Abstract:
Data-driven modal decomposition is a fundamental approach for identifying and extracting multiscale coherent structures in complex vortical flow fields. To address the limitations of classical proper orthogonal decomposition, including spectral mixing among multiscale vortical structures and limited physical interpretability, this study proposes a Coherence-Recurrence Proper Orthogonal Decomposition method, abbreviated as CR-POD, based on spatial coherence analysis. Starting from the coherence-density distribution characteristics of multiscale flow structures, the proposed method integrates coherence analysis with the DBSCAN density-based clustering algorithm and establishes a hierarchical framework in which singular value decomposition is recursively applied to residual fields. In this way, the conventional global low-rank approximation is transformed into a sequence of layer-wise local optimal approximations, enabling the natural separation of flow-field structures from dominant, secondary, to fine-scale components. CR-POD is applied to the analysis of unsteady pressure-field evolution over a 65° swept delta wing undergoing large-amplitude pitching motion. The results show that more than 90% of the total energy can be captured using only five modal layers. The decomposed modes are highly consistent with the physical evolution from large-scale primary vortices to fine-scale turbulent structures. Moreover, the obtained modes remain orthogonal, exhibit no evident spectral aliasing, and each modal layer corresponds to physically meaningful flow structures with clear interpretability. Compared with standard POD, CR-POD preserves modal orthogonality and optimal convergence while effectively overcoming the difficulty of adaptive hierarchical separation of multiscale coherent structures in complex vortical flows.