Tunable diffusion in wave-driven two-dimensional turbulence

We report an abrupt change in the diffusive transport of inertial objects in wave-driven turbulence as a function of the object size. In these non-equilibrium two-dimensional flows, the turbulent diffusion coefficient D of finite-size objects undergoes a sharp change for values of the object size r(p) close to the flow forcing scale L-f. For objects larger than the forcing scale (r(p) > L-f), the diffusion coefficient is proportional to the flow energy U-2 and inversely proportional to the size r(p). This behaviour, D similar to U-2/r(p), observed in a chaotic macroscopic system is reminiscent of a fluctuation-dissipation relation. In contrast, the diffusion coefficient of smaller objects (r(p) < L-f) follows D similar to U/r(p)(0.35). This result does not allow simple analogies to be drawn but instead it reflects strong coupling of the small objects with the fabric and memory of the out-of-equilibrium flow. In these turbulent flows, the flow structure is dominated by transient but long-living bundles of fluid particle trajectories executing random walk. The characteristic widths of the bundles are close to Lf. We propose a simple phenomenology in which large objects interact with many bundles. This interaction with many degrees of freedom is the source of the fluctuation-dissipation-like relation. In contrast, smaller objects are advected within coherent bundles, resulting in diffusion properties closely related to those of fluid tracers.