稳态风沙流沙粒起跳速度概率分布模型

doi:10.13866/j.azr.2023.09.02

摘要/Abstract

摘要：

颗粒起跳速度概率分布函数是泥沙输运和粉尘释放模型中的重要输入参数。然而，为了可靠描述这种分布函数，需要准确测量近地层风沙流内起跳颗粒的运动轨迹。本文使用高速摄影系统和颗粒轨迹检测算法相结合测量了风洞沙床面附近部分溅射颗粒、没有引起溅射的反弹颗粒以及引起1个溅射的反弹颗粒的轨迹，通过分析三种起跳模式对应的起跳速度概率分布构建稳态风沙流跃移颗粒起跳速度的概率分布模型。结果表明：（1）三种起跳模式的起跳角度和起跳速度均服从Lognormal概率分布。（2）所有起跳颗粒的起跳角度概率分布方程几乎不受起跳模式影响。（3）所有起跳颗粒的起跳速度概率分布方程主要受溅射颗粒数与反弹颗粒数比值的控制，预示着风沙流发育过程或湍流波动将会对起跳速度概率分布函数产生重要影响。因此，我们的研究结果提供了关于近床面风沙跃移过程的新认识，并对模拟风沙输运中的粒-床相互作用和地貌动力学模型具有重要意义。

关键词: 起跳速度, 反弹颗粒, 溅射颗粒, 粒-床碰撞过程, 高速摄影技术

Abstract:

The probability distribution function (PDF) of the liftoff velocities of aeolian (wind-blown) sand particles, an important parameter in sediment transport and dust emission models, remains poorly understood due to the challenges in tracking particle dynamics during the liftoff process. To reliably describe this distribution function, measurements of the individual particle trajectories near the sand-bed during sediment transport are required. In this study, we address this issue by employing an improved particle tracking velocimetry technique, enabling us to capture the particle-bed collision process of many liftoff grains in consecutive images and, consequently, to obtain multiple liftoff particle trajectories with different liftoff modes during sand transport in a boundary layer wind tunnel. Subsequently, using the wind tunnel, we measured the trajectory of splash particles, rebound particles that generated no splash particles, and rebound particles that generated only one splash particle near the sand bed. By analyzing the probability distribution of the liftoff velocities of these three liftoff modes, a probability distribution model for the liftoff velocities of particles in a steady-state wind-sand flow was constructed. The results indicate the following: (1) The liftoff angles and speeds of the three liftoff modes all follow a Lognormal probability distribution. (2) The PDF for the liftoff angle of the total liftoff particles is largely unaffected by the liftoff mode. (3) The PDF for the liftoff velocity of the total liftoff particles is mainly controlled by the number of splash particles to that of rebound particles. This indicates that the development process of wind-sand flow or turbulence fluctuations impacts the PDF of liftoff velocity. The different shapes of the probability distribution curve for liftoff velocities may only reflect the specific development of wind-sand flow. Our results offer new insights into the aeolian sand saltation process near the bed surface and are crucial for simulating particle-bed interactions and improving geomorphic dynamics models in aeolian sand transport. Our study on the probability distribution model of liftoff velocity opens a new avenue of investigation in the aeolian and soil sciences and aids the understanding of the dynamics of near-bed particle transport. This transport plays an essential role in aeolian research, as well as in the geomorphodynamics of Earth, Mars, and other celestial bodies within our solar system.

Key words: liftoff velocity, rebound particles, splash particles, particle-bed collision process, high-speed photography

蒋缠文,王晓艳. 稳态风沙流沙粒起跳速度概率分布模型[J]. 干旱区研究, 2023, 40(9): 1382-1390.

JIANG Chanwen,WANG Xiaoyan. Liftoff velocity distribution model of aeolian sand grains in saturated wind-sand flow[J]. Arid Zone Research, 2023, 40(9): 1382-1390.

图/表 10

图1

表1

表2

各统计变量Lognormal分布方程的拟合参数"

变量	$A 0$	$λ$	$δ$	$R 2$	$μ$	$σ$
$θ$	4.6536	3.1581	0.7977	0.9882	26.2	18.2
$V s 1$	0.0962	-1.2714	0.5386	0.9935	0.31	0.17
$V r 0$	0.2914	-0.2919	0.6105	0.9956	0.81	0.49
$V r 1$	0.3193	0.2228	0.6348	0.9720	1.29	0.69

表2

图2

图3

图4

图5

图6

图7

图8

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实验组	沙样	d/mm	u_*/（m·s^-1）	u_*_ti/（m·s^-1）	N_s₀	N_s₁
G₁	自然沙	0.1~0.12	0.25	0.14	67	19
G₂	人造石英砂	0.1~0.2	0.26	0.16	81	17
G₃	人造石英砂	0.2~0.3	0.28	0.20	61	23
G₄	人造石英砂	0.3~0.4	0.31	0.24	39	14
G₅	人造石英砂	0.4~0.5	0.33	0.27	138	17
G₆	人造石英砂	0.6~0.7	0.45	0.33	91	14
G₇	人造石英砂	0.7~0.8	0.49	0.35	119	17