This work investigates the accuracy of commonly used bed-load transport models when applied in combination with high-resolution Navier-Stokes solvers. Empirical bed-load models predict the transport rate of sediments based on the average bottom shear-stress, while eddy-resolving approaches allow for a space- and time-dependent description of the bottom shear-stress distribution. We discuss the effect that a fine-graining of the stress distribution provided by the flow solver has on the transport model prediction, and we examine the space and time scales at which the averaged values of the transport rate, obtained using the local stress distribution, converge to the transport rate predicted using the average stress. To this aim, we performed Direct Numerical Simulation of a channel flow and used the resulting database to mimic Wall-Resolved and Wall-Modelled Large-Eddy Simulations. We compared the prediction of several bed-load transport models to experimental measurements in order to identify and highlight the limitations that stem from the coupling of these models with eddy-resolving techniques. We find that for small values of the Shields parameter (ratio of viscous and gravitational forces) the fine spatial and temporal resolution of wall-resolved simulations can yield overestimation of the bed-load transport rate; whereas more coarse-grained methods, such as wall-modelled Large Eddy Simulation, result in improved predictions. We also show that a short-time averaging of the force exerted by the fluid on the sediments, which we tested in three different configurations (channel flow with smooth and rough walls and flow over an idealized two-dimensional river dune), improves the accuracy of the bed-load transport predictions, thus providing indications about the flow scales that control the transport process.
