Evolution of oil droplet size distributions entrained by breaking waves

Lab experiments were conducted to investigate the time development of oil droplet size distribution and volume-based median diameter, d₅₀^v, under a spilling breaking wave. Results show that the size distribution varies continuously during the experiment. To aid the discussion, we introduce a conceptual framework describing the phases of the entrainment process, comprising injection, breakup, turbulent transport, and buoyant rise and resurfacing. A one-dimensional model was implemented, describing the turbulent transport and buoyant rise phases based on a stochastic transport equation and vertical diffusivity profile: These are the same vertical transport mechanisms found in operational oil spill models. It was found to reproduce the time development of the d₅₀^v after the breakup phase well, when initialized with a suitably fitted log-normal droplet size distribution. The measurements showed a decrease in d₅₀^v with time, after the breakup phase, as t^-0.537 and t^-0.443 at two different sampling locations. The model can reproduce these results, but is sensitive to the initial size distribution, both initial median diameter and standard deviation. Our results highlight the inherent challenges in measuring oil droplet size distributions that change with both time and spatial location, and never truly reach an equilibrium. We believe that a way forward is to use models actively in the interpretation of experimental results, acting as "digital twins" of the system studied in the lab.