  We study the dispersion of light particles floating on a flat shear-free
surface of an open channel in which the flow is turbulent. This configuration
mimics the motion of buoyant matter (e.g. phytoplankton, pollutants or
nutrients) in water bodies when surface waves and ripples are smooth or absent.
We perform direct numerical simulation of turbulence coupled with Lagrangian
particle tracking, considering different values of the shear Reynolds number
(Re{\tau} = 171 and 509) and of the Stokes number (0.06 < St < 1 in viscous
units). Results show that particle buoyancy induces clusters that evolve
towards a long-term fractal distribution in a time much longer than the
Lagrangian integral fluid time scale, indicating that such clusters over-live
the surface turbulent structures which produced them. We quantify cluster
dynamics, crucial when modeling dispersion in free-surface flow turbulence, via
the time evolution of the cluster correlation dimension.
