Dynamic mode decomposition and Koopman spectral analysis of boundary layer separation-induced transition

In the present work, dynamic mode decomposition (DMD) and Koopman spectral analysis are applied to flat plate particle image velocimetry experimental data. Experiments concerning separated-flow transition process were carried out in a test section allowing the variation of the Reynolds number (Re), the adverse pressure gradient (APG) and the free-stream turbulence intensity (Tu). The analysis accounts for two different Re numbers, two different Tu levels, and a fixed APG condition inducing flow separation, as it may occur in low pressure turbine-like conditions. For every flow condition, instantaneous velocity fields clearly show the formation of Kelvin-Helmholtz (KH) vortices induced by the KH instability. The most effective definition of the observable matrix for Koopman analysis able to characterize these vortices is addressed first for a reference Tu and Re number condition. Successively, the robustness of DMD and Koopman modal decomposition has been examined for different Tu levels and Re numbers. On a short time trace (10 KH periods), the Koopman analysis is shown to identify the proper KH vortex shedding frequency and wavelength for every condition tested, while DMD fails especially with low Tu and high Re. To validate the results on a longer time trace, a statistical analysis of the dominant unstable eigenvalues captured by the two procedures is successively performed considering several temporal blocks for different inflow conditions. Overall, the Koopman analysis always performs better than DMD since it finds a larger number of unstable eigenvalues at the KH instability frequency and wavelength.