We perform direct numerical simulation to study the transport of gas and heat as passive scalars in free-surface turbulence. Our analysis focuses on the surface age of surface fluid particles, i.e. the time elapsed since the last surface renewal they experienced. Using Lagrangian tracing of fluid particles combined with heat diffusion analysis, we are able to directly quantify surface age to illustrate scalar characteristics at different stages of interfacial transfer. Results show that at the early stage of surface renewal, vertical advection associated with upwellings greatly enhances surface gas flux; random surface renewal model does not apply at this stage when most of the interfacial gas transfer occurs. After a fluid particle leaves the upwelling region, it may enter a nearby downwelling region immediately, where the gas flux is sharply reduced but the variation in surface temperature is small; alternatively, the fluid particle may travel along the surface for some time before it is absorbed by a downwelling, where the surface temperature has changed significantly due to long duration of diffusion and the gas flux is also reduced. To gain further insight into the relationships between surface velocity and scalar quantities, we perform a statistical analysis of upwellings using clustering and nonlinear regression. With this analysis, we are able to provide qualitative and quantitative descriptions of the skewed probability density functions associated with the surface divergence, temperature and gas flux that support our physics-based investigation of surface renewal and surface age.

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.

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