Two-dimensional turbulence and dispersion in a freely decaying system

We report experimental results obtained on freely decaying two-dimensional turbulence. The flow is produced in a thin stratified layer of electrolyte, using an electromagnetic forcing. The velocity and vorticity fields are me asured using a particle image velocimetry technique. The study of the tempo ral evolution of the system confirms in detail the scaling theory of Carnev ale ct al. [Phys. Rev. Lett. 66, 2735 (1991)]; the experimental value we fi nd for the exponent characterizing the decay of the vortex density is xi=0. 7+/-0.1. We further sigma(v)(2) Of the vortices. We measure the collision t ime tau, the mean free path lambda, and the mean square displacement l, fin d the following laws: tau similar to t(0.57), lambda similar to t(0.45), an d sigma(v)(2)similar to t(1.3). The statistics of passive particles (albeit virtual) in the system is also studied. They move hyperdiffusively, with a n exponent similar to that obtained for the vortex motion. The dispersion o f the particles is controlled by Levy flights, produced by the jets formed by the dipoles. The distribution of flight times t(f) is t(f)(-2.6). Furthe r analysis of the data indicates that the vortices dipoles. undergo collisi ons whose geometrical aspects are analogous to those of an ordinary gas, an d their motion is essentially Brownian diffusion in an expanding geometry. We finally underline the close relationship between the decay of turbulence and the dispersion phenomena. [S1063-651X(98)07410-8].