[SBanerjee]

If POD or DMD is applied to flows which are not turbulent in a broad sense, which means that there is not much chaotic mixing, will they carry any significance? Because there will be not many spatial and temporal scales like in a turbulent flow.

[LuckyTran]

POD and DMD extracts correlation/covariance in data. They are well-suited for flows with spatiotemporal coherence and actually not so well suited for turbulent flows (because turbulence is chaotic). POD and DMD works really well for flows with hydrodynamic instabilities (the laminar kind that have nothing to do with turbulence), flows laden with acoustics (which are temporally coherent and not chaotic), and other intrinsic instabilities. It also nicely extracts response of externally forced flows (like pulsatile flows) or even flow response of FSI because the energy is predominantly carried in the modes.

There are many more flows for which POD and DMD can extract data (and even more clearly extract data) than turbulent flows Although turbulent flows exhibit many spatial and temporal scales, they aren't modes.