Time-stepping Global Stability Analysis Using Dynamic Mode Decomposition for Hypersonic Boundary Layer

This study applies time-stepping global stability analysis (GSA) using dynamic mode decomposition (DMD) to a hypersonic flow over a cone. Compared with the conventional Arnoldi-based GSA, the use of DMD avoids generating non-physical zero-frequency unstable modes. Parameter sensitivity analysis confirms that dominant eigenvalues converge with an increased low-rank matrix size, which is hard to be achieved by the Arnoldi-based method, while highlighting the necessity of a sufficient number of snapshots for improved convergence. When applied to flow conditions corresponding to experiments with and without turbulent transition indication, the method successfully extracts the Mack's second mode and its harmonics, capturing instability differences consistent with the present experimental results. Furthermore, the obtained results suggest that identifying the spatial location of the maximum mode amplitude offers a potential approach for simplified transition prediction.