Scale-Resolving Neural Data Assimilation for Lagrangian Particle Tracking

Lagrangian particle tracking (LPT) is a powerful tool for measuring 3D turbulent velocity fields by tracking a dense set of particles trajectories in the flow, a.k.a. tracks. These tracks are scattered in space, and data assimilation (DA) algorithms are often used to reconstruct the flow (“fill in the gaps”) by combining the tracks with the governing equations. This task is complicated by large gaps between particles, localization and tracking errors, and inertial transport effects. To address these problems, we developed Neural-Implicit Particle Advection (NIPA): a novel LPT DA algorithm that simultaneously reconstructs flow states, corrects particle tracks, and accounts for particle dynamics to handle inertia. We assess NIPA and adaptive Gaussian windowing (an interpolation method) using experimental and synthetic LPT measurements of homogeneous isotropic turbulence and turbulent boundary layers. Various inter-particle distances, tracking error magnitudes, and particle Stokes numbers are tested. Kinetic energy, pressure, and velocity error spectra of the reconstructions are analyzed. Trends in reconstruction accuracy are presented relative to the particle-Nyquist frequency to elucidate the action of the DA algorithm. We comment on the performance limits of NIPA and speculate about the limits of DA for turbulent flow reconstruction using LPT data, in general.