A three-species model of aeolian saltation incorporating cooperative splash

Most aeolian sand transport models incorporate a so-called splash function that describes the number and velocity of particles ejected by the splash of an impacting particle. It is usually obtained from experiments or simulations in which an incident grain is shot onto a static granular packing. However, it has recently been discovered that, during aeolian sand transport, the bed cannot be considered as static, since it cannot completely recover between successive impacts. This led to a correction of the splash function accounting for cooperative effects [1], which were shown to be responsible for an anomalous third-root scaling of the sand flux with the particle-fluid density ratio s, observed in discrete-element-method-based simulations of aeolian sand transport across six orders of magnitude of s [2]. The model by [1] represents the aeolian transport layer by two species: high-energy saltons that eject low-energy reptons upon impact. While it quantitatively captures measurements and the simulated sand flux scaling, it does not recover the scaling laws of the simulated transport threshold and vertical flux at the bed. Here, we improve the model by [1] by means of a three-species saltation model. The additional species, called leapers, represent the fastest reptons, ejected by saltons in rare extreme ejection events. Together, saltons and leapers quantitatively reproduce the threshold and sand flux scaling behaviors, whereas reptons are predominantly responsible for the vertical bed surface fluxes seen in the simulations.

[1] Tholen, Pähtz, Kamath, Parteli, Kroy, Anomalous scaling of aeolian sand transport reveals coupling to bed rheology, Physical Review Letters 130 (5), 058204 (2023). https://doi.org/10.1103/PhysRevLett.130.058204

[2] Pähtz, Durán, Scaling laws for planetary sediment transport from DEM-RANS numerical simulations, Journal of Fluid Mechanics 963, A20 (2023). https://doi.org/10.1017/jfm.2023.343