Turbulence generation by gravity waves within upper-level jet-front systems

The cascade of energy from gravity-inertia waves generated by unbalanced jet streak dynamics to turbulent eddies has been simulated and observed. This energy cascade process is studied with an idealized model of a baroclinic three-dimensional jet streak initialized by inverting a specified potential vorticity field, multi-scale numerical weather prediction model simulations of an intense upper-level jet/frontal system, and high-resolution dropwindsonde and 25-Hz in-situ measurements collected by the Gulfstream-IV research aircraft. The clear-air turbulence event is simulated with the 20-km hydrostatic Rapid Update Cycle (RUC) model and a nested 1-km version of the nonhydrostatic Clark-Hall (CH) cloud-scale model.

The idealized model produces packets of gravity-inertia waves in the exit region of an increasingly unbalanced upper-level jet streak, as well as along the upstream side of the trough in a region of very strong horizontal shear. Using horizontal grid resolutions as high as 250 m, the model shows wave sharpening and energy cascade down to smaller scales, where wave fronts become steeper and may break, leading to generation of sub-grid scale turbulent kinetic energy.

Diagnostic analyses of the RUC and CH model simulations and the G-IV observations reveals that turbulence occurred in association with a broad spectrum of upward-propagating gravity waves above the jet core along the upstream side of the trough. Inertia-gravity waves were generated within a region of unbalanced frontogenesis in the vicinity of a complex tropopause fold. Turbulent kinetic energy fields forecast by the models displayed a strongly banded appearance associated with these mesoscale gravity waves (horizontal wavelengths of ~120–220 km). Smaller-scale gravity wave packets (horizontal wavelengths of 1–20 km) within the mesoscale wave field perturbed the background wind shear and stability, promoting the development of bands of reduced Richardson number conducive to the generation of turbulence.

Spectra from the G-IV observations exhibit a k-5/3 behavior for scales down to 40 m, extending the range found from previous analyses (Lilly 1983; Nastrom and Gage 1985). While spectral analysis identifies the presence of the wave signals, it does not permit recovery of rapid changes in wave amplitudes and phase and frequency shifts. By combining cross-spectral and wavelet analysis methods, we are able to show that intermittent episodes of high turbulent energy were closely associated with gravity wave occurrences. Introduction of the wavelet cross-spectrum technique into the Stokes parameter methodology reveals 1) small-scale gravity waves possess distinctive polarization signatures, 2) the turbulence production is closely related to an enhanced level of polarization and coherency in the two components of the horizontal wind in the gravity waves, and 3) turbulence surges are accompanied by an instantaneous reduction of polarization of the progenitor gravity waves. Third-order structure function analysis provides evidence that turbulence was most strongly forced at a horizontal scale of 700 m. In summary, the picture that emerges is one of forcing of gravity-inertia waves at the jet streak scale, the continuous generation of gravity waves over a broad spectrum of smaller scales, reduction of the Richardson number by sharpening of the wave fronts at the smallest (kilometer-scale) end of the wave spectrum, and generation of turbulent kinetic energy by wave breaking.