ON WAVELET ANALYSIS OF NONSTATIONARY TURBULENCE

Wavelets are new tools for turbulence analysis that are yielding impor tant insights into boundary-layer processes. Wavelet analysis, however , has some as yet undiscussed limitations: failure to recognize these can lead to misinterpretation of wavelet analysis results. Here we dis cuss some limitations of wavelet analysis when applied to nonstationar y turbulence. Our main point is that the analysis wavelet must be care fully matched to the phenomenon of interest, because wavelet coefficie nts obscure significant information in the signal being analyzed. For example, a wavelet that is a second-difference operator can provide no information on the linear trend in a turbulence signal. Wavelet analy sis also yields no meaningful information about nonlinear behavior in a signal - contrary to claims in the literature - because, at any inst ant, a wavelet is a single-scale operator, while nonlinearity involves instantaneous interactions among many scales.