Lagrangian investigations of turbulence

A Lagrangian description of turbulence has unique physical advantages that are especially important in studies of mixing and dispersion. We focus on fundamental aspects, using mainly data from direct numerical simulations capable of great detail and precision when specific accuracy requirements are met. Differences between time evolution in Eulerian and Lagrangian frames illustrate the dominance of advective transport. We examine basic results in Kolmogorov similarity, giving an estimate of an inertial-range universal constant and the grid resolution and Reynolds number needed to attain the requisite scaling range of time lags. The Lagrangian statistics of passive scalars are discussed in view of current efforts in model development, with differential diffusion between multiple scalars being characterized by shorter timescales. We also note the need for new data in more complex flows and in other applications where a Lagrangian viewpoint is especially useful.