Objective Determination of Optimal POD Modes for Large-Scale Motion Reconstruction in Turbulent Flows

This study proposes and evaluates an objective method for identifying the optimal number of proper orthogonal decomposition (POD) modes. The method is implemented for two frictional Reynolds numbers, Re𝜏, 500 and 1000, to account for both moderate and high Reynolds numbers. The physical structures of large-scale motions (LSM) are identified using two-point correlations. We then apply the method of snapshots POD to decompose the flow field and develop a novel approach using two-point correlations to determine the precise number of POD modes necessary for realistic reconstruction of LSM. This method addresses the limitations of arbitrary mode selection in snapshot POD analysis, which can lead to the visualization of large-scale structures that do not exist in the physical flow domain. By comparing the reconstructed fields with fully resolved DNS data, we assess the effectiveness of our approach in capturing the essential features of LSM at different Reynolds numbers. Our findings provide new insights into the implication of low-order models to effectively capture both spatially and energetic large-scale motions.