Transport mass of creeping sand grains and their movement velocities

Authors

  • Cheng Hong,

    Corresponding author
    1. State Key Laboratory of Earth Surface Processes and Resource Ecology, MOE Engineering Center of Desertification and Blown-sand Control, Beijing Normal University, Beijing, China
    • Corresponding author: Cheng Hong, State Key Laboratory of Earth Surface Processes and Resource Ecology, MOE Engineering Center of Desertification and Blown-sand Control, Beijing Normal University, Beijing 100875, China. (chengh@bnu.edu.cn)

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  • Zou Xueyong,

    1. State Key Laboratory of Earth Surface Processes and Resource Ecology, MOE Engineering Center of Desertification and Blown-sand Control, Beijing Normal University, Beijing, China
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  • Liu Chenchen,

    1. State Key Laboratory of Earth Surface Processes and Resource Ecology, MOE Engineering Center of Desertification and Blown-sand Control, Beijing Normal University, Beijing, China
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  • He Jiajia,

    1. State Key Laboratory of Earth Surface Processes and Resource Ecology, MOE Engineering Center of Desertification and Blown-sand Control, Beijing Normal University, Beijing, China
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  • Wu Yongqiu

    1. State Key Laboratory of Earth Surface Processes and Resource Ecology, MOE Engineering Center of Desertification and Blown-sand Control, Beijing Normal University, Beijing, China
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Abstract

[1] Aeolian sand transport is an important component of material circulation above terrestrial surfaces and can include processes of creep, saltation, and suspension. The complex movement of material and energy during aeolian transport has meant that these processes have previously been examined in isolation. Although a significant amount of research has been conducted on aeolian sand transport, this focused primarily on saltation. As a result, there are few data available on sand grain creep, primarily due to a lack of theoretical models and the difficulty of direct measurements. In this study, we present novel methods and instrumentations to accurately measure the transport mass and the velocity of creeping sand grains. Using data collected with above instrumentations and a ladder sampler at four friction velocities (u* = 0.26, 0.35, 0.47, and 0.56 m s−1) in a wind tunnel, we studied the transport mass of creeping sand grains and their movement velocities, as well as other key parameters of aeolian sand transport. Four major conclusions can be drawn from this study: (1) The transport mass (q0) of creeping sand grains increases with increasing frictional wind velocity (u*). The relationship between these variables is represented by the power function q0 = −0.053 + 9.195u*2.800. (2) The contribution of creep to total aeolian sand transport decreases with increasing frictional wind velocity. Creep contributed 57% of total aeolian transport at the lowest frictional wind velocity but only 19% at the highest velocity. (3) The threshold frictional wind velocity for entrainment was 0.158 m s−1. (4) The movement velocity of creeping sand grains ranged from 0 to 0.14 m s−1, but more than 70% of recorded velocities were less than 0.02 m s−1. Although the results of this study require further validation, they provide a strong basis for future research and help deepen our understanding of aeolian sand transport.

1 Introduction

[2] Aeolian sand flow is a special case of two-phase gas-solid flow that results from wind-driven spatial displacement of sand particles [Zou et al., 2001]. The solid phase is asymmetrically distributed, and the shapes of sand beds change in response to wind and particle collisions. Many direct and indirect factors influence the nature of this process [Cheng et al., 2007]. Limitations imposed by experimental conditions have thus far prevented detailed and accurate observations of near-bed sand motion. There are complex exchanges of material and energy among the three main modes of sand grain displacement (creep, saltation, and suspension) [Bagnold, 1941]. This is particularly important during creep and saltation of sand grains, which together account for 95% of the total aeolian transport mass [Bagnold, 1941]. To clarify the dynamic processes of material and energy transfer between sand grains during creep and saltation, the fundamental behaviors of these transport modes must first be understood. In comparison with the many studies of saltation of sand grains [Owen, 1964; White and Schulz, 1977; Anderson and Haff, 1988; Zou et al., 2001; Cheng et al., 2007], few data exist on creeping sand grains.

[3] In addition to the difficulty of direct measurement and scarcity of theoretical information, previous studies have focused less on sand grain creep as it was found to only account for approximately 25% of the total aeolian transport mass [Bagnold, 1941]. As a result, engineering applications, such as measures to control desertification, are based on the assumption that saltation is the primary transport mode that needs to be addressed. Recently, some studies have demonstrated that Bagnold [1941] underestimated the contribution of creeping sand grains to total aeolian transport [Horikawa, 1960; Anderson et al., 1991], and several researchers have suggested that the importance of creep varies with wind velocity and particle size [Chepil, 1959; Dong et al., 2002; Wu, 2003; Wang and Zheng, 2004].

