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 beta values, or the velocity gradient into the free surface, from these measurements. Hanratty's beta 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 beta 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 beta values. Instead, the locations of high-vorticity gradients on the free surface will also create the divergence required for high beta values, occurring at the edges of a large upwelling event. Because the beta 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 beta values for this nonsheared surface. The larger beta 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 beta 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.