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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.

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The natural and bypass routes to boundary-layer transition to turbulence are traditionally investigated independently in fluid mechanics applications. Nevertheless, in certain flow regimes both mechanisms could coexist and interact. In this work, large-eddy simulations (LES) were performed for a zero-pressure gradient boundary layer developing over a flat plate to investigate the transition mechanism for variable free-stream turbulent properties. Four different combinations of turbulence intensity and integral length scale were analyzed, and two main transition mechanisms were observed. High free-stream turbulence intensity instigates pure bypass transition through the amplification of a continuous Orr–Sommerfeld (O–S) mode that breaks down after secondary instability. Instead, at low free-stream turbulence intensity, discrete and continuous O–S modes interact and are both involved in the transition process. Visual inspection of the LES snapshots provides a detailed insight in Tollmien–Schlichting (TS) waves–streaks mutual interaction and clearly identifies two main mechanisms involved in turbulence breakdown. On one hand, TS waves trigger varicose instability of streaky structures. On the other hand, streaks cause secondary instability of TS waves with emerging Λ-structure formation. Then, dynamic mode decomposition (DMD) is applied to extract the main stability properties for both types of transition route and to highlight coherent structure dynamics, which is hardly observable in the literature. Specifically, for low-medium free-stream turbulence levels, DMD extracts unstable modes clearly related to streaks–TS waves interaction and leading to the formation of Λ structures. Therefore, the streaks–TS waves interaction is proved to be destabilizing and to trigger secondary instability leading to turbulence breakdown.