Multi-scalar mixing and Lagrangian approaches

Fundamental challenges in the statistical description of multi-scalar mixing in homogeneous turbulence are considered, with particular emphasis on the differential diffusion of multiple passive scalars with different molecular diffusivities. New concepts and difficulties arising in addition to those in single-scalar mixing are discussed using typical results from direct numerical simulations of isotropic turbulence. The latter include both Eulerian and Lagrangian quantities, such as multi-variate conditional expectations of molecular diffusion, the time series of scalar fluctuations following fluid particle trajectories, and the dispersion between different species molecules which diffuse relative to the fluid. Knowledge of small-scale processes is important for improvements in Lagrangian statistical modeling.