Quasi-wavelet formulations of turbulence and other random fields with correlated properties

Quasi-wavelets (QWs) are similar to customary wavelets in that they are based on translations and dilations of a parent function; however, their positions and orientations are random. QWs are convenient for representing random fields with a self-similar structure. In this paper, a general, multi-dimensional treatment of QW fields is presented that includes scale-dependence in the number density and amplitude of the QWs. Previous QW formulations are extended to include anisotropy and correlations among several properties of the random fields. These extensions would be difficult (if not impossible) to achieve systematically by Fourier methods. As an example application, it is shown how QW models can be constructed to produce constant turbulent flux layers. Heat flux in buoyantly driven turbulence is modeled as a collection of QWs with predominantly horizontal rotation coupled with dipole scalar perturbations. Predictions for spectra in the presence of fluxes are obtained.