Study of dynamics in unsteady flows using Koopman mode decomposition

The Koopman Mode Decomposition (KMD) is a data-analysis technique which is often used to extract the spatio-temporal patterns of complex flows. In this paper, we use KMD to study bifurcations of the lid-driven flow in a two-dimensional square cavity based on rigorous theorems related to the spectrum of the Koopman operator. We adopt a new computational algorithm, which is capable of detecting true Koopman modes and eigenvalues in post-transient flows with mixed spectra. Properties of the Koopman operator spectrum are linked to the sequence of bifurcations occurring between $Re=10000$ and $Re=30000$, and changing the flow nature from steady to aperiodic. The associated Koopman modes show remarkable robustness even as the temporal nature of the flow is changing substantially. We observe that KMD outperforms the Proper Orthogonal Decomposition in reconstruction of the flow, as long as quasi-periodic features are present in the flow.