Intrinsic phase-based proper orthogonal decomposition (IPhaB POD) for near-periodic flows: details and applications*

Many fluid flows are dominated by near-periodic large-scale dynamics, which are difficult to represent as relevant physical processes (modes) for many data-based modal analysis methods, such as proper orthogonal decomposition (POD). This challenge led to the development of an intrinsic phase-based proper orthogonal decomposition (IPhaB POD) technique, which produces modes that vary in time along a single characteristic cycle of the large-scale dynamics. The IPhaB POD formulation provides the advantage of working in the physical time domain as a function of the phase of the large-scale, while also retaining the benefits of the traditional POD formulation. The resulting method has been shown to better segregate the driving periodic behavior from dynamical processes that are distinct but tethered to that periodic behavior. We present IPhaB POD, provide details on identifying the underlying periodic behavior, and demonstrate the method's utility on complex flows.