Contributions of different scales of turbulent motions to the mean wall-shear stress in open channel flows at low-to-moderate Reynolds numbers

Smooth-walled open channel flow datasets, covering both the direct numerical simulation and experimental measurements with a friction Reynolds number Re-tau at a low-to-moderate level of 550 similar to 2400, are adopted to investigate the contributions of different scale motions to the mean wall-shear stress in open channel flows (OCFs). The FIK identity decomposition method by Fukagata et al. (Phys. Fluids, vol. 14, 2002, L73) combined with a scale decomposition is chosen for this research. To see whether/how the contributions in OCFs differ with those in closed channel flows (CCFs), comparisons between the two flows are also made. The scale-decomposed 'turbulent' contribution results of present OCFs exhibit two dominant contribution modes (i.e. large-scale motions (LSMs) and very-large-scale motions (VLSMs)) at a streamwise wavelength lambda(x) = 1 similar to 2h and O(10h), where h is the water depth. The large scales with lambda(x) > 3h and lambda(x) > 10h are demonstrated to contribute to over 40% and 20% of the mean wall-shear stress, respectively. Compared with CCFs, slightly higher and lower contributions in the lambda(x) > O(10h) and lambda(x) < O(10h) wavelength ranges are observed in OCFs, revealing the important free-surface effects in OCFs. Possible mechanisms are discussed to lend support for the observed differences between the two flows.