"Multiresolutional-proper orthogonal" hybrid analysis on turbulent structures in open-channel complex geometry flows

We propose a hybrid expansion that consists of a multiresolution approximation (MRA) and a proper orthogonal decomposition (POD) to analyze turbulent flow structures in open-channel flows with complex geometries. The open-channel cavity flows are examined here and their velocity vectors are measured by using particle image velocimetry (PIV). In the first step of the hybrid expansion, the velocity time-series are classified into three distinct components using the MRA, i.e. pseudo-mean velocity, organized turbulence in a mixing shear layer, and incoherent turbulence. In the next step, these velocity components are decomposed by applying the POD. The principal components of the pseudo-mean velocity and the organized turbulence disclose the predominant flow characteristics, such as spatial structures of recirculating flows in the cavity and organized turbulent motions along the mixing shear layer, hysteretic behavior in modal time-series, and so forth. The results strongly support that the present hybrid analysis is effective for detecting spatiotemporal hierarchical structures in turbulent flows with complex geometries.