Spatial and temporal scales of free-surface turbulence

We study the motion of tracer particles floating on the free surface of turbulent water. Experiments are carried out in a large open channel flow facility, over the fully developed region behind a square mesh grid. Millions of floating tracer trajectories are reconstructed by particle tracking velocimetry, allowing to explore single-point and two-point statistics in both the Eulerian and the Lagrangian frames. We focus on a regime in which turbulence is not strong enough to significantly deform the free surface against gravity and surface tension. Despite the tracer being confined to a quasi-flat material surface, their motion is consistent with the canons of Kolmogorov’s classic theory of homogeneous isotropic turbulence. This is revealed by their velocity fluctuations, accelerations, and velocity structure functions, and by Lagrangian dispersion displaying the expected ballistic-to-diffusive transition. The key parameters of the free-surface flow, including the turbulence dissipation rate and integral length scale, closely match those of the sub-surface turbulence as measured by particle image velocimetry. The floating tracers cluster due to the compressibility of the free surface, and do so over spatial and temporal scales even larger than the integral scales of the turbulence.