Transport of Oil Droplets in the Upper Ocean: Impact of the Eddy Diffusivity

The transport of oil droplets following a surface oil spill was investigated using a uniform vertical eddy diffusivity model and the K-profile parameterization model, which assumes a maximum K value at 1/3 depth of the mixed layer. The initial droplet size distribution was obtained based on the Delvigne and Sweeney (1988, https://doi.org/10.1007/s13131-013-0364-7) model. Using a uniform eddy diffusivity K_ave, an exact analytical solution was used to produce the transient and steady state profile of the concentration of droplets of all sizes. It was found that the concentration at the surface is proportional to the droplet rise velocity and inversely proportional to K_ave. Thus, small droplets (smaller than 100 μm) do not persist at the water surface. It was found that K-profile parameterization produces smaller concentrations at the water surface than the uniform K model. The impact of waves was introduced into the K-profile parameterization model through a roughness height, z_o, that is comparable to the wave height. The investigation herein reveals that the Delvigne and Sweeney approach, commonly used in oil spill modeling, is not sufficient to predict the oil droplet size distribution, and that one needs to use a vertical eddy diffusivity to accurately predict the transport in the following hours and days. A new dimensionless formulation was provided to generalize the results, and showed that transport depends on three major parameters, the water friction speed, the mixed layer depth, and the droplet diameter.