  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 forwards and backwards 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.
