Tutorial

An Introduction to Lagrangian Statistics in Turbulence

Guido Boffetta
Dip. Fisica Generale
University of Torino

The knowledge of the statistical properties of particle tracers advected by a fully developed turbulent flow is a key ingredient for the development of stochastic Lagrangian models in such diverse contexts as turbulent combustion, pollutant dispersion, cloud formation and industrial mixing.

The statistics of Lagrangian dispersion is historically one of the first issues which has been quantitatively addressed in the study of fully developed turbulence. This was done by Richardson, in a pioneering work on the properties of dispersion in the atmosphere in 1926, 15 years before the theoretical developments by Kolmogorov and Obukhov. Despite this fact, there are still relatively few experimental studies on turbulent Lagrangian dispersion. This is essentially due to the difficulties to obtain Lagrangian trajectories in fully developed turbulent flow.

In this Lecture the statistical properties of Lagrangian tracers in fully developed turbulence will be reviewed on the basis of a set of high resolution Direct Numerical Simulations and compared with predictions based on Kolmogorov similarity theory.

The first part of the Lecture will be devoted to single particle statistics, in particular acceleration and velocity increments along particle trajectories. Comparison with Kolmogorov-Yaglom theory and the effects of intermittency corrections will be discussed.

In the second part I will discuss multiparticle statistics, starting from the problem of pair dispersion introduced by Richardson. Finally the evolution of shapes, defined on the basis of 3 or 4 particle statistics will be illustrated.