A new approximation to modulation-effect analysis based on empirical mode decomposition

Abstract

The modulation effect, namely, the amplification or attenuation of near-wall small-scale (SS) structures by outer large-scale (LS) structures, is one of two commonly accepted ways that outer LS turbulent fluctuations can influence near-wall ones. Mode decomposition based on filtering is widely used to analyze the modulation effect. In the present study, a new approximation is proposed based on empirical mode decomposition (EMD) to investigate the aforementioned amplitude modulation effect. Both methods are used, and their results are compared for two-point and single-point analyses. It has been shown that the LS and SS signals that are decomposed by filtering and EMD follow identical paths. Despite the similarities of the signals, the suggested method exhibits a slightly higher correlation coefficient R compared to the method based on filtering for the two-point analysis. For the one-point analysis, however, the suggested method gives a rational correlation coefficient for the one-point analysis compared to the two-point analysis, while the existing method seems far from giving a rational correlation coefficient value, which is too low compared to that of the two-point analysis. The suggested method is relevant to many recent studies that questioned the reliability of calculating the correlation coefficient with the existing method. The variation of R for identical signals extends the discussion of the correlation-coefficient calculations to the very first process, namely, obtaining LS and SS data from the original signal.