[4] The physical mechanics of creeping sand grains were first reported through studies of total sand mass transported through this mode. Bagnold [1941] reported the transport mass of creeping sand grains based on experimental data derived from a bed trap placed in a wind tunnel, but he did not accurately present the transport mass of creeping sand grains because his research results included some saltating sand grains. He noted that the width of the bed trap was 1–3 mm, which as this study found would cause the trap to capture both creeping and saltatating sand grains. According to Bagnold's method with accurate [Wu et al., 2011] and inaccurate [Chepil, 1959; Qi et al., 2001; Wu, 2003] width and length of bed trap, subsequent studies also failed to accurately measure the transport mass of creeping sand grains. Dong et al. [2002] calculated the transport mass of creeping sand grains by using the inverse of the vertical distribution of saltating sand grain flux at zero height, but the result still included some saltating particles. In general, measured results [Bagnold, 1941; Chepil, 1959; Qi et al., 2001; Wu, 2003; Wu et al., 2011] and calculated results [Dong et al., 2002; Wang and Zheng, 2004] have exaggerated the transport mass of creeping sand grains. Recently, Wang et al. [2009] provided an optical method for measuring the transport mass of creeping sand grains, using high-speed digital photography to determine the number of grains that passed over a setline. However, the optical method displayed a significant deficiency at high rates of aeolian sand flow [Zhang et al., 2010]. Furthermore, the optical method assumed that sand grain creep only occurred to a finite depth and regarded the bed as a flat surface. Consequently, the optical method underestimated the transport mass of creeping sand grains. Accurately measuring transport mass of creeping sand grains remains crucial to understanding the physical mechanics of this transport.

[5] The velocity of motion is another key parameter required to understand the mechanics of sand grain creep. Few previous studies have reported creep velocities. Studies that implemented the optical method [Wang et al., 2005; Zhang et al., 2010, 2011] reported average velocities of greater than 0.1 m s−1 [Wang et al., 2005]. However, the concerns regarding the optical method remain, and the method may be further questioned, as creep velocities were reported to increase with particle size [Wang et al., 2005]. In addition, the optical method only recorded movement on the top surface where velocities are likely to have been higher, and the creep velocity of grains at depth was not considered. Such grains are likely to have experienced lower velocities, and as such the average velocities for transport through creep may have been overestimated.

[6] The threshold frictional wind velocity for sand grain transport has been a significant focus of previous research. Although numerous studies have addressed this issue [Bagnold, 1941; Chepil, 1959; Zingg, 1953; Lyles and Krauss, 1971; Liu, 1993; Chen et al., 1999; Wu, 2003], there are few experimental data to verify the findings, as it is difficult to determine the point at which particle movement is initiated. Recently, Qi et al. [2001] and Wu et al. [2011] studied the threshold frictional wind velocity of sand grains by assuming that the mass transported by creep was zero. Following this assumption, the inversion method used in this study could provide a value for the threshold frictional wind velocity for sand grain entrainment. Obviously, how to accurately measure transport mass of creeping sand grains is a very key problem to inverse the threshold frictional wind velocity.

[7] In this study, we present a novel method, as well as instrumentation, to accurately determine the transport mass of creeping sand grains and their movement velocities. Based on experimental data using four friction velocities (u* = 0.26, 0.35, 0.47, and 0.56 m s−1), we studied the transport mass and movement velocities of creeping sand grains. We also determined the threshold frictional wind velocity for sand particles and the contribution of particles transported through creep to total aeolian transport. The results provide a strong foundation for future research and improve our current understanding of aeolian sand transport.

