Bed shear stress in bedload transport: new methods of sidewall correction and bed surface determination

The study-to-study variability of bedload flux measurements in turbulent sediment transport borders an order of magnitude, even for idealized laboratory conditions. This uncertainty stems from physically poorly supported, empirical methods to account for channel geometry effects in the determination of the transport-driving bed shear stress and from study-to-study grain shape variations. Here, we derive a universal procedure of bed shear stress determination. It consists of a physically-based definition of the bed surface and a channel sidewall correction that does largely not rely on empirical elements, except for well-established scaling coefficients associated with Kolmogorov's theory of turbulence. Application of this procedure to bedload transport of spherical grains---to rule out grain shape effects---collapses data from existing laboratory measurements and grain-resolved CFD-DEM simulations for various channel geometries onto a single curve. By contrast, classical sidewall corrections, such as the Einstein-Johnson method, as well as an alternative bed surface definition, are unable to universally capture these data, especially those from shallow or very narrow channel flows. The sidewall correction method is also independently supported by data from systematic experiments of open-channel flows over fixed rough beds with various width-to-depth ratios.