The Global Atmospheric Sampling Program provided data on the horizontal kinetic and potential energy spectra near the tropopause (Nastrom and Gage, 1985). While the steep synoptic-scale part of the energy spectrum agrees well with Charney's theory of geostrophic turbulence, its break to a shallower -5/3 slope in the mesoscale remains a subject of controversy.
Several homogeneous turbulence studies have addressed the issue. In particular, Bartello (2010) presented numerical simulations of decaying triply-periodic rotating-stratified Boussinesq turbulence. It was found that the steep geostrophic spectrum eventually crosses a shallower ageostrophic spectrum at large-enough Rossby numbers. The total energy spectrum thus exhibits a slope break similar to that observed. The assumption of vertical periodicity limits this study to case of constant stratification. Near the tropopause, however, stratification undergoes a rapid change.
A similar slope break can also occur within the quasigeostrophic (QG) framework when vertical boundaries are taken into account (Tulloch and Smith, 2006). A discontinuous jump in stratification generates a delta sheet of QG potential vorticity acting like rigid lid on which buoyancy is materially conserved. This leads to a forward cascade of buoyancy variance and is associated with a shallower, approximate -5/3 spectrum (Held et al. 1995). In this surface quasigeostrophic (SQG) model, the stratification jump at the tropopause plays a crucial role in the slope break and ageostrophic motion is ignored. In the homogeneous turbulence model, it is the other way round.
In this contribution, we aim to reconcile these two mutually exclusive perspectives. To do so, we model the near-tropopause flow in the framework of Boussinesq dynamics. The tropopause is modeled as a continuous yet rapid change in background stratification. A companion QG model is used to produce control runs with identical initial conditions. Implications for the interpretation of the atmospheric spectrum will be discussed.