2 Wind Tunnel Experiments

[8] The experiments were performed in a 66.6 m long wind tunnel at the State Key Laboratory of Earth Surface Processes and Resource Ecology of Beijing Normal University, Beijing, China. We used a 24 m long section of this wind tunnel, with a cross-section 3 m wide and 2 m high (Figure 1). The wind velocity at the central axis of the wind tunnel can be continuously varied from 1 to 45 m s−1, with a turbulence intensity of less than 0.8%. The Experimental sand grains were taken from the central part of the Taklimakan Desert, China. Analysis of particle size of sand gains was conducted in the Key Laboratory of Environmental Change and Natural Disaster, Ministry of Education of China, Beijing Normal University; Malvern particle size analyzer 2000 was used to measure the particle size of experiment sand grains. Figure 2 illustrates the test results for particle size distribution of the experimental sand grains, whose volume mean diameter was 0.124 mm. To create stable aeolian sand flow, we spread a layer of sand 10 m long, 1 m wide, and 3.5 cm thick over the surface of the wind tunnel. The windward edge of this sand layer was positioned 9 m downwind of the start of the experimental section of the wind tunnel. A scheme of wind tunnel experiment is shown in Figure 3.

Figure 1.

Schematic of the wind tunnel.

Figure 2.

Particle size distribution of the experimental sand grains.

Figure 3.

A scheme of wind tunnel experiment.

2.1 Measurement of the Airflow Field in the Wind Tunnel

[9] We measured wind velocity at seven different heights above the surface (1, 3, 5, 7, 10, 15, and 20 cm), using a pitot tube located 7 m downwind of the start of the experimental section. The wind velocity profile was shown in Figure 4, which showed that the wind velocity profile generally followed the logarithmic law, consistent with the results of previous studies [Bagnold, 1941; Owen, 1964; Ungar and Haff, 1987]. Based on the curve (u = a ln(z) + b) fitted to the wind velocity profile in Figure 2 and following the method presented by Dong et al. [2001], in which u* = k × a, where k is the von Karman constant (k = 0.4), the corresponding friction velocities (u*) were 0.26, 0.35, 0.47, and 0.56 m s−1.

Figure 4.

Wind velocity profile at 7 m downwind of the experimental section.

2.2 Measurement of Transport Mass of Saltating Sand Grains

[10] We used a 60 cm high and 2 cm wide flat sampler to collect saltating sand grains at 2 cm intervals over 30 different heights (0–2 cm up to 58–60 cm), and the efficiency of the flat sampler exceeded 90% [Wang et al., 2005]. The sampler was located 8.5 m downwind of the start of the sand bed, and the base of the sampler was positioned on the sand surface.

2.3 Measurement of Transport Mass of Creeping Sand Grains

[11] Bed trapping has been the only method previously used to measure the transport mass of creeping sand grains [Bagnold, 1941]. However, this method provides inaccurate results because large quantities of saltating sand grains can enter the trap along with the creeping sand. A measurement of saltating sand captured in the bed trap is therefore crucial to determine the transport mass of creeping sand grains. The amount of creeping sand falling into the trap should not change with widths of the bed trap. In theory, the width of the bed trap directly affects the mass of captured saltating sand grains. More saltating sand grains are captured in wider bed traps. In general, narrower bed traps have been used in previous studies in an attempt to reduce the quantity of saltating sand grains entering the trap. However, when the width of a bed trap becomes too narrow, it is possible that moving sand grains can fully or partially bury it (Figure 5a). For example, as shown in Figure 5a, bed traps with widths of 0.45 and 0.60 mm were fully buried by sand grains, and bed traps with a width of 0.75 mm were partially buried (Figure 5b).

Figure 5.

Diagram of bed traps used for collecting creeping sand grains. (a) The entrances of bed traps with widths of 0.45 and 0.60 mm were fully buried by sand grains, and the entrance of a bed trap with a width of 0.75 mm was partially buried. Furthermore, (b) the entrance was divided into several segments by moving sand grains. In theory, the results from bed traps with a narrow entrance should provide an accurate measure of the transport mass of creeping sand grains. However, the width of the bed trap was too narrow and therefore introduced error into the results.

[12] To eliminate the effect of saltating sand grains and the width of the bed trap, this study presented a novel technique to determine an accurate transport mass of creeping sand grains. The main principles were that the amount of creeping sand grains falling into the trap should not change for different widths of the bed trap and was only relative with length of the bed trap and that the amount of saltating sand grains falling into the trap was relative with the area of entrance the bed trap, and the area was determined by the widths and length of the bed trap. The unit of captured creeping sand grains was g m−1 s−1, while the unit of captured saltating sand grains was g m−2 s−1. Based on conservation of mass, the captured sand grains by trap were equal to captured creep plus captured saltation. In order to illustrate the above principle, we assumed several parameters: (1) Mi was the mass of captured sand grains by bed traps (g s−1), (2) q0 was the transport mass of creeping sand grains per unit time and unit length (g m−1 s−1), and (3) k0 was the mass of saltating sand grains in the bed trap per unit time and unit area (g m−2 s−1), respectively. The relationship among M, q0, and k0 can be expressed as follows:

display math(1)

