On wavelet analysis of nonstationary turbulence

Wavelets are new tools for turbulence analysis that are yielding important 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 discuss some limitations of wavelet analysis when applied to nonstationary turbulence. Our main point is that the analysis wavelet must be carefully matched to the phenomenon of interest, because wavelet coefficients 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 analysis also yields no meaningful information about nonlinear behavior in a signal — contrary to claims in the literature — because, at any instant, a wavelet is a single-scale operator, while nonlinearity involves instantaneous interactions among many scales.

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