Structure-preserving wavelet decompositions of intermittent turbulence

Abstract

We have analyzed signals containing intermittent coherent structures using a nonorthogonal dyadic wavelet transform. The coherent structures may be zones of concentrated shear or zones determined by regions of turbulent transport of scalar fields. Coherent structures in velocity or scalars have important influences on flux transport. Additionally, coherent structures in velocity determine certain spectral characteristics of the velocity signals. Therefore, the decomposition of observed signals into structures and non-structures is important for associating mechanisms to flux transport and characterizing spectra of signals exhibiting intermittent events.

We develop techniques based on the wavelet transform to provide a signal decomposition which preserves coherent structures. The decomposition is used to separate the signal into two components, one of which contains the important structures. Embedded within the technique are a coherent structure detection mechanism, an analysis of intermittency resulting in an intermittency index, and a filtering technique. We illustrate the dependence of the coherent structure detection mechanism on the choice of analyzing wavelet, demonstrating that anti-symmetric wavelets are better suited to detecting zones of concentrated shear, while symmetric wavelets result in detection of zones of concentrated curvature.

We apply these techniques to the velocity components, virtual potential temperature, and buoyancy flux density records from a portion of the data collected during the First International Satellite Land Surface Climatology Project (ISLSCP) Field Experiment 87 (FIFE87). An analysis of buoyancy flux in a convective, unstable boundary layer shows that the buoyancy flux is due to a combination of temperature structures and momentum structures which is consistent with conceptual models of a convective boundary layer. Spectral estimates of each of the partitions for the velocity signals are compared to the non-partitioned velocity signals. The characteristics of the partition reveal that the structure-containing component of the velocity records follows a classical spectral description having a −5/3 slope in the inertial range, while the non-structure component is essentially flat or has a −1 slope. These can then be associated with strong and weak turbulence regimes, respectively. Furthermore, the −5/3 region in the structure component may be attributed to the effects of intermittency, providing some evidence that large-scale eddies transfer energy directly to small scales.