  We present direct numerical simulation results of turbulent open channel flow at bulk Reynolds numbers up to 12000, coupled with (passive) scalar transport at Schmidt numbers up to 200. Care is taken to capture the very large scale motions which appear already for relatively modest Reynolds numbers. The transfer velocity at the flat, free surface is found to scale with the Schmidt number to the power "-1/2", in accordance with previous studies and theoretical predictions for uncontaminated surfaces. The scaling of the transfer velocity with Reynolds number is found to vary, depending on the Reynolds number definition used. To compare the present results with those obtained in other systems, we define a turbulent Reynolds number at the edge of the surface-influenced layer. This allows us to probe the two-regime model of Theofanous [Turbulent mass transfer at free, gas-liquid interfaces, with applications to open-channel, bubble and jet flows. Int. J. Heat Mass Transfer 19, 613--624, 1976], which is found to correctly predict that small-scale vortices significantly affect the mass transfer for turbulent Reynolds numbers larger than 500. It is further established that the root-mean-square of the surface divergence is, on average, proportional to the mean transfer velocity. However, the spatial correlation between instantaneous surface divergence and transfer velocity tends to decrease with increasing Schmidt number and increase with increasing Reynolds number. The latter is shown to be caused by an enhancement of the correlation in high-speed regions, which in turn is linked to the spatial distribution of surface-parallel vortices. 
Direct numerical simulation of turbulent mass transfer at the surface of   an open channel flow