  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 the dynamics of the lid-driven flow in a
two-dimensional square cavity based on theorems related to the spectral theory
of the Koopman operator. We adapt two algorithms, from the classical Fourier
and power spectral analysis, to compute the discrete and continuous spectrum of
the Koopman operator for the post-transient flows. Properties of the Koopman
operator spectrum are linked to the sequence of flow regimes occurring between
$Re=10000$ and $Re=30000$, and changing the flow nature from steady to
aperiodic. The Koopman eigenfunctions for different flow regimes, including
flows with mixed spectra, are constructed using the assumption of ergodicity in
the state space. 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
flows with strong quasi-periodic components.c features are present in the flow.
