Eulerian techniques for Lagrangian investigation of wall-bounded turbulent flows

The Lagrangian viewpoint, following fluid particles, is effective for understanding turbulent diffusion, which is fundamental to mixing, dispersion, entrainment, and turbulence modeling. However, Lagrangian studies of turbulence are sparse due to the high cost and complexity of tracking exceedingly large number of space-filling tracer particles. In this talk, we showcase our recent work with novel Eulerian approaches that allow computation of key Lagrangian kinematics/statistics without explicit particle tracking. First, the reference map (RM) technique, originally developed for Eulerian treatment of solid mechanics, replaces particle tracking by returning initial tracer locations sampled at grid points and updating them through the Eulerian transport equation. The RM allows computation of Lagrangian coherent structures (finite-time Lyapunov Exponent, FTLE) and material surface tracking. Second, we compute Lagrangian mean fields (averaged along tracer trajectories) by solving their exact transport equations. We apply these techniques to turbulent channel flow at Re_τ=180. Suprisingly, Largrangian mean fields computed over one eddy turnover time contain spatial features finer than the instantaneous counterparts. The Lagrangian covariance field is highly correlated with FTLE. We also demonstrate how the RM can be leveraged to compute ensemble particle statistics such as particle displacement variance.