A wind tunnel investigation on the transverse motion of aeolian sand

ZhenTing Wang , QianHua Zhang , ZhiBao Dong

1. Key Laboratory of Desert and Desertification, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou, Gansu 730000, China

2. School of Physical Science and Technology, Lanzhou University, Lanzhou, Gansu 730000, China

*Correspondence to: Dr. ZhenTing Wang, Research Assistant of Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences. No. 320, Donggang West Road, Lanzhou, Gansu 730000, China.

Email: wang_zhen_ting00@sohu.com

A wind tunnel investigation on the transverse motion of aeolian sand

ZhenTing Wang1*, QianHua Zhang2, ZhiBao Dong1

1. Key Laboratory of Desert and Desertification, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou, Gansu 730000, China

2. School of Physical Science and Technology, Lanzhou University, Lanzhou, Gansu 730000, China

*Correspondence to: Dr. ZhenTing Wang, Research Assistant of Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences. No. 320, Donggang West Road, Lanzhou, Gansu 730000, China.

Email: wang_zhen_ting00@sohu.com

A wind tunnel experiment was performed to investigate aeolian grain motions in the transverse direction, which is perpendicular to the incoming flow and parallels the sand bed. The trajectories in the horizontal plane were recorded by high-speed camera. Statistical analysis of 630 trajectories shows that both the motion orientation and the time-averaged speed follow Gaussian distributions. An exclusive method was used to analyze the driving mechanism. It was concluded that the three-dimensional turbulent air flow, rather than the spin of grain or grain-bed collisions, controls the transverse motion.

aeolian sand transport; transverse motion; wind tunnel

1. Introduction

The aeolian transport of sand is essentially a four-dimensional process,i.e., three spatial coordinates and time. As pointed out by many researchers (Baas, 2003; Livingstoneet al., 2007), the current aeolian transport models based on the assumptions of being steady and uniform are severely limited and in need of great improvement. Obviously, comprehensive experimental investigations of four-dimensional aeolian sand transport are essential to the development of theory. The characteristics in the vertical and streamwise directions have been frequently considered in the traditional time-average models of saltation (Shao,2000). Following the development of experimental technologies, more and more details of aeolian sand transport have been revealed (Livingstoneet al., 2007; Baas, 2008).Compared with fruitful experimental results of temporal variations of sediment transport (Butterfield, 1998; Sterket al., 1998; Walker, 2005), the investigation of transverse or spanwise motion is lacking. Both the dispersion of colored sand (Hatanoet al., 2004) and various numerical simulations of ripples (Landry and Werner, 1994; Zhang and Miao,2003; Wuet al., 2008) indicate that the transverse motion plays an important role in the processes of aeolian sand transport and desert geomorphological dynamics. A direct evidence is that several trajectories with obvious turning points in the horizontal plane were obtained by using high-speed camera (Zhanget al., 2007a,b). In this paper, we report more detailed experimental results of transverse motion of grain and then analyze the driving mechanism.

2. Materials and methods

The experiments were performed in 2009 at the Yuzhong branch school of Lanzhou University, P.R. China.The longitudinal air flow was produced by a multifunctional wind tunnel with a total length of 85 m and a working section that is 20 m long, 1.3 m wide, and 1.3 m high. The wind speed on the axis of the tunnel can be continuously changed from 1.0 m/s to 40 m/s. The well-distributed roughness elements at the entrance to the working section ensure that saltations occur inside the boundary layer of the so-called

"steady" and "homogeneous" turbulence flow. We chose a coordinate system such that the wind direction wasx, the direction perpendicular to the sand bed wasz, and the transverse direction wasy(see figure 1). A horizontal laser sheet with a wavelength of 532 nm and the thickness of about 5 mm and a high-speed complementary metal oxide semiconductor (CMOS) camera (FASTCAM-APX) in the direction of +zwere employed to record the trajectories of sand grains. The laser sheet was very close to the sand bed or the plane ofz= 0. The frame rate, spatial resolution, and exposure time were adjusted to 3,000 fps, 1,024 × 1,024 pixels, and 1/3,000 s, respectively. A natural dune sand with a mean diameter ofd= 319 μm was used for the test.Figure 2 gives the grain size distribution. The thickness of the flat sand bed in the working section of the wind tunnel was about 7 to 8 cm.

Figure 1 Schematic diagram of the experimental apparatus

Figure 2 The grain size distribution of the natural dune sand

The raw images recorded by the high-speed camera were not always trenchant enough to observe the grain movements directly. The disturbances that could be obtained by averaging a large number of recordings (Zhanget al.,2007a) were first eliminated from every raw image. The binary images further given by Otsu’s method (Otsu, 1979)were used to distinguish sand grains from the background. A simply connected region with an area larger than 9 pixels was recognized as a grain. The position of one grain in the following image can be found in its neighborhood. Due to irregular shapes and spin motions, the two-dimensional projection of the same grain in two adjacent temporal records was not completely identical. The area error was controlled as＜5% in the image processing.

3. Results and discussions

The vertical profile of time-averaged wind speed in saltation can be approximately fitted by the logarithmic function ofu= (u*/κ)·log(z/z0), whereκ,u*, andz0are the Karman constant, the modified friction velocity, and the roughness, respectively. The wind speeds at different heights measured simultaneously by several Pitot tubes are shown in figure 3, whereu*= 1.88 m/s andz0= 3.1 mm. It was very difficult or impossible to capture the whole trajectory in the horizontal plane because the thickness of the light sheet was much less than the typical height of saltation. Only those partial trajectories with horizontal displacements larger than 10-d were taken into further consideration. The total number was 630. Most trajectories behave like straight lines.Analogous to a vector, we defined two parameters to quantitatively describe the movement of sand grains. One was the angleαbetween the motion orientation and thexaxis. The other was the mean speedvin the direction of +y. Both of them followed Gaussian distributions:

Figure 3 The vertical profile of wind speed in saltation

Figures 4(a) and 4(b) show the comparisons between equations(1)and(2)and the experimental data. Different from the maximum value ofαmax= 2π/9 given by Zhanget al. (2