Bi-Fractal Energy Exchange between Turbulence and Multimodal Gravity Waves in a Dynamically Unbalanced Upper-Level Jet–Frontal System

High-resolution aircraft measurements and simulations from numerical models are analyzed for a clear-air turbulence event associated with an intense upper-level jet/frontal system. Cross spectral, wavelet, structure function and Stokes parameter analyses performed with the 25-Hz in-situ aircraft data are used to investigate the relationship between gravity waves and turbulence. Mesoscale dynamics are analyzed with the 20-km hydrostatic Rapid Update Cycle (RUC) model, and a nested 1-km simulation with the nonhydrostatic Clark-Hall (CH) cloud-scale model.

The turbulence generation process could be described as an energy cascade process, initiated as gravity-inertia waves were produced in a region of diagnosed unbalanced upper-level frontogenesis near a tropopause fold. Turbulent Kinetic Energy fields forecast by the models displayed a strongly banded appearance associated with these mesoscale gravity waves. 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.

The wavelet analysis revealed that brief episodes of high turbulent energy were closely associated with gravity wave occurrences. Structure function analysis provided evidence that turbulence was most strongly forced at a horizontal scale of 700 m. By combining cross-spectral and continuous wavelet transformation, the temporal and spatial characteristics of the waves could be extracted. Upon further introduction of these results into a Stokes parameter analysis for partially polarized internal waves, it was revealed that gravity waves possess distinctive polarization and coherency signatures allowing clear separation of waves from turbulence, such that the turbulence production is closely related to an enhancement in both the polarization and coherency above a threshold value in the Cartesian wind components. Notably, turbulent surges are accompanied by a tendency for an abrupt reduction of the polarization and shifting of the horizontal wave vector.

The implications of this research are that unbalanced upper-level jets may generate a broad spectrum of gravity waves, which at the shorter wavelengths, develop a tendency to steepen and break, resulting in surges of turbulent bursts that are readily identifiable using spectral, wavelet, and structure function techniques. This research indicates that episodes of high turbulent kinetic energy were the result of upscale feedback effects ("inverse energy cascade" processes linked to wave breaking). The bi-fractal nature of the gravity waves and turbulence suggest new approaches for parameterizing sub grid-scale effects caused by the interaction of waves and turbulence in numerical models.