Analytical model for flux saturation in sediment transport

Added-mass force in dry granular matter

From two-dimensional (2D) numerical simulations of the motion of a circular intruder into a dry granular packing, we provide evidence for a specific force term in the case of unsteady motion in addition to the force corresponding to a steady motion. We show that this additional term is proportional to the acceleration of the intruder relative to the grains as the added-mass force known for simple fluids. This force term corresponds to a variation in the kinetic energy of the surrounding flow and is characterized by a coefficient C_{AM} which is intrinsically linked to the nature of the granular media. An analytical calculation of the added-mass coefficient C_{AM} is developed based on the specific velocity field known for 2D granular flow around a cylinder. The theoretical value is shown to depend on the grain-cylinder size ratio, in good agreement with the measurements from our unsteady simulations.

Improved analytical model for the relaxation process of aeolian sand transport

The process from the initial sand movement to sand flux saturation is described as the relaxation of aeolian sand transport. For this relaxation process, most existing models distinguish the conditions with and without upwind sand flux, therefore lacking in generality. An improved analytical model is proposed in this paper, which incorporates the phenomena of "overshoot" and "equilibrium" and the concept of the region of initiation by fluid, and is able to unify the cases with and without upwind sand flux. Within the proposed model, a new definition of the saturation length is proposed based on the analogy between two damping oscillation models, and its constancy is physically interpreted and verified with wind tunnel experimental data. In comparison with the existing models, the proposed model agrees better with the measurements of the process of sand transport, thereby shedding light on the understanding of aeolian sand transport under complex circumstances.

Toward a large-scale particle-based parallel simulator of Aeolian sand transport, including a model for mobile sand availability

We develop a numerical tool for particle-based simulations of Aeolian sand transport. Our model combines a Discrete-Element-Method for the sand particles with an efficient hydrodynamic description of the average turbulent horizontal wind velocity field over the granular bed, which has been developed in previous work and accounts for the two-way coupling of the granular and fluid phases. However, here we implement our model within the open source library LAMMPS for granular massively parallel simulations and incorporate a new grid coarsening scheme for the wind model. We show that our model quantitatively reproduces observed values of the steady-state (saturated) sand flux under various flow conditions. Furthermore, we model different conditions of mobile sand availability and find a strong dependence of the sand flux on this availability.

Numerical simulation of wind field and sand flux in crescentic sand dunes

Sand flux is the key factor to determine the migration of sand dunes and the erosion to the surrounding environment. There are crescent-shaped sand dunes of various scales in the desert, and there are significant differences in spatial wind field and sand flux among them. However, due to the difficulty of monitoring, it is difficult to continuously observe the spatial wind field and sand flux around the larger crescentic dunes. On the basis of the Reynolds-Average Navier-Stokes (RA-NS) equation and the stress and sand flux model, the distribution of wind field and sand flux of a circular dune with a height of 4.2 m and a length of about 100 m during the four evolutionary periods of the evolution into a crescentic dune was simulated in this study. By comparing with the measured results, we verified that the closer to the leeward side, the more the simulated values of the velocity in wind field and sand flux were in line with the measured results. In order to further analyze the influence of the height of dune and other relevant parameters on sand flux, we simulated the influence on wind field and sand flux by changing the air viscosity and wind velocity of upper boundary. We found that the air viscosity mainly affected the amount of deposited sand on the leeward side of sand dune, while the increase of wind velocity would undoubtedly increase the sand flux of the whole sand dune. In addition, the simulation results also showed that the influence of changes in height of dune on the turbulent intensity of leeward side was very significant, and the turbulent intensity increased with the height of dune. The height changes of tall dunes gradually affected the transport of sand caused by wind flow behind the leeward side because that the rotation of the wind flow would form new vortexes at the large pores behind the leeward side, which would increase the turbulent energy in space and thus would increase the distance of migration of the lifting sand. While the low sand dunes could not form extra small vortexes at the bottom of the leeward side, so the wind velocity was small and the eddy currents behind the leeward side were more stable. The simulation results indicated that wind velocity was not the only reason for increasing the amount of sand flux, and the fluctuation of wind flow caused by turbulence could also stimulate the movement of sand particles on the ground.

