Simulation of vertical dispersion of oil droplets by Langmuir supercells through a Reynolds-averaged Eulerian formulation combined with Lagrangian particle tracking

Langmuir supercells (LS) are full-depth Langmuir circulations in unstratified shallow shelves. A Reynolds-averaged Eulerian formulation is developed resolving LS as a secondary component to the wind-driven mean shear current. This formulation is combined with Lagrangian particle tracking to investigate oil droplet entrainment induced by LS as a function of wind stress. Two cases are simulated, one in which 500-μm oil droplets are released into a steady field of LS generated by a wind stress of 0.1 N m⁻² and waves of intermediate wavelength λ=6H where H=15 m is the water column depth, significant amplitude of 0.6 m and period of 8 s. In the second case, the 500-μm oil droplets are released into a steady field of LS generated by the same wave forcing but with a weaker wind stress of 0.025 N m⁻². It is found that the greater wind stress leads to LS able to spread the droplets throughout upwelling and downwelling limbs of the cells within the first 80 minutes after release. The weaker wind leads to weaker LS that, within the same time after release, limit the dispersion of the droplets to the downwelling limbs of the cells forming Stommel retention zones for a prolonged time.