Estimating Global and Local Scaling Exponents in Turbulent Flows using Wavelet Transformations

High frequency longitudinal velocity (u) measurements were performed in the atmospheric boundary layer to investigate the inertial subrange structure of turbulence. Global and local scaling exponent distributions and other statistical properties were derived using continuous (CWT ) and critically sampled orthonormal (OWT ) wavelet transformations. These statistical measures were contrasted to similar statistical measures derived by applying CWT and OWT to a fractional Brownian motion (fBm) time series with a Hurst exponent of 1=3. This study demonstrated that both CWT and OWT were able to resolve intermittency-based departures from global power-laws observed in higher-order structure functions. Particularly, the global power laws inferred from OWT were in excellent agreement with the She-L evêque vortex lament model. However, these wavelet computed intermittency departures were smaller than those computed by the extended self similarity structure function approach. The e ects of vortex stretching on the dimensionless structure skewness were well captured by CWT and OWT coe cients. However, the CWT was not able to discern any fundamental di erences in the u and fBm local scaling exponent distributions.