Relative Dispersion in Free Surface Turbulence*

Transport along the free surface of turbulent flows is crucial in nature and industrial settings, but our understanding of this process is complicated by the fact that the surface velocity field is compressible. Here we report on an experimental study in which Lagrangian tracking is applied to millions of microscopic particles floating on the free surface of turbulent water. The experiments are carried out in a 2 cubic meter tank with randomly actuated jet arrays, leaving the free surface marginally deformed by the turbulence. We find that the surface divergence is prevalently positive at small (near-dissipative) scales, indicating fast separation rates of nearby particles. Based on this observation, we present a generalization of pair dispersion by classifying particle pairs based on their initial separation rate. When this does not exceed the relative velocity prescribed by Kolmogorov theory, the expected scaling of the Eulerian velocity structure functions is retrieved. Moreover, the separation of such particles in the inertial sub-range is compared with Richardson's theory. These findings highlight the degree of applicability of classic results derived for incompressible turbulence to free-surface transport, while revealing specific features of this type of flows.