Reconstructing the time evolution of wall-bounded turbulent flows from non-time-resolved PIV measurements

Particle image velocimetry (PIV) systems are often limited in their ability to fully resolve the spatiotemporal fluctuations inherent in turbulent flows due to hardware constraints. In this study, we develop models based on rapid distortion theory (RDT) and Taylor's hypothesis (TH) to reconstruct the time evolution of a turbulent flow field in the intermediate period between consecutive PIV snapshots obtained using a non-time resolved system. The linear governing equations are evolved forward and backward in time using the PIV snapshots as initial conditions. The flow field in the intervening period is then reconstructed by taking a weighted sum of the forward and backward estimates. This spatiotemporal weighting function is designed to account for the advective nature of the RDT and TH equations. Reconstruction accuracy is evaluated as a function of spatial resolution and reconstruction time horizon using direct numerical simulation data for turbulent channel flow from the Johns Hopkins Turbulence Database. This method reconstructs single-point turbulence statistics well and resolves velocity spectra at frequencies higher than the temporal Nyquist limit of the acquisition system. Reconstructions obtained using a characteristics-based evolution of the flow field under TH prove to be more accurate compared to reconstructions obtained from numerical integration of the discretized forms of RDT and TH. The effect of measurement noise on reconstruction error is also evaluated.