Advection-based temporal reconstruction technique for turbulent velocity fields

Characterization of turbulent flows is challenging due to the interaction of widespread spatiotemporal scales. Experimental techniques such as Particle Image Velocimetry (PIV) can be used to obtain spatially resolved flow measurements, however, these systems often suffer from limited acquisition rates. The present work investigates the ability of an advection-based flow reconstruction technique to increase the temporal resolution of turbulent flow data without any prior knowledge of the flow physics. A semi-Lagrangian technique is suggested to obtain fluid trajectories through a forward and backward integration of the available spatiotemporal data. The estimates are then fused using a temporal weighting scheme to yield velocity fields at intermediate times. The performance of the method is verified against three-dimensional direct numerical simulation (DNS) data of a plane jet at Re = 10000. Extracting time series data from the spatially and temporally resolved DNS results, five test cases with artificially lowered sampling frequencies were generated. Spectral analysis revealed that the characteristic frequency found in shear-layer dominated flows can be obtained even for the most extreme case. Additionally, spectral information up to two orders of magnitude beyond the Nyquist criteria is successfully recovered throughout the entire spatial domain -- surpassing the performance of previously introduced methods. The maximum spectral reconstruction error of the suggested method, defined as net energy loss or gain, fell within the bounds of [-5, 3]%, with a corresponding global energy difference in the range of [-2, 1]%. Furthermore, the spatially averaged reconstruction error for the velocity fluctuations was bound by [6 +/- 6]%.