Dispersion in freely decaying and forced 2D turbulence

Abstract

We report experimental results obtained on freely decaying and forced two-dimensional turbulence. The flow is produced in a thin stratified layer of electrolyte, using an electromagnetic forcing. The velocity and vorticity fields are measured using a particle image velocimetry (PIV) technique. The dispersion of passive particles is studied by numerical computation of lagrangian trajectories from the experimentally obtained velocity fields. We find that the properties of the decaying and forced systems are completely different. In the decaying case, the passive particles move hyperdiffusively, with an exponent identical to that obtained for the vortex motion (Hansen et al. 1998) and their dispersion appears to be controlled by Levy flights. In the forced case, in the presence of an inverse cascade range with k −5/3 scaling, the dispersion of pairs of passive particles is found to be controlled by Richardson law (Richardson 1926) throughout the inertial range of scales revealed by the analysis of the flow field. Moreover, we find that the probability density functions of pair separations at times corresponding to the Richardson scaling law are self-similar and that their shape is a stretched exponential, thus suggesting that the relative dispersion is not controlled by Levy flights.