Chengyuan Wu, Huachu Sun, Shun He
Dynamic mode decomposition (DMD) is a powerful data-driven technique for identifying low-dimensional representations of complex flows. However, existing dominant mode selection methods suffer limitations of lack of physical interpretability across different truncation ranks. To address this, a novel framework with rank stability is introduced to select the dominant modes through cohesive and multi-stage processes. The framework begins with the construction of a stabilization diagram by applying DMD across a range of truncation ranks to visualize all potential modes. Then, a Density-Based Spatial Clustering of Applications with Noise algorithm, coupled with automated hyperparameter optimization, is employed to objectively identify candidate clusters from the stabilization diagram. Finally, these candidates are filtered by using the coefficient of variation criterion to ensure the physical consistency of retained modes. The proposed framework was validated by three benchmark cases of increasing complexity, i.e., a laminar cylinder flow (Re = 60), a transitional cavity flow (Re = 3000), and a practical case of transonic buffet over a NACA 0012 airfoil (Re = 3 × 106). Comparative results demonstrate the advantage of our method in consistently identifying physical modes, compared to the amplitude method, the I-criterion and the optimization-based sparsity-promoting DMD method. It provides a robust framework for identifying dominant flow structures in multiple flow regimes, making it a valuable tool for data-driven fluid dynamics research and engineering.