On Boussinesq Dynamics near the Tropopause

The near-tropopause energy spectrum closely follows a −5/3 power law at mesoscales. Most theories addressing the mesoscale spectrum assume unbalanced dynamics but ignore the tropopause (near which the bulk of the data were collected). Conversely, it has also been proposed that the mesoscale spectrum results from tropopause-induced alterations of geostrophic turbulence. This paper seeks to reconcile these a priori mutually exclusive theories by presenting simulations that permit both unbalanced motion and tropopause-induced effects. The model integrates the nonhydrostatic Boussinesq equations in the presence of a rapidly varying background stratification profile (an idealized tropopause). Decaying turbulence simulations were performed over a wide range of Rossby numbers. In the limit of weak flow (U ≲ 1 m s−1), the essential features of the Boussinesq simulations are well captured by a quasigeostrophic version of the model: secondary roll-ups of filaments and shallow spectral slopes are observed near the tropopause but not elsewhere. However, these tropopause-induced effects rapidly disappear with increasing flow strength. For flow strengths more typical of the tropopause (U ~ 10 m s−1), the spectrum develops a shallow, near −5/3 tail associated with fast-time-scale, unbalanced motion. In contrast to weak flows, this spectral shallowing is evident at any altitude and regardless of the presence of a tropopause. Diagnostics of the fast component of motion reveal significant inertia–gravity wave activity at large horizontal scales (where the balanced flow dominates). However, no evidence points to such activity in the shallow range. That is, the mesoscale of the model is dominated by unbalanced turbulence, not waves. Implications and limitations of these findings are discussed.