[13] Equation (1) could also be expressed as

display math(2)

[14] If Mi/L is regarded as qi, equation (2) could also be expressed as

display math(3)

[15] Equation (3) clearly shows a linear relationship between the mass of captured sand grains and the entrance width of the sand trap. Furthermore, the slope (k0) of the linear relationship represents the effect of saltating sand grains on the mass of captured sand grains, and the intercept (q0) of the linear relationship is the transport mass of creeping sand grains as determined using the method described in this study.

[16] To determine the intercept (q0) and the slope (k0) in equation (3), we developed a set of bed traps with six different entrance widths (D = 1, 2, 3, 4, 5, and 6 mm) for the bed trap but maintained a constant length (L = 20 mm; Figure 6). The six bed traps were positioned in a line perpendicular to the wind direction. We altered the relative position of each bed trap in each experiment to eliminate any possible effects arising from the position of the traps. The transport mass of creeping sand grains for each wind velocity were calculated by averaging the results from three locations in the sand bed. The bed traps were generally cuboid-shaped, with length (L) of 20 mm, width (d) of 15 mm, and height (H2) of 130 mm. To avoid the effect of slumping sand grains on the data collected, we installed the upwind surface of the bed traps at an angle (α) of 45° to the sand bed. They had a trap area with length (L) of 20 mm, width (D) of 1, 2, 3, 4, 5, or 6 mm, and height (H1) of 20 mm (Figure 6). The bed traps were positioned 7.35 m downwind from the sand bed, with the upper trap area at the height of the sand bed.

Figure 6.

Schematic diagram of a bed trap. The angle (α) between the upwind surface of the bed trap and the sand bed was 45°, to avoid the effect of slumping sand gains on data collected. H1 (20 mm), H2 (130 mm), L (20 mm), and d (15 mm) were set to ensure a sufficient number of sand grains could be trapped. D was 1.0, 2.0, 3.0, 4.0, 5.0, and 6.0 mm, respectively.

2.4 Measurement of Movement Velocities of Creeping Sand Grains

[17] The velocity of motion is a key parameter required to understand the mechanics of sand grain creep. However, this parameter has rarely been reported previously, and there is no specialized instrumentation available to measure it. This study implemented a novel method for accurately measuring creep velocities of sand grains, and we developed an instrument (Figure 7) for this purpose. The general shape of the instrument is designed to be similar to that used for measuring the transport mass of creeping sand grains, as shown in Figure 6. However, in contrast to that instrument, for measuring the velocity of motion, a latch-up area with length (L) of 20 mm and width (D2) of 8 mm was added, to ensure trapped sand grains moved a predefined horizontal distance (D1 or D1 + D2). Below this, there were 60 cavities, 2 cm wide and 2 cm high, to catch grains and classify them by their motion velocities. A hopper was placed at the bottom of the cuboid to collect sand grains that had insufficient velocity to be captured by any of the cavities above (Figure 7). The trap was again cuboid-shaped, with length (L) 20 mm, width (d) 24.14 mm, and height (H2) 1435 mm. The trap area had length (L) 20 mm, width (D1 + D2) 10 mm, and height (H1) 20 mm (Figure 7). Again, the trap area had an angle (α) of 45° between the upwind surface and the sand bed to avoid the effects of slumping sand grains. Again, the trap was installed 7.57 m downwind from the start of the sand bed, level with the top of the sand surface.

Figure 7.

Schematic diagram of the instrument used to measure creeping velocity. The entrance was a rectangle with length (L) and width (D1). A latch-up area with length (L) and width (D2) was used to force sand grains to move a defined horizontal distance (D1 or D1+D2). Sixty sand-collecting cavities with 2 cm height and 2 cm width and a hopper were used to classify creeping velocities. α was set to 45° to avoid the effect of slumping sand gains. L (20 mm) and d (15 mm) were set to ensure the capture of sufficient sand grains, while H1 (20 mm) and H2 (1435 mm) were set to increase the number of sand-collecting cavities.

