On the testing of grain shape corrections to bedload transport equations with grain-resolved numerical simulations

Abstract

Using grain-resolved LES-DEM simulations, Zhang et al. (J. Geophys. Res. Earth Surf. 130, e2024JF007937, 2025) aimed to validate a grain-shape-corrected bedload transport equation proposed earlier by the same group. It states that grain shape effects are captured through a modified Shields number that depends, among others, on the drag coefficient, $C_{D_\mathrm{settle}}$, determined from the force balance for a grain settling in a fluid at rest. To independently vary $C_{D_\mathrm{settle}}$ in their simulations, the authors changed the boundary conditions on the grains' surfaces: By artificially shifting the locations of the no-slip conditions from the actual grain surface to a virtual surface a distance $l$ into the grain interior, they hoped to well approximate Navier-slip conditions with a slip length $l$. Here, we argue that this approximation is appropriate only if the thickness of the boundary layer that forms around the virtual surface is much larger than $l$, which we demonstrate was not the case for the authors' simulations. In particular, using independent DNS-DEM grain settling simulations for the same hydrodynamic conditions, we directly show that this approximation substantially overestimates the value of $C_{D_\mathrm{settle}}$ of a Navier-slip sphere. This implies that the conditions created with their artificial method do not correspond to physically realistic scenarios and therefore do not support the authors' grain shape correction. To support this conclusion, we demonstrate that their entire numerical data can be alternatively explained by a simple null hypothesis model, without grain shape correction, based on the virtual-grain rather than the actual-grain size.