Turbulent diffusivity and effective rise velocity of buoyant particles in a free-surface boundary layer

Predicting the transport of buoyant particles in a free-surface boundary layer is important to the study of many environmental systems, including microplastics in the upper ocean. Current transport models, adapted from sediment transport theory, typically rely on assumptions of a quiescent rise velocity and gradient diffusion with an uncertain turbulent Schmidt number $Sc_t$. Here, we test this type of model against experiments by studying the vertical mixing of near-neutrally buoyant, finite-size spheres, rods, and disks in a wind-driven, wavy free-surface flow. We measure particle diffusivity directly from Lagrangian trajectories and compare against Eulerian concentration-based estimates. Overall, we find that particle buoyancy is the main control on the diffusivity, and that the diffusivity decreases as particle rise velocity grows relative to the turbulent fluctuations. These observations we find to be consistent with the crossing-trajectories theory, even in the presence of waves. In addition, we find that inferring the diffusivity from concentration profiles with an assumed quiescent rise velocity overestimates the diffusivity by up to a factor of $5$, consistent with effective rise velocities up to $80\%$ lower than the corresponding quiescent values. We also directly measure $Sc_t \approx 1$ for the neutrally-buoyant particles and $Sc_t > 1$ for the buoyant particles. Together, these experimental results demonstrate how standard model closures may be biased in both their diffusivities and rise velocities when applied to buoyant particles at the ocean surface.