A Conceptual Model of Energy Partitioning in the Collision of Saltating Grains with an Unconsolidated Sediment Bed

Abstract

Abstract Grain-bed collision is a key component of saltation, but substantial uncertainty remains regarding many aspects of this process. Previous empirical work is used to develop a conceptual model of this process that accounts for the partitioning of impact energy between rebounding grains and the bed. The model envisions two distinct collision regimes: (i) a quasi-elastic regime at low impact speeds and (ii) an inelastic regime at high impact speeds. In the quasi-elastic regime, colliding grains retain a constant proportion of their kinetic energy, and thus rebound at speeds that are proportional to the impact speed and shear velocity. In the inelastic regime, colliding grains retain a fixed and limited amount of kinetic energy, transferring any excess above this limit to the bed. Rebound speeds are thus constant and independent of both impact speed and shear velocity. Impact energy transferred to the bed is expended in “deformation” (i.e., ejection, rearrangement, etc. of bed grains). These two collision regimes are separated by a critical impact speed/kinetic energy level that is controlled by bed texture (more directly, by the inertia or resistance to motion of the bed grains). Field measurements under near-threshold conditions are found to correspond to the higher speed inelastic regime, suggesting that inelastic collisions predominate in aeolian saltation on loose, unconsolidated sand beds. The quasi-elastic regime might therefore only be pertinent for reptating grains, or in situations in which interparticle bonding (from crusts, surface moisture, etc.) increases the “effective” inertia of bed grains and thus the critical impact speed separating the two regimes. It is also shown that rebound speed in the inelastic regime varies in inverse proportion to grain size (mass), so that particles rebound with an approximately constant level of kinetic energy regardless of size. Thus, larger grains will rebound at smaller speeds and follow lower, shorter trajectories, providing a mechanism that accounts for the commonly observed size sorting of grains subjected to aeolian saltation.