基于数字化轨迹的跃移粒子群速度剖面研究

doi:10.7522/j.issn.1000-694X.2024.00134

摘要/Abstract

摘要：

研究跃移运动时，速度是一个重要参数。采用高速摄影技术在风洞中获得了松散沙面上跃移沙粒在上升段和降落段的平均速度垂直剖面。结果表明：垂直方向上的颗粒湍流强度高于水平方向1~2个数量级，造成颗粒速度在水平方向上很好地服从正态分布，而在垂直方向上则较为分散且范围较窄（0~1 m·s^-1）。同一高度处，降落段的平均水平速度是上升段的1.6~1.8倍，而降落段的垂直速度则略小于上升段。两段的相对平均水平速度（v_x / $g d$ ，g为重力加速度，d为颗粒粒径）均与相对高度（z/Z，z为距床面高度，Z为边界层厚度）的平方根以及相对风速（u_*/u_*_ti，u_*为摩阻风速，u_*_ti 为冲击阈值）呈正比。上升段和降落段的平均垂直速度总体上均呈现随高度略微增加的趋势。上升段的平均垂直速度略高于降落段。平均垂直速度分布模式以及随高度变化特征的潜在机制需要通过进一步研究来阐明。

关键词: 风沙跃移, 平均速度, 垂直变化, 数字化轨迹, 高速摄影技术

Abstract:

Velocity serves as a crucial parameter in the study of saltation motion. We utilized high-speed photography technology to acquire the vertical profiles of the average velocities of saltating sand grains on a loose sand surface during the ascending and descending phases within a wind tunnel. The outcomes reveal that the particle turbulence in the vertical direction is one to two orders of magnitude greater than that in the horizontal direction， inducing the particle velocities to conform well to a normal distribution in the horizontal direction. Meanwhile， they are more dispersed and have a narrower range （approximately 0-1 m·s^-1） in the vertical direction. At the identical height， the average horizontal velocity in the descending phase is approximately 1.6-1.8 times that in the ascending phase， whereas the vertical velocity in the descending phase is marginally smaller than that in the ascending phase. The relative average horizontal velocities （v_x / $g d$ ， where g represents the gravitational acceleration and d denotes the particle diameter） in both phases are proportional to the square root of the relative height （z/Z， where z is the height from the bed surface and Z is the thickness of the boundary layer） and the relative wind speed （u_*/u_*_ti， where u_* stands for the friction wind speed and u_*_ti is the impact threshold）. The average vertical velocities in both the ascending and descending phases typically exhibit a slightly ascending trend with height. The average vertical velocity in the ascending phase is slightly higher than that in the descending phase. The underlying mechanisms of the average vertical velocity distribution patterns and the characteristics of variation with height necessitate further investigation for clarification.

Key words: aeolian saltation, average velocity, vertical variation, digital trajectory, high-speed photography technology

中图分类号:

X169

蒋缠文, 董治宝, 罗万银, 钱广强, 张正偲, 逯军峰, 王晓艳. 基于数字化轨迹的跃移粒子群速度剖面研究[J]. 中国沙漠, 2024, 44(6): 231-239.

Chanwen Jiang, Zhibao Dong, Wanyin Luo, Guangqiang Qian, Zhengcai Zhang, Junfeng Lu, Xiaoyan Wang. Research on velocity profiles of saltating particles based on their digital trajectories[J]. Journal of Desert Research, 2024, 44(6): 231-239.

图/表 10

图1 实验布置示意图

Fig.1 Layout of the experiment

图2 自由风速剖面

Fig.2 Velocity profiles for the approaching ?ow as a function of height above the surface

表1 实验条件

Table 1 Experimental conditions

实验组	沙样	d/mm	u_*/（m·s^-1）	u_*_ti /（m·s^-1）	z₀/mm
1	人造石英沙	0.1~0.2	0.26	0.16	0.0243
2	人造石英沙	0.2~0.3	0.28	0.20	0.0260
3	人造石英沙	0.3~0.4	0.31	0.24	0.0258
4	人造石英沙	0.4~0.5	0.33	0.27	0.0261

图3 颗粒湍流强度与距沙床面高度关系

Fig.3 Relationship between particle turbulence intensity and height above the sand-bed surface

图4 典型水平速度概率分布

Fig.4 Typical probability distribution of horizontal particle velocity

图5 典型垂直速度概率分布

Fig.5 Typical probability distribution of vertical particle velocity

图6 无量纲水平速度与相对高度关系

Fig.6 Variation of the dimensionless horizontal particle velocity （vx /gd） as a function of relative height （z/Z）

表2 图6中各实验组使用式（5）的拟合结果

Table 2 The fitting results of each experimental group in Figures 6A-B using equation （5）

实验组	d/mm	上升段		降落段
实验组	d/mm	$a u p$	R²	$a d o w n$	R²
1	0.1~0.2	142.0090	0.9429	233.5624	0.9658
2	0.2~0.3	86.1428	0.9700	148.7638	0.9809
3	0.3~0.4	78.3712	0.9477	131.5276	0.9275
4	0.4~0.5	67.2285	0.9455	109.9196	0.9606

表2 图6中各实验组使用式（5）的拟合结果

Table 2 The fitting results of each experimental group in Figures 6A-B using equation （5）

实验组	d/mm	上升段		降落段
实验组	d/mm	$a u p$	R²	$a d o w n$	R²
1	0.1~0.2	142.0090	0.9429	233.5624	0.9658
2	0.2~0.3	86.1428	0.9700	148.7638	0.9809
3	0.3~0.4	78.3712	0.9477	131.5276	0.9275
4	0.4~0.5	67.2285	0.9455	109.9196	0.9606

图7 拟合回归参数a与相对风速关系

Fig.7 Variation of the constant a with dimensionless wind speed velocity （u*/u*ti ）

图8 垂直速度与高度关系

Fig.8 Variation of the vertical particle velocity as a function of height

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