Investigating intermittent behaviors in transitional flows using a novel time–frequency-based method

The intermittency characteristics in transitional and turbulent flows can provide critical information on the underlying mechanisms and dynamics. While time–frequency (TF) analysis serves as a valuable tool for assessing intermittency, existing methods suffer from resolution issues and interference artifacts in the TF representation. As a result, no suitable or accepted methods currently exist for assessing intermittency. In this work, we address this gap by presenting a novel TF method—a Fourier-decomposed wavelet-based transform—which yields improved spatial and temporal resolution by leveraging the advantages of both integral transforms and data-driven mode decomposition-based TF methods. Specifically, our method combines a Fourier-windowing component with wavelet-based transforms such as the continuous wavelet transform (CWT) and superlet transform, a super-resolution version of the CWT. Using a peak-detection algorithm, we extract the first, second, and third most dominant instantaneous frequency (IF) components of a signal. We compared the accuracy of our method to traditional TF methods using analytical signals as well as an experimental particle image velocimetry (PIV) dataset capturing transition to turbulence in pulsatile pipe flows. Error analysis with the analytical signals demonstrated that our method maintained superior resolution, accuracy, and, as a result, specificity of the instantaneous frequencies. Additionally, with the pulsatile flow dataset, we demonstrate that IF components of the fluctuating velocities extracted by our method decompose energy cascade components in the flow. Additional investigations into corresponding spatial frequency structures resulted in detailed observations of the inherent scaling mechanisms of transition in pulsatile flows.