Particle motion and irreversibility of turbulent flows

In three-dimensional turbulent flows, the flux of energy from large to small scales breaks time-reversal symmetry. I will discuss how this irreversibility can be observed by following the trajectories of tracers, moving with the fluid. For the problem of relative particle dispersion, irreversibility implies that particles separate slower forward in time than backward. This property can be understood in terms of an exact relation, established directly from the Navier-Stokes equations. A more surprising observation is that a tracer particle needs more time to build up large kinetic energy, than to dissipate it. This allows us to quantify the irreversibility of the turbulent fluid.