Extracting target-related flow structures using a time-lagged cross-correlation ranking criterion

Abstract

Structures with large global contributions to a flow field are not necessarily those that are most closely associated with a specified engineering observable. We propose a time-lagged cross-correlation (TCC) ranking criterion to extract target-related dynamical structures from a fixed modal expansion while preserving existing spatial modes and temporal coefficients. The criterion ranks mode groups by the mean squared norm of cross-responses between their flow contributions and the observable over a lag window. It is tested separately using dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD). TCC-DMD analysis shows that TCC recovers three low-contribution target structures from a dominant background in a synthetic flow. The reconstruction error for the target subfield is 2.15\%. In the cylinder wake, different force observables select structures associated with the vortex-shedding fundamental, slow drag variations, and the second harmonic. In the cavity case, selected modes connect two main frequency bands of the target observable to distinct spatial amplitude and phase distributions. TCC-POD analysis shows that the criterion minimises the weighted truncation error of the correlation operator among equally sized subsets of the fixed orthogonal basis. A comparison with canonical correlation decomposition further reveals differences between fixed-direction selection and correlation-based basis construction in the spatial structure and retention of flow information. Lag aggregation can improve structure identification when zero-lag association is insufficient. The gains depend on the cross-response distribution and window selection. TCC separates target-related ranking from mode-set construction, enabling comparison of spatial structures associated with different observables within the same modal expansion.