Application of wavelet analysis techniques to the study of turbulence and gravity waves using aircraft data and mesoscale-model fields

The nature of the relationship between gravity waves and turbulence has been a topic of considerable theoretical investigation for several decades. However, confirmation of theoretical predictions from direct observations is very much missing. Customary spectral techniques applied to data do not lend themselves well to a proper understanding of the highly intermittent and non-stationary nature of interactions between waves and turbulence. Using 25-Hz aircraft data taken through a turbulent upper-level jet stream in the atmosphere, we show here that wavelet transformation techniques offer a better understanding of such temporally evolving interactions. The frequency-time domain analyses of the in situ aircraft data suggest a close relationship between turbulence intensity and gravity-wave activities. Our results indicate that clear-air turbulence is strongly associated with a spectrum of gravity waves associated with a strong tropopause folding event. Upon applying the wavelet technique to the polarization relationship associated with gravity waves and to a Stokes parameter analysis, we show that gravity waves and turbulence possess distinctive polarization signatures, and that the intermittence of gravity-wave generated turbulence in the atmosphere is closely related to the changing polarity of gravity waves.

The wavelet transformation technique also has been adapted to the study of data from the 20-km Rapid Update Cycle (RUC) model, which is used operationally as guidance for predicting the occurrence of turbulence. Future use of wavelet techniques in analyzing mesoscale model data shows promise for determining with great precision time-varying gravity wave propagation characteristics and wave-wave interactions.