One of the main properties of turbulence is its efficiency in mixing advected tracers. This is well known in everyday life as we start making use of turbulent transport in early morning for mixing milk and coffee (or, even earlier, for preparing a cocktail).

From a phenomenological point of view, in presence of turbulence molecular transport coefficients (such as the diffusion coefficient) are replaced by an effective turbulent coefficients, often orders of magnitude larger (this procedure is called renormalization).

Despite its practical importance (one example: dispersion of pollutants in the atmosphere) the theoretical computation of turbulent diffusivity is in general impossible and one has to make use of experiments or numerical simulations. Earlier experiments were done following balloons in the atmosphere: an expensive procedure with several limitations, meanly the non controlled variability of the flow. Another possibility are laboratory experiments in which one follows small reflecting particles (of the same density of the fluid) by means of high speed cameras.

An alternative approach is based on direct numerical simulations (DNS) of Navier-Stokes equations for an incompressible flow. The advantage of this approach is that one can follow an arbitrary number of particles collecting all the possible physical quantities (velocities, accelerations) for arbitrary long time. The main drawback is the moderate Reynolds number or, which is the same, the limited resolutions.

Our group has been recently participated to the DNS of a turbulent flow at a resolution 1024^3 corresponding to Reynolds_lambda=248. The integration was done on the Cray SP4 at CINECA (Bologna, Italy) by means of a fully parallel (MPI) pseudo-spectral code implemented over 64 processor. The average performance reached was 10 Gflops, each time step lasted about 90 sec and the total processor occupation has been 48000 CPU/h.

The first movie (QT) shows the evolution of few particles in the computational box with periodic boundary conditions.

The second movie (QT) is the same simulations seen from the Lagrangian viewpoint. The camera is placed on one particle and looks in the direction of velocity. Observe the absence of collisions as a consequence of incompressibility.

The third movie (QT) shows the evolutions of tetrahedra, i.e. a cluster of 4 Lagrangian particles which start close at initial time. Initial shapes are regular and the formation of very irregular, elongated shapes, are a consequence of the turbulent flow.