[18] The principle employed for measuring the creep velocities of sand grains was that once a sand grain fell into the trap, it was then subjected to gravity and would therefore be collected by the appropriate cavity of the device, as defined by the horizontal velocity (Vcreep_x) when the grain entered the trap. Their moving horizontal distance and moving vertical distance after they fall into the entrance of the instrument could be determined by the corresponding cavity. Based on horizontal and vertical moving distances of sand grains, we can calculate their moving velocities according to their kinematical equation.

[19] For creeping sand grain, we assumed that (1) Vcreep_x is its horizontal velocity; (2) t is its moving time after they fall into the entrance of the instrument; (3) H is the moving vertical distance after they fall into the entrance of instrument; and (4) L is the moving horizontal distance after they fall into the entrance of instrument. Due to the nature of the movement of creeping sand grains, it fell into the measuring instrument at the upwind edge of the entrance (Figure 7). Therefore, L = D1 + D2. Based on their kinematical equation, the vertical distance traveled before being collected (H) can be related to the initial horizontal motion through the following expressions:

display math(4)
display math(5)

[20] For saltating sand grain, we assumed that (1) Vsaltating_x is its horizontal velocity; Vsaltating_z is its vertical velocity; (2) t is its moving time after they fall into the entrance of instrument; (3) H is the moving vertical distance after they fall into the entrance of instrument; and (4) L is the moving horizontal distance after they fall into the entrance of instrument. Furthermore, due to the nature of their movement, they can enter into the instrument at any point along the entrance of instrument. Therefore, L could change from D2 to D1 + D2.

[21] For saltating sand grains that fall into the measuring instrument at the downwind edge of the entrance, its horizontal motion can be expressed as

display math(6)

[22] For saltating sand grains that fall into the measuring instrument at the upwind edge of the entrance, horizontal motion can be expressed as

display math(7)

[23] The vertical motion for all saltating sand grains is given as

display math(8)

[24] As discussed in section 2.3, D1 determined the mass of captured sand grains, including saltating sand grains and creeping sand grains, and D2 was the key parameter to determine the mass of sand grains captured in each cavity. When D2 was high, most of the mass of captured sand grains was concentrated in the cavity at the bottom of the measuring instrument. In contrast, when D2 was low, most of the sand grains were captured in the cavity at the top of the apparatus. Therefore, it was essential to determine an appropriate value for D2.

[25] The upper cavities of the apparatus were expected to capture sand grains with higher initial horizontal velocities, whereas the lower cavities should capture grains with lower velocities. In general, velocities of saltating sand grains would be higher than those of creeping sand grains. On the basis of the difference in velocity between saltating sand grains and creeping sand grains, we subtracted the mass of sand grains from the bottom of the sand-collecting cavity until the subtracted mass of sand grains was equal to the mass of creep sand grains for the corresponding frictional wind velocity. The movement velocity for sand transported by creep could then be calculated by taking the inverse of the depth at which these grains were trapped.

3 Results and Discussion

3.1 Transport Mass of Creeping Sand Grains

[26] Figure 8 shows the mass (q) of captured sand grains from the bed traps (Figure 6) with six different entrance widths (X = 1, 2, 3, 4, 5, and 6 mm) at four different friction velocities (0.26, 0.35, 0.47, and 0.56 m s−1). In this case, the horizontal axis is the entrance width of the sand trap, and the vertical axis is the mass of captured sand grains for each bed trap. Figure 8 clearly shows that the mass of captured sand grains rapidly increased as the width of the bed trap increased. Based on equation (3), there is a linear relationship between the entrance width of the bed trap and the mass of captured sand grains for each bed trap.

Figure 8.

Relationship between the mass (q) of collected sand grains and the width of the trap entrance (X).

[27] We determined the intercept (q0) of the slope (k0) in equation (3) by fitting a curve based on experimental data using TableCurve software. The regression results are shown in Figure 8. All correlations (R2) were 0.94 or higher, indicating that equation (3) provides a reliable description of the relationship between the mass of sand grains trapped and the bed trap width. Comparing equation (3) and the linear relationship (q = aX + b) between the mass of captured sand grains and the entrance width of the sand trap in Figure 8, we find that the intercept (b) of the linear relationship represents the transport mass of creeping sand grains per unit time and unit length, and the slope (a) of the linear relationship characterizes the mass of saltating sand grains per unit area of the trap. Therefore, for the friction velocities tested (0.26, 0.35, 0.47, and 0.56 m s−1), transport masses of creeping sand grains were 0.12, 0.51, 1.00, and 1.80 g (2 cm)−1 min−1, respectively. The corresponding falling masses of saltating sand grains in the traps were 0.04, 0.20, 0.29, and 0.52 g (2 cm)−1 (mm)−1 min−1, respectively.

