Addressing bedload flux variability due to grain shape effects and experimental channel geometry

Abstract

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 method of bed shear stress determination. It consists of a granular-physics-based definition of the bed surface and a channel sidewall correction based on linking Reynolds stress to bulk flow properties via Kolmog\'orov's theory of turbulence. Application of this method 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. In contrast, classical sidewall corrections, as well as an alternative bed surface definition, are unable to universally capture these data, especially those from shallow or very narrow channel flows. We then apply our method to an extended grain-shape-controlled data compilation, complemented by literature data for non-spherical grains and from grain-unresolved CFD-DEM simulations. This compilation covers a very diverse range of transport conditions, ranging from very narrow to infinitely wide channels, from shallow to deep channel flows, from mild to steep bed slopes, and from weak to intense transport. We generalize an existing physical bedload flux model to account for grain shape effects and show that it explains almost all the compiled data within a factor of only $1.3$.