Wind modification and bed response during saltation of sand in air

Summary

A model of eolian sediment transport has been constructed, a special case of which is that corresponding to sand-sized mineral grains subjected to moderate winds: saltation. The model consists of four compartments corresponding to (1) aerodynamic entrainment, (2) grain trajectories, (3) grain-bed impacts, and (4) momentum extraction from the wind. Each sub-model encapsulates the physics of the process, and is constrained where necessary by experimental data. When combined, the full model allows simulation of eolian saltation from inception by aerodynamic entrainment to steady state.

Many observed characteristics of natural saltation systems are reproduced by the simulations. Steady state mass flux and concentration profiles all display rapid decay with height above the bed, representing the preponderance of short, low-energy trajectories in the saltation population. Yet the role of less abundant, longer, higher energy trajectories is a strong one: at steady state the entire population of saltating grains is controlled by high-energy bed impacts rather than aerodynamic entrainment. Because the nature of the grain splash process is such that high-energy impacts are much more efficient at ejecting other grains from the bed, the response time of the system to changes in wind velocity is determined by the hop time of these long trajectories. Several hop times, or roughly 1–2 seconds, are required.

Varying wind velocity among the simulation runs allows mapping of the relation between steady state mass flux and wind velocity-the mass flux “law”-which may be expressed as a power law of the excess shear velocity. The hysteresis that led Bagnold to define both fluid and impact thresholds for saltation is apparent, reinforcing our conclusion that it is the impacts of saltating grains that supports the large population of saltating grains at steady state.