Small-scale dynamics and structure of free-surface turbulence

The dynamics of small-scale structures in free-surface turbulence is crucial to large-scale phenomena in natural and industrial environments. Here, we conduct experiments on the quasi-flat free surface of a zero-mean-flow turbulent water tank over the Reynolds number range $Re_{\lambda } = 207$ –312. By seeding microscopic floating particles at high concentrations, the fine scales of the flow and the velocity-gradient tensor are resolved. A kinematic relation is derived expressing the contribution of surface divergence and vorticity to the dissipation rate. The probability density functions of divergence, vorticity and strain rate collapse once normalised by the Kolmogorov scales. Their magnitude displays strong intermittency and follows chi-square distributions with power-law tails at small values. The topology of high-intensity events and two-point statistics indicate that the surface divergence is characterised by dissipative spatial and temporal scales, while the high-vorticity and high-strain-rate regions are larger, long-lived, concurrent and elongated. The second-order velocity structure functions obey the classic Kolmogorov scaling in the inertial range when the dissipation rate on the surface is considered, with a different numerical constant than in three-dimensional turbulence. The cross-correlation among divergence, vorticity and strain rate indicates that the surface-attached vortices are strengthened during downwellings and diffuse when those dissipate. Sources (sinks) in the surface velocity fields are associated with strong (weak) surface-parallel stretching and compression along perpendicular directions. The floating particles cluster over spatial and temporal scales larger than those of the sinks. These results demonstrate that, compared with three-dimensional turbulence, in free-surface turbulence the energetic scales leave a stronger imprint on the small-scale quantities.