Developing a universal metric to assess the progression of transition to turbulence in pulsatile pipe flow*

Transition to turbulence in pulsatile flow has been observed to occur in the left ventricle of the heart, cerebral aneurysms, etc. The intermittent and fluctuating flow behavior associated with it has been shown to affect key hemodynamic metrics such as wall shear stress (WSS) and pressure, as well as contribute to disease progression. Unfortunately, despite the clear need, no metrics or analysis tools exist to assess the magnitude of transitional flow behavior present for a given flow. In this work, we aim to address this gap by identifying and establishing a metric capable of estimating the progression of transition within a flow environment. We developed a continuous wavelet transform (CWT)-based time-frequency analysis (TFA) method capable of evaluating the instantaneous frequency of the flow. We apply our TFA method to 2D planar particle image velocimetry (PIV) data of transitional flow collected in-house. The 2D PIV data includes both steady and pulsatile flow cases with mean Reynolds numbers (Re_m) ranging from 500-5000. Specifically, we examine the temporal evolution of spatial frequency structures across different waveforms and Re_m. We show that the spatial structures undergo a transformation from coarser to finer spatial scales and serve as a metric in identifying progression of transition to turbulence.