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

TL;DR

The paper critically examines Zhang et al.'s grain-shape correction to bedload transport by (i) analytically showing the Navier-slip approximation via artificial boundary-shift is not physically valid due to boundary-layer thicknesses, and (ii) performing independent DNS-DEM tests that reveal overestimation of the drag coefficient when using the artificial-shrinkage method. It then demonstrates that Zhang et al.'s data can be interpreted by a null-hypothesis model without grain-shape correction when recast in transformed variables, implying the observed trends arise from the transformed system rather than actual grain-shape effects. Consequently, the claimed grain-shape correction to bedload transport remains unsupported by physically realistic simulations, and a grain-shape–free explanation suffices to describe the data. The work highlights the need for physically consistent approaches to incorporating grain shape into bedload transport models and casts doubt on the utility of the artificial-shrinkage method for exploring parameter spaces relevant to turbulent bedload transport.

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.

Figures (3)

• Figure 1: The "measured" settling drag coefficient $C_{D_\mathrm{settle}}$ obtained from equation (\ref{['CDsettle']}) approximately captures the expected behavior of $C_{D_\mathrm{settle}}$ predicted by equation (\ref{['CdEmp']}) after Feng10. In both equations, $C_{D_\mathrm{settle}}$ is calculated using the settling velocities $\omega_s$ determined from DNS-DEM simulations of a settling sphere for condition 1 (close to Stokes flow) and various slip lengths $l$. Note that, to work well, $l$ should be smaller than the mesh grid size $\Delta x$, which explains the slightly increasing deviation from the expected value with increasing $l$.
• Figure 2: Settling drag coefficient $C_{D_\mathrm{settle}}$ obtained from equation (\ref{['CDsettle']}) for condition 2, using the settling velocities $\omega_s$ determined from DNS-DEM simulations of a settling sphere, versus nondimensionalized slip length $l/d_p$. The blue symbols correspond to actual Navier-slip boundary conditions on the sphere surface, the red symbols to the approximation from the artificial-shrinkage method by Zhangetal25, where a no-slip condition is applied to the surface of a virtual shrunk sphere with diameter $d^\prime_p=d_p-2l$. Note that the values of $C_{D_\mathrm{settle}}$ for the open blue symbols are less reliable and should be treated with caution, since the slip length $l$ exceeds the mesh grid size $\Delta x$.
• Figure 3: Test of null hypothesis model, equation (\ref{['Q2']}), against varying-shrinkage simulation data by Zhangetal25 for natural gravel (NG) grains in a narrow-flume ("flume") or wide-channel ("wide") configuration. The symbol code is the same as in their figures 7(c) and 7(d). Those of the symbols of their figures 7(c) and 7(d) that do not appear in the present plot are from experiments or spherical grain (SP) conditions for which no shrunk-grain simulations were carried out.