| 06 Nov 2025
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, CDsettle, determined from the force balance for a grain settling in a fluid at rest. To independently vary CDsettle 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 CDsettle 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.
Competing interests: O.D. is a member of the editorial board of Earth Surface Dynamics.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.
This manuscript examines the validity of an “artificial-shrinkage” method used in grain-resolved bedload transport simulations to mimic Navier-slip boundary conditions. The authors combine analytical boundary-layer estimates with independent DNS-DEM settling simulations to show that the imposed slip lengths are not small relative to the boundary-layer thickness, meaning the method cannot reproduce true Navier-slip behavior. Their results demonstrate that the resulting drag coefficients are substantially overestimated and do not correspond to any physically realistic fluid–particle interaction. They further present a null-hypothesis model showing that the trends in Zhang et al. (2025) can be reproduced without invoking grain-shape corrections, but simply by accounting for the virtual grain size used in the artificial shrinkage. Overall, the manuscript argues convincingly that the artificial-shrinkage method is inappropriate for testing grain-shape corrections in bedload transport equations. This reviewer has nothing to add to the arguments provided here.