Free‐surface turbulence and mass transfer in a channel flow

Free‐surface turbulence in a fully developed, open‐channel flow was measured for Reynolds numbers of 8,500–45,000. An analysis method of the 2‐ D divergence on the free surface has been developed to extract Hanratty's β values, or the velocity gradient into the free surface, from these measurements. Hanratty's β is the parameter that relates most directly to the turbulence effect on the liquid‐film coefficient. Its measurement is a direct measurement of surface renewal. The spatial scales of β were 3 to 5 times smaller than those of the large upwelling events (boils) normally identified as surface renewal. The hypothesis is that the large upwelling events do not have the high‐vorticity gradients associated with large β values. Instead, the locations of high‐vorticity gradients on the free surface will also create the divergence required for high β values, occurring at the edges of a large upwelling event. Because the β frequency spectrum has properties to characterize the liquid‐film coefficient, it was normalized to be determined from its maximum value, the wave number of this maximum value, and a shape factor used to scale the frequency. Measurements of the liquid‐film coefficient from prior studies were also used to characterize the liquid‐film coefficient by measured β values for this nonsheared surface. The larger β scales predominantly influence the liquid‐film coefficient, in contrast to a previous study of a shear‐free surface published by McCready et al. in 1986, where all β frequencies were equally important. Generally, higher frequency turbulence is more significant at a sheared water surface than at a water surface with minimal shear stress.