Identification and analysis of very-large-scale turbulent motions using multiscale proper orthogonal decomposition

To identify and characterize very-large-scale motions (VLSM) in turbulent channel flows, direct numerical simulations are performed at Re tau = 906 and 3216. The turbulence structure is then analyzed by proper orthogonal decomposition (POD) and multiscale POD (mPOD). Unlike POD, mPOD is able to distinguish the most energetic modes at selected scales (or frequencies) by imposing spectral cutoffs to separate VLSM, large-scale motions (LSM), and small-scale motions. The VLSM can be clearly visualized from the most energetic spatial modes of the mPOD analysis at both Reynolds numbers. The mPOD results identify a new energetic mode that is aligned in the streamwise direction with a characteristic length covering the whole domain length. This new mode (called eVLSM mode) contains substantial energy, making it an important component of the VLSM in the flow field. The other energetic modes typically appear in pairs with specific streamwise phase shifts. The large-scale structures (apart from eVLSM) are inclined to the streamwise direction and appear to be responsible for the typical meandering behavior or even for the breakup of VLSM.