The trouble with shear stress

Predicted bedload fluxes often have large errors partly because calculations usually do not include spatial and temporal flow variability. Sediment motion is driven by a temporal distribution of applied fluid forces, which are often simplified into time-averaged flow velocities or shear stresses in sediment transport equations. Spatial variations in these flow parameters are also often neglected. Given the nonlinearities in the relation between flow and sediment flux, the reach-averaged sediment flux calculated with an average velocity or shear stress will not necessarily equal the measured spatially averaged bedload flux. Such spatial and temporal flow variations are ignored with the commonly used reach-averaged shear stress (τ_ds) that is a function of the flow depth and channel slope. To demonstrate the uncertainties with using reach-averaged shear stresses, and even local shear stresses, to predict bedload transport rates, we have three goals. First, we outline the derivations and assumptions involved with commonly used estimates of shear stress. Second, we summarize the literature on the uncertainties involved with using shear stress, and other space- and time-averaged flow parameters, to predict sediment flux. Third, we use a new data set from experiments to add further support to a growing body of literature that suggests τ_ds may not be linked to the mechanics of bedload transport. We show considerable uncertainties exist in estimating a reach-averaged shear stress, by comparing τ_ds and near-bed shear stresses calculated from velocity profiles, Reynolds stresses, and local turbulence. For example, τ_ds was systematically greater than these near-bed stresses even for experiments without large bed roughness. We also find that correlations between local time-averaged sediment fluxes and local Reynolds stresses or turbulence intensities are relatively poor. The near-bed, time-averaged local flow velocity has the strongest relation with the time-averaged local bedload flux because it is closely related to the forces that actually drive sediment transport. However, sediment transport rates in individual experiments could still vary by orders of magnitude for a given value of this flow velocity, suggesting that additional work is needed to identity a parameter, or distributions of parameters, that will best predict sediment fluxes.