Lagrangian simulation of oil droplets transport due to regular waves

Dispersed oils (i.e., oil droplets) at sea are transported by convection due to waves and buoyancy and by turbulent diffusion. This work follows the common approach in the oil community of using a Lagrangian approach instead of the Eulerian approach. Our focus was on small scale simulation of oil plumes subjected to regular waves. Stokes' theory was used to obtain analytical expressions for wave kinematics. The velocity above the Mean Water Level was obtained using a second order Taylor's expansion of the velocity at the MWL. Five hundred droplets were used to simulate the plume for a duration of 60 wave periods. A Monte Carlo framework (300 simulations) was used to compute theoretical mean and variance of plumes. In addition, we introduced a novel dimensionless formulation, whose main advantage was to allow one to report distances in terms of the wave length and times in terms of the wave period. We found that the Stokes' drift was the major mechanism for horizontal transport. We also found that lighter oils propagate faster but spread less than heavier oils. Increasing turbulent diffusion caused the plume to disperse deeper in the water column and to propagate less forward. The spreading in both vertical and horizontal directions increased with an increase in turbulent diffusion. The increase in wave slope (or wave steepness) caused, in general, an increase in the downward and horizontal transport. In the context of mixing in the water column, the dimensionless formulation showed that small steepness waves with a large turbulent diffusion coefficient could result in essentially the same spreading as large steepness waves with a small turbulent diffusion coefficient.