles (e.g. the Nastrom and Gage spectral break).