Resolvent-based phase estimation for spectral analysis of temporally uncorrelated PIV snapshots

Recent years have witnessed the development of a large variety of spectral analysis methodologies successful at extracting coherent dynamical features from complicated and noisy flows. Common to these methods is the requirement of a time-resolved sequence of measurements – but such data may be difficult to acquire, especially for high-speed flows. Snapshot-based systems may instead provide spatially resolved data, but at widely spaced intervals in time. In this talk, we discuss methods to recover likely temporal coherence from such data, using phase estimation based on modes obtained from resolvent analysis, which incorporates knowledge of the Navier-Stokes equations governing the flow. In addition to identifying coherent dynamics, our hybrid physics-based and data-driven approach also provides insights into methods that are either purely physics-based or purely data-driven. We apply our method to Planar PIV measurements and numerical simulations of a turbulent boundary layer flow past a circular cylinder held a short distance above the wall.