Decomposition of multi-scale coherent structures in a turbulent boundary layer by variational mode decomposition

Turbulent boundary layer (TBL) is believed to contain a wide spectrum of coherent structures, from near-wall low-speed streaks characterized by inner scale to log-layer large-scale coherent motions (LSM and VLSM) characterized by outer scale. Recent studies have evidenced the interaction between these multi-scale structures via either bottom-up or top-down mechanisms, which implies the possibility of identifying the coexistence of their footprints at medium flow layer. Here, we propose a Quasi-Bivariate Variational Mode Decomposition method (QB-VMD), which is an update of the traditional Empirical Mode Decomposition (EMD) with bandwidth limitation, for the decomposition of the PIV measured 2D flow fields with large ROI ($\Delta x\times \Delta z\sim 4\delta \times 1.5\delta $ ) at specified wall-normal heights ($y/\delta =0.05\sim 0.2$ ) of a turbulent boundary layer with $Re_{\tau } =3460$. The empirical modes identified by QB-VMD well capture the characteristics of log-layer LSMs as well as that of near-wall streak-like structures. The lateral scales of these structures are analyzed and their respective energy contribution are evaluated.