METR 6103: Turbulence (University of Oklahoma)

Introduction

Gravity waves (GWs) are sub-mesoscale motions that can simply be defined as vertical waves in the atmosphere. There must be a trigger mechanism for them to form, such as topography, low-level jets, or convection, yet the atmosphere must be stable. Air parcels will then be driven to rise from the trigger in place, but the environmental stability will cause them to sink again. This repeats inducing wave-like motions, and with enough momentum gravity waves can be created. Another essential atmospheric constituent includes a temperature inversion near the surface to enable support of horizontal and vertical spreading of the waves. In class, it was discussed that in the boundary layer, stable atmospheric conditions can be subject to intermittency. Laminar flow followed by irregular flow can develop in these conditions leading to an environment sufficient for GWs. Past studies document the effect of gravity waves on turbulence and vice versa (Phillips, 1959; Hodges 1967; Stein 1967). In particular, Koch et al. (2005) found high turbulent energy to be closely related to GWs. Still, there has not been much emphasis on comparing the turbulence of GWs that originate from differing trigger mechanisms. It is of interest to dig deeper into comparing these instances to view turbulence variations associated with the waves.


One way to do this is with a wavelet transform or decomposition. Wang et al. (2013) applied a wavelet transform procedure to deduce vertical flux and gave a good representation of how waves evolve when they are generated from the low-level jet. This is a useful method for its time scaling abilities and has many applications in the scientific community for signal processing, scientific calculation, and imaging processing. (Meneveau, 1991; Farge et al. 1992; Priestley, 1996). It is similar to the Fourier transform technique, which converts an input signal to sinusoidal and cosine waves. When the inclination is to merely assess the frequency of a signal, such as for stationary flow, Fourier transform is practical. However, most atmospheric processes are non-stationary and require outputs of time and frequency to be relevant information. This is the beauty of wavelet transformation, where the output wavelets can be analyzed on both a time and frequency domain. Wavelet decomposition operates by reproducing a signal as multiple wavelets, which are derived from a “mother function.” There are two types of commonly used wavelet transform methods: discrete and continuous. In general, turbulence studies adopt the continuous wavelet transform because it is well-suited for extracting features of the signal, whereas discrete transformations are more valuable for data compression and noise reduction (Wiebe et al. 2011). However, the discrete wavelet transformation (DWT) method contains an orthogonal wavelet family called “Sylmets” that (Wang et al. 2013; Farge et al. 1992) proved to be useful in separating large scale and turbulent flow of gravity waves in the atmosphere. Since this is a key step in retrieving the turbulent intensity results, its application is worth consideration.


Once the turbulent section is obtained, one can evaluate the intensity of the fluctuations. As discussed in class, statistical techniques can assist in quantitatively computing turbulence information about turbulence in a fashion that makes it easier to understand. One example is the variance. It accounts for the dispersion of data about a mean value, and determines the intensity of turbulent flow with a single numeric value. The variance is proportionally related to the standard deviation, meaning if the standard deviation is large, the turbulent intensity will be as well. Koch et al. (2005) and Lecoanet and Quataert (2013) developed research that made use of the variance parameter, but comparing its calculations of certain types of GWs is still an untouched topic. Knowledge about turbulence intensity could answer pending questions related to daytime turbulence evolution during these GW events (e.g., does turbulence intensity increase in the afternoon during convection-initiated waves?).


The following analysis was conducted to view the diurnal evolution of turbulence from gravity wave events that differ in initiation. Cases of GWs were examined during June 10th, 2014, and November 4th, 2015. The June case waves were triggered by flow off of the updrafts of an existing thunderstorm east of Lamont, while the November case waves were generated by vertical speed shear, among other favorable atmospheric conditions.