[28] These findings clearly demonstrate that the transport mass of creeping sand grains rapidly increases with increasing wind velocity. This result is consistent with the results of previous qualitative research [Bagnold, 1941; Qi et al., 2001; Dong et al., 2002; Wang et al., 2005; Wu et al., 2011]. Bagnold [1941] first studied the transport mass of creeping sand grains by using bed traps with widths from 1 to 3 mm but did not accurately report the width or length of the bed traps, and assumed creep accounted for only 25% of aeolian sediment transport. Qi et al. [2001] reported the transport mass of creeping sand grains over a mobile sand surface and a surface of alternating sand and straw but did not present any information on the width and length of the bed trap used. Therefore, it is not possible to compare the results of our study with those of Bagnold [1941] and Qi et al. [2001]. Although Wu et al. [2011] reported the transport mass of creeping sand grains over a mobile sand surface and reported the width (22 cm) and length (1 cm) of the bed trap, the relatively large area (22 cm2) of the entrance of the bed traps likely resulted in the inclusion of many saltating sand grains that fall into the entrance. In order to compare with prior result [Wu et al., 2011], we changed the falling mass of saltating sand grains in the bed trap (Figure 8) into that of prior result with the same unit (g (2 cm)−1 (cm)−1 min−1), The fallen mass of saltating sand grains in the bed trap with an area of 2 cm wide and 1 cm length was 0.421, 1.966, 2.921, and 5.174 (g (2 cm)−1 (cm)−1 min−1) for each of the four friction velocities (0.26, 0.35, 0.47, and 0.56 m s−1), respectively. The falling mass of saltating sand grains in the bed trap was therefore 3.41, 3.89, 2.91, and 2.91 times the transport mass of creeping sand grains at the four friction velocities. Using a similar research method, Dong et al. [2002] reported the transport mass of creeping sand grains at each frictional wind velocity (0.26, 0.35, 0.47, and 0.56 m s−1) as 0.301, 3.00, 5.386, and 12.549 g (2 cm)−1 (cm)−1 min−1, respectively. This result showed that Dong et al. [2002] and Wu et al. [2011] overestimated the transport mass of creeping sand grains [Zhao and Li, 2008]. In contrast, the method employed by Wang et al. [2005] underestimated the transport mass from creeping sand grains, because high-speed digital photography was insufficient to capture high rates of aeolian sand flow [Zhang et al., 2010], and the method inherently assumed that sand grain creep only occurred over a finite bed thickness. For example, transport mass of creeping sand grains with particle size 125–200 µm, for a frictional wind velocity of 0.60 m s−1, was only 0.002 g (2 cm)−1 min−1. In this study, transport mass of creeping sand grains with particle size of 124 µm at a frictional wind velocity of 0.56 m s−1 was 1.779 g min−1 (2 cm)−1.

[29] Figure 9 shows the transport mass of creeping sand grains (qc) and friction velocities (u*). The horizontal axis in this case is the frictional wind velocity (m s−1), and the vertical axis is the mass of captured sand grains for each bed trap (g min−1 (2 cm)−1). As previously discussed, the transport mass of creeping sand grains rapidly increases with increasing wind velocity. The best regression result provided by the TableCurve software can be expressed as the power function qc = −0.053 + 9.195u*2.800, with the correlation R2 = 0.99. However, the fitted relationship is inconsistent with results of previous studies [Qi et al., 2001; Wu et al., 2011] because it did not depict a linear relationship. This may result from saltating sand grains being included in the results of previous studies, consequently producing an overestimate of the transport mass of creeping sand grains [Zhao and Li, 2008].

Figure 9.

The relationship between transport mass of creeping sand grains and friction velocities.

