Fusion of physics-based models with field measurements for turbulent flow reconstruction

Particle Image Velocimetry (PIV) systems are often limited in their ability to fully resolve the broadband temporal fluctuations associated with turbulent flows due to hardware limitations or cost constraints. In this study, we use physics-based models grounded in Rapid Distortion Theory (RDT) to reconstruct the time evolution of wall-bounded turbulent flows between consecutive PIV snapshots. The linear RDT equations are integrated forwards and backwards in time from the PIV snapshots, and the flow field in the intervening period is estimated via a weighted summation of these forward- and backward-time estimates. The weights used for this fusion are formulated to account for the advective nature of the RDT equations. The backward-time integration is unstable over longer time horizons due to negative diffusion. To overcome this problem, the linear RDT equations are further simplified to retain just the advective term. In other words, Taylor’s frozen turbulence hypothesis is employed for the backward-time integration. Reconstruction accuracy is evaluated as a function of spatial resolution and time horizon using Direct Numerical Simulation (DNS) data for turbulent channel flow from the Johns Hopkins Turbulence Database.