Transport of passive scalar in turbulent shear flow under a clean or surfactant-contaminated free surface

Abstract

Direct numerical simulation is performed to study the turbulent transport of passive scalars near clean and surfactant-contaminated free surfaces. As a canonical problem, a turbulent shear flow interacting with a flat free surface is considered, with a focus on the effect of splats and anti-splats on the scalar transport processes. Using conditional averaging of strong surface flux events, it is shown that these are associated with coherent hairpin vortex structures emerging from the shear flow. The upwelling at the splat side of the oblique hairpin vortices greatly enhances the scalar surface flux. In the presence of surfactants, the splats at the surface are suppressed by the surface tension gradients caused by spatial variation of surfactant concentration; as a result, scalar flux is reduced. Conditional averaging of weak surface flux events shows that these are caused by anti-splats with which surface-connected vortices are often associated. When surfactants are present, the downdraught transport at the surface-connected vortices is weakened. Turbulence statistics of the velocity and scalar fields are performed in terms of mean and fluctuation profiles, scalar flux, turbulent diffusivity and scalar variance budget. Using surface layer quantification based on an analytical similarity solution of the mean shear flow, it is shown that the depth of the scalar statistics variation is scaled on the basis of the Schmidt number. In the presence of surfactants, the scalar statistics have the characteristics of those near a solid wall in contrast to those near a clean surface, which leads to thickened scalar boundary layer and reduced surface flux.