  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.
