Analysis of correlated flow fields via extended cluster-based network models

This study introduces the Extended Cluster-based Network Modeling (eCNM), an innovative approach designed to enhance the understanding of coherent structures in turbulent flows. The eCNM focuses on characterizing the dynamics within specific subspaces or subsets of variables, providing valuable insights into complex flow phenomena. In the context of Proper Orthogonal Decomposition, several extended approaches have been proposed to tackle these challenges, such as Extended POD (EPOD) and Extended SPOD (ESPOD). One powerful method for data-driven modeling of complex nonlinear dynamics is the standard Cluster-based Network Modeling (CNM), consisting in an unsupervised machine learning procedure to reduce a dataset of snapshots to a few representative flow states. However, the presence of variable heterogeneity and measurement noise, both in time and space, can complicate interpretations and model training. The Extended Clustering approach offers enhanced control over the clustering process, can lead to significant computational savings, enables the extraction of dynamical features correlated with a specific subdomain or subset of variables, and facilitates the clustering of heterogeneous variables that are challenging to incorporate in a spatial norm. To demonstrate the effectiveness of the eCNM, it has been employed for the analysis of a swirl flame in unforced conditions, characterized by a precessing vortex core (PVC).