Criterion for temporal up-sampling limits of advection-based techniques for PIV data

Experimental investigations for turbulent shear flows are challenging due to the interaction of widespread spatiotemporal scales. Particle image velocimetry (PIV) can yield spatially resolved flow measurements, but recording equipment often lack sufficient temporal sampling rates. The inadequate resolution of smaller temporal scales poses further difficulties for studying turbulent motion. This work investigates the ability of linear and non-linear advection-based flow reconstruction techniques to increase the temporal resolution of under-sampled turbulent flows. A modified semi-Lagrangian technique is used to obtain the instantaneous fluid trajectories through forward and backward integration of PIV spatiotemporal data. The estimates for the PIV data are then fused using a temporal weighting scheme to yield velocity fields at intermediate times. The performance of the method is benchmarked against the DNS of a plane jet, demonstrating that spectral information can be estimated up to two orders of magnitude beyond the Nyquist limit. The uncertainty and up-sampling threshold of the technique is investigated for PIV data of a turbulent round jet. An a priori criterion for the recovery of spectral content is proposed based on the spatiotemporal resolution of the measurements.