Estimating global and local scaling exponents in turbulent flows using discrete wavelet transformations

High frequency longitudinal velocity (u) measurements were performed in the atmospheric surface layer to investigate the inertial subrange structure o f turbulence. The u measurements, collected over a wide range of atmospheri c stability conditions, were used to investigate local and global intermitt ency buildup in the inertial subrange. Global scaling exponents and other s tatistical properties were derived using nondecimated (NDWT) and critically sampled orthonormal (OWT) wavelet transformations. These statistical measu res were contrasted to similar statistical measures derived by applying NDW T and OWT to an ensemble of fractional Brownian motion (fBm) time series wi th Hurst exponent of 1/3. Such comparisons permit direct assessment as to w hether discrepancies in observed intermittency corrections are artifacts of wavelet transformations or limitations in sample size. This study demonstr ated that both NDWT and OWT were able to resolve intermittency-based depart ures from global power laws observed in higher-order structure functions of turbulence time series. Particularly, global power laws inferred from OWT and NDWT were consistent with new intermittency correction results derived from the dynamics of the fourth order structure functions. This study is th e first to report on the ensemble behavior of such a power law for a wide r ange of surface boundary conditions (e.g., variable surface heating and fri ction velocity). The wavelet computed global intermittency departures from the classical Kolmogorov theory (or K41) were marginally smaller than those computed by the traditional structure function approach. In terms of local exponents, we found that the application of NDWT to fBm time series result ed in a wide empirical frequency distribution of local scaling exponents (a lpha). The latter finding clearly demonstrates that previous and present al pha determined by wavelet analysis cannot be used as evidence for multifrac tality in turbulence. We also demonstrated that the classical local regress ion estimation of alpha is theoretically impaired by heteroscedascity when the local scale is finite. While the spread in alpha does not reflect any m ultifractal signatures, the modes of the local alpha frequency distribution support findings from global exponent analysis. We found that the modes of the local alpha distribution are well reproduced by global intermittency m odels for u and by K41 for the fBm. (C) 2001 American Institute of Physics.