[30] Using a similar method to Qi et al. [2001] and Wu et al. [2011], we found that by extrapolating the power function equation for creeping transport mass and friction velocity, the threshold friction velocity of sand grains (u* = 0.158 m s−1) could be determined by assuming no transport mass of creeping sand grains (qc = 0). This produced an axial wind velocity of 4.090 m s−1 in the wind tunnel for the threshold frictional wind velocity, compared with 4.5 m s−1 [Qi et al., 2001] and 7.59 m s−1 [Wu et al., 2011] in previous studies. In addition to the previously discussed reasons for overestimating the transport mass of creeping sand grains, this discrepancy may be due to the particle size of sand grains used. The mean particle size of sand grains in this study was 0.124 mm, whereas the mean particle size of sand grains used by Qi et al. [2001] and Wu et al. [2011] was 0.25 mm and 0.27 mm, respectively. Considering this difference, the value calculated for the threshold frictional wind velocity of sand grains in this study is considered to be reasonable.

3.2 Distribution of Transport Mass Between Creep and Aeolian Sand Flow

[31] In the experimental setup used, the lower entrance of the flat sampler could trap both saltating and creeping sand grains in section 2.2. To separate grains transported by different modes, we determined the true transport mass of saltating sand grains by subtracting the mass of creep sand grains (as measured by the instrument in section 2.3 shown in Figure 7) from the total mass of transported grains (as measured by the instrument in section 2.2). These results are listed in Table 1. The transport mass of saltating sand grains measured at friction velocities of 0.26, 0.35, 0.47, and 0.56 m s−1 was 0.103, 1.103, 2.765, and 8.251 g (2 cm)−1 min−1, respectively. This rapid increase with increasing wind velocity is consistent with results from previous studies [Anderson and Hallet, 1986; Huang, 2002; Wu, 2003; Cheng et al., 2007]. The ratios of mass transported by creep to mass transported by saltation are listed in Table 1. This clearly shows that the proportion of sand grains transported by creep decreases significantly with increasing wind velocity, indicating a transformation from transport by creep to transport by saltation.

Table 1. Relative Contributions of Creep to Saltation and Total Mass Transport of Aeolian Sand Flow for Four Friction Velocities
u*(m s−1)Transport Mass of Saltating Sand Grains (g min−1 (2 cm)−1)Ratio of Creep Transport Mass to Saltating Transport MassRelative Contribution of Creep to Total Transport Mass
0.260.1031.190.57
0.351.1030.460.33
0.472.7650.360.27
0.568.2510.220.19

[32] Previous studies have experienced difficulties in measuring the transport mass of suspending sand grains. In this study, we calculated this value based on previous research which showed that suspended sand grains account for 5% of the total aeolian sand transport mass [Bagnold, 1941]. For friction velocities of 0.26, 0.35, 0.47, 0.56 m s−1, the proportion of aeolian sand transport composed of sand transported by creep was 0.57, 0.33, 0.27, and 0.19, respectively, providing a mean value of 0.34 (Table 2). The decreasing contribution of creep to total aeolian transport with increasing wind velocity is consistent with the majority of previous results [Chepil, 1959; Horikawa, 1960; Anderson et al., 1991; Dong et al., 2002; Wu, 2003; Wang and Zheng, 2004]. However, the mean contribution is higher than the figure of 25% suggested by Bagnold [1941]. The decreasing contribution of creep with increasing wind velocity can be explained by the fact that creeping sand grains gain energy from increasing wind velocity, resulting in a change from creep to saltation. This also explains why transport mass lower in the aeolian sand flow profile decreases with increasing wind velocity, while transport mass higher in the profile increases with increasing wind velocity [Wu, 2003].

Table 2. Creep Velocity of Sand Grains as a Percentage of Total Creep Transport Mass
Creeping Velocities of Sand Grains (m s−1)Friction Velocities
0.26 m s−1 (%)0.35 m s−1 (%)0.47 m s−1 (%)0.56 m s−1 (%)
0.00–0.0273.2096.4676.3387.46
0.02–0.044.560.942.465.94
0.04–0.061.020.991.612.56
0.06–0.081.000.880.921.39
0.08–0.1015.250.7318.032.65
0.10–0.120.000.000.000.00
0.12–0.144.970.000.650.00

[33] It is interesting to note that the relative contribution of the transport mass of creeping sand grains to aeolian sand flow was higher than 50% at low wind velocities. Therefore, creeping sand grains may have a significant influence on the formation of aeolian sand geomorphology over extensive areas, such as the Taklimakan Desert. For example, based on measurements from 1 January 1999 to 30 June 2010 at the Tazhong meteorological station located in the center of the Taklimakan Desert, wind velocity only exceeded 10 m s−1 for 2.36% of the record, while 74.38% of recorded wind velocity ranged from 5 to 7 m s−1. Previous work has considered saltation as the primary mechanism for determining geomorphology in such environments. However, given that lower wind velocities are considerably more frequent, transport from both saltation and creep may significantly influence geomorphic change. We hope to conduct future research to assess the role of creep in driving geomorphic change.

