Particle-resolved simulations of antidune migration in supercritical flows

Antidunes are an important feature in the morphodynamics of streams over steep slopes. These bed forms are short-wave periodic disturbances that develop on the surface of loose granular beds in response to the interaction with supercritical and near-critical shallow, turbulent flows. They arise in fluvial, coastal, and submarine environments and are closely tied to the resulting flow resistance, turbulence, and sediment transport. Antidunes are the only type of bedform that can migrate upstream under the presence of a free surface. This seems counterintuitive and has caught strong interest in hydraulic research. However, up to date little is known about the migration mechanism in connection to turbulence, bed morphology, and sediment transport, because of the challenging supercritical flow conditions, often associated to low submergences. This is in part related to the inherent technical challenges to reproduce rapid flows over an erodible bed in laboratory flumes, as well as to the difficulties to perform non-intrusive measurements. Consequently, experimental data sets in published literature are scarce. Numerical simulations of supercritical flows above an erodible bed can therefore constitute a methodological alternative for the study of antidunes. Such simulations, however, need to properly reflect the interplay of the fluid phase, the sediment particles, and the gas phase above the free surface. In this work we propose to use particle-resolved direct numerical simulations (pr-DNS) in conjunction with a deformable fluid surface to simulate the formation and propagation of upstream migrating antidunes in supercritical flows with high fidelity. We aim to numerically reproduce the experimental campaign recently reported by Pascal et al. (2021), who managed to measure the propagation of upstream migrating antidunes with a high spatial and temporal resolution. For this, we combine the lattice Boltzmann method with the discrete element method to simulate the fluid–particle and particle–particle dynamics (Rettinger & Rüde, 2022) and extend it with a volume of fluid scheme (Schwarzmeier et al., 2023) to track the strongly deformable free fluid surface. The parameter choices of Pascal et al. (2021), with coarse sediment grains and low relative submergence of the particles, allow for a direct overlap of experimental conditions with pr-DNS. In this manner, our simulations successfully close the gap between river morphodynamics experiments and pr-DNS, to couple bedform and free-surface interactions with large-scale simulations consisting of a sediment bed comprising thousands of particles in unidirectional, supercritical turbulent flows.

Schwarzmeier, C., Holzer, M., Mitchell, T., Lehmann, M., Häusl, F. & Rüde, U. (2023). Comparison of free-surface and conservative Allen–Cahn phase-field lattice Boltzmann method. Journal of Computational Physics 473, 111753 .

Rettinger, C., & Rüde, U. (2022) An efficient four-way coupled lattice Boltzmann – discrete element method for fully resolved simulations of particle-laden flows. Journal of Computational Physics 453, 110942

Pascal, I., Ancey, C., & Bohorquez, P. (2021). The variability of antidune morphodynamics on steep slopes. Earth Surface Processes and Landforms, 46(9), 1750-1765.