Comparing performances of a triangular embankment and a rigid wall-type barrier in sandstorms using simulation and a wind tunnel test

The movement of sand particles and their accumulation on railway tracks are among the major problems observed in desert areas, which may impose huge maintenance and repair costs. One solution is to create a protective barrier in the vicinity of railway tracks to reduce sand deposition on these tracks. The present study introduced a triangular embankment due to its construction simplicity and low cost and compared it with a rigid wall-type barrier. At first, both models were compared in terms of the streamline and the sand mass flux with a two-phase flow of sandstorm numerical calculations. Then, the sand mass flux was measured for the rigid wall-type barrier using an experimental wind tunnel test. Moreover, the effects of wind speed, wall height, the zero-porosity barrier on the mass flux profile, and the deposition reduction of sand particles were examined after the barrier placement. Finally, the triangular embankment behavior was studied in a wind tunnel. The results revealed that the triangular embankment could increase the safe area after the barrier placement by up to 25%. Further, the triangular embankment was proven to be a permanent and cost-effective solution for protecting railway tracks in windblown sand-prone areas.

Unification of Aeolian and Fluvial Sediment Transport Rate from Granular Physics

One of the physically least understood characteristics of geophysical transport of sediments along sediment surfaces is the well-known experimental observation that the sediment transport rate Q is linearly dependent on the fluid shear stress τ applied onto the surface in air, but is nonlinearly dependent on τ in water. Using transport simulations for a wide range of driving conditions, we show that the scaling depends on the manner in which the kinetic fluctuation energy of transported particles is dissipated: via predominantly fluid drag and quasistatic contacts (linear) versus fluid drag and quasistatic and collisional contacts (nonlinear). We use this finding to derive a scaling law (asymptotically Q∼τ^{2}) in simultaneous agreement with measurements in water and air streams.

An analytical model for the growth and migration of a transverse dune

The growth and migration speed formulae for a 2-d transverse dune are derived under the assumptions of shape similarity, the near surface airflow independent of height, and the 100% sand trapping efficiency of lee face during dune evolution. Although very simple, this analytical model can quantificationally reflect the field investigations of barchan migrations and the chronological data of mega-dune growth.

Two-dimensional airflow modeling underpredicts the wind velocity over dunes

We investigate the average turbulent wind field over a barchan dune by means of Computational Fluid Dynamics. We find that the fractional speed-up ratio of the wind velocity over the three-dimensional barchan shape differs from the one obtained from two-dimensional calculations of the airflow over the longitudinal cut along the dune’s symmetry axis — that is, over the equivalent transverse dune of same size. This finding suggests that the modeling of the airflow over the central slice of barchan dunes is insufficient for the purpose of the quantitative description of barchan dune dynamics as three-dimensional flow effects cannot be neglected.

Intermittency of aeolian saltation

Saltation motion of sand grains in a steady wind was measured using a high-speed camera at very high frequency in a wind tunnel. A Heaviside-type function was defined to quantificationally describe an inherent property of saltation, i.e. intermittency. Kurtosis and periodicity of state function are statistical manifestations of intermittency. In addition, the strong autocorrelation of time series of volume concentration clearly confirms that saltation is not a completely random process at the timescale of subsecond. Formation mechanism, especially turbulent structures responsible for intermittent saltation, remains to be revealed from the viewpoint of classical mechanics.

Numerical modeling of wind-blown sand on Mars

Recent observation results show that sand ripples and dunes are movable like those on Earth under current Martian climate. And the aeolian process on Mars therefore is re-attracting the eyes of scientific researchers in different fields. In this paper, the spatial and temporal evolution of wind-blown sand on Mars is simulated by the large-eddy simulation method. The simulations are conducted under the conditions of both friction wind speed higher and lower than the "fluid threshold", respectively. The fluid entrainment of the sand particles, the processes among saltation sand particles and sand bed, and the negative feedback of sand movement to flow field are considered. Our results show that the "overshoot" phenomenon also exists in the evolution of wind-blown sand on Mars both temporally and spatially; impact entrainment affects the sand transport rate on Mars when the wind speed is smaller or larger than the fluid threshold; and both the average saltation length and height are one order of magnitudes larger than those on Earth. Eventually, the formulas describing the sand transport rate, average saltation length and height on Mars are given, respectively.