Multi-component variational mode decomposition and its application on wall-bounded turbulence

Scale decomposition is an important issue in the study of wall-bounded turbulence. Existing scale decomposition tools, such as Fourier analysis, empirical mode decomposition (EMD), and variational mode decomposition (VMD), can only deal with one component at a time. This constrains a full comprehension on the multi-scale characteristics of the multi-component turbulent fluctuations. Here, we extend the original VMD algorithm (Dragomiretskiy and Zosso in IEEE Trans Signal Process 62(3):531–544, 2014) to multi-component version, i.e., MC-VMD and MC-QBVMD, to simultaneously decompose multiple components in 1D and 2D scenarios, respectively. One of the attracting features of VMD-based method is that the decomposition is based on the bandwidth of the instantaneous scales of a non-stationary signal, so that the scale interface is not a predetermined input but an output. The performance of MC-VMD and MC-QBVMD is tested on the velocity fields of a canonical turbulent boundary layer (TBL) obtained via both direct numerical simulation (DNS) and particle image velocimetry (PIV) (with Re_τ= 1750 and 2400, respectively). Comparison with existing decomposition tools, including complex VMD (C-VMD), quasi-bivariate VMD (QBVMD), and proper orthogonal decomposition (POD) shows that MC-VMD and MC-QBVMD lead to scale decomposition with scale interface being consistent across multiple components. This is ideal for the study of the scale interaction taking all the velocity components into consideration. Moreover, a small-scale spectral peak is identified at about λx+≈300, invariant among all the velocity components. This length scale may be related with the energetic vortical structures dominating the near-wall self-sustaining cycle.