Skewness-induced asymmetric modulation of small-scale turbulence by large-scale structures

Abstract

Several recent studies discuss of role of skewness of the turbulent velocity fluctuations in near-wall shear layers, in the context of quantifying the correlation between large-scale motions and amplitude variations of small-scale fluctuations—referred to as “modulation.” The present study is based on the premise that the skewness of the small-scale fluctuations should be accounted for explicitly in the process of defining their envelope, which characterizes their amplitude variations. This leads to the notion of two envelopes, one for positive and the other for negative small-scale fluctuations, and hence also to two corresponding correlation coefficients. Justification for this concept is provided first by an examination of a high-frequency synthetic signal subjected to realistic skewness-inducing modulation. A new formalism is provided for deriving the two envelopes, and its fidelity is demonstrated for the synthetic test case. The method is then applied to a channel flow at a friction Reynolds number of 4200, for which direct numerical simulation (DNS) data are available. The large-scale and small-scale fields are separated by the empirical mode decomposition method, and the modulation of the small-scale fluctuations by the large scales is examined. Separate maps of the correlation coefficient and of two-point correlations, the latter linking the large-scale motions and the envelopes of the small-scale motions, are derived for the two envelopes pertaining to positive and negative small-scale fluctuations, and these demonstrate a significant sensitivity to the envelope-definition process, especially close to the wall where the skewness of the small-scale fluctuations is the dominant contributor to the total value.