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 of finite-size objects undergoes a sharp change for values of the object size close to the flow forcing scale. For objects larger than the forcing scale (L_f), the diffusion coefficient is proportional to the flow energy and inversely proportional to the size. This behaviour, observed in a chaotic macroscopic system is reminiscent of a fluctuation-dissipation relation. In contrast, the diffusion coefficient of smaller objects (r_p) follows. 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. 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.