Clustering dynamics of Lagrangian tracers in free-surface flows

We study the formation of clusters of passive Lagrangian tracers in a non-smooth turbulent flow in a flat free-slip surface as a model for particle dynamics on free surfaces. Single particle and pair dispersion show different behavior for short and large times: on short times particles cluster exponentially rapidly until patches of the size of the divergence correlation length are depleted; on larger times the pair dispersion is dominated by almost ballistic hopping between clusters. We also find that the distribution of particle density is close to algebraic and can trace this back to the exponential distribution of the divergence field of the surface flow.