Wind modification and bed response during saltation of sand in air

Abstract

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 procees, 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.

An improved parameterization of wind‐blown sand flux on Mars that includes the effect of hysteresis

“…The trajectory-averaged drag force in the horizontal direction (F D;x ), which has a double overbar to represent the average over the trajectory of the 'average' saltating particle, can be approximated as [Anderson and Haff, 1991] …”

Wind shear with a blowing‐sand boundary layer

“…[13] The force exerted on wind by moving particles results in deviation of the wind-velocity profile from the logarithmic law and variation of the wind-shear stress as a function of height [Anderson and Haff, 1991]. The shear stress at different heights can be calculated from the velocity profiles of the wind.…”

“…However, in the presence of aeolian saltation, the wind-shear stress no longer holds constant because saltating particles participate in momentum exchange with the airflow [e.g., Owen, 1964;Anderson and Haff, 1991;McKenna Neuman and Nickling, 1994]. Consequently, the wind profile within an aeolian saltation layer must be modified, which exhibits the gross effect of the interaction between the airflow and the moving particles.…”

“…Having noticed the presence of a gradually curved transition in the velocity profile [Gerety, 1985], some researchers [e.g., McKenna Neuman and Nickling, 1994;Dong et al, 2003] have used a single power relation instead of a segmented log-linear function to describe the full velocity profile. Although the last two decades have witnessed considerable progress in calculating wind profiles during sediment transport by analyzing particle trajectories and the forces exerted on the wind by saltating particles [Ungar and Haff, 1987;Anderson and Haff, 1991;McEwan andWilletts, 1991, 1993;Li et al, 2003], most of the theoretical calculations were based on the movement of individual particles whose behavior in the air was poorly understood, especially in terms of the interaction between moving particles.…”

Aeolian sand transport: a wind tunnel model

“…They suggested the upward convex wind profiles in the blowing sand cloud. Recent self-regulatory models of saltation (Anderson and Haff, 1991;McEwan and Willetts, 1991;McEwan, 1993) predict that the velocity profile is convex, particularly within the lowest 10 mm because of variation with height of fluid and grainborne shear stress. Velocity profiles reported from other published sources show that the convexity includes the whole of the saltation cloud (McKenna Neuman and Nickling, 1994).…”