De-asymmetry of small-scale motions in wall-bounded turbulence

Abstract

The present work focuses on the symmetry-breaking phenomenon in large-to-small amplitude modulation (AM) of wall-bounded turbulence. Using the recently proposed multi-component variational mode decomposition method, the volumetric velocity fields of a spatially developing turbulent boundary layer being obtained by direct numerical simulation are decomposed into four three-dimensional intrinsic mode functions (IMFs), whose spanwise length scales are fully separated from each other. It is found that the first IMF mainly characterizes the streamwise large-scale (LS) and very-large-scale turbulent motions. Splatting and sputtering events are observed in the second IMF (2IMF), leading to the biased conditional probability density functions of near-wall u2IMF and v2IMF under the condition of extreme large-scale motions. This is in distinct contrast to the hierarchical self-similarity of the wall-normal profiles of Reynolds shear stress (RSS) of the last two IMFs (3IMF and 4IMF). When treating 2IMF as components of small-scale (SS) turbulent motions, such splatting and sputtering events lead to asymmetric AM effect; that is, the AM coefficients corresponding to positive and negative LS motions are asymmetric to each other. The underlying reason is that these strong quadrant events are spatially asymmetric and are tightly coupled with local LS motions. Based on this observation, a de-spatial-asymmetry (DSA) method is proposed to obtain asymmetry-free “universal” SS turbulent motions. This method includes the removal of the transitional 2IMF from SS motions, the de-amplitude modulation, and the length-scale rescaling. Analysis of single-point velocity statistics, RSS, as well as velocity spectrum, shows that the “universality” of SS motions derived from the DSA method is remarkably improved.