[34] Several previous studies have observed the influence of particle size on the contribution of creep to aeolian transport [Horikawa, 1960; Anderson et al., 1991; Dong et al., 2002], as the proportion of mass transported by creep decreased with increasing particle size. In future research, we intend to study the effect of particle size in more detail by performing multiple wind tunnel experiments using several uniform particle diameters and a variety of grain size distributions.

3.3 Movement Velocities of Sand Grain Creep

[35] Based on equations ((4)) and ((5)) in section 2.4, we derived the velocity distribution of sand grain creep from the wind tunnel experiments. The velocity distribution of creeping sand grains at the four friction wind velocities used (0.26, 0.35, 0.47, and 0.56 m s−1) is listed in Table 2. Creep velocities ranged from 0 to 0.12 m s−1 and were primarily concentrated in the range of 0–0.02 m s−1. The percentages of creep velocities within this range at each of the four friction velocities were 73.20%, 96.46%, 76.33%, and 87.46%. However, there was no clear relationship between the transport mass of creeping sand grains and their movement velocities. For example, for u* = 0.26 m s−1, 73.20% of the mass was transported at a velocity of 0.00–0.02 m s−1, 4.56% at 0.02–0.04 m s−1, 1.02% at 0.04–0.06 m s−1, 1.00% at 0.06–0.08 m s−1, 15.25% at 0.08–0.10 m s−1, 0.00% at 0.10–0.12 m s−1, and 4.97% at 0.12–0.14 m s−1. The irregular distribution of mass over the range of creep velocities suggests that creeping movement is a stochastic process, occurring as a result of collisions between sand grains. Collisions between sand grains within the sand bed and with saltating sand grains are the main drivers of sand creep [Bagnold, 1941].

[36] Wang et al. [2005] provide the only previous report of sand grain creep velocities and suggest that creep velocities are greater than 0.1 m s−1 for sand grains with diameters less than 1.00 mm. In particular, for a frictional wind velocity (u*) of 0.60 m s−1, creep velocities of sand grains were 0.132, 0.117, 0.129, and 0.143 m s−1 for sand grains with diameters less than 0.10 mm, 0.10–0.125 mm, 0.125–0.15 mm, and 0.20–0.25 mm, respectively. In comparison with the results of Wang et al. [2005], this study measured relatively low velocities of creep. This is possibly because the optical method used by Wang et al. [2005] only viewed the upper surface, where the creep velocity is likely to be higher than at depth. However, the majority of creep movement occurs below this surface and is likely to be of lower velocity.

4 Conclusion

[37] Sand grain creep is an important process in defining overall sand motion. However, there is a paucity of data detailing the mechanics of the process, primarily due to the lack of theoretical analysis and the difficulty of measuring creep directly. In this study, we presented a novel method and associated instrumentation to accurately determine the transport mass and movement velocity of creeping sand grains. Based on experimental data obtained using four friction velocities (u* = 0.26, 0.35, 0.47, or 0.56 m s−1) in a wind tunnel, four key characteristics of sand creep and aeolian sand transport were demonstrated. (1) The transport mass (q0) of creeping sand grains increases with increasing frictional wind velocity (u*). This relationship can be described by the power function q0 = −0.053 + 9.195u*2.800. (2) The relative contribution of sand grain creep to total aeolian transport mass decreases with increasing friction velocities. (3) The threshold frictional wind velocity required to entrain sand grains was 0.158 m s−1. (4) The velocity of motion of creeping sand grains ranged from 0 m s−1 to 0.14 m s−1, though more than 70% of movement velocities measured were less than 0.02 m s−1. Although the results of this study require additional experimental validation, they provided a strong basis for future research and help to deepen our understanding of aeolian sand transport.

Acknowledgments

[38] The authors gratefully acknowledge the three reviewers, whose valuable comments and suggestions led to the improvement of our manuscript. The authors also gratefully acknowledge the National Natural Science Foundation of China (grant 41271020), the Program for New Century Excellent Talents in University (NCET-10-0236), the Fundamental Research Funds for the Central Universities (grant 2009SAT-6), and the National Basic Research Program of China (2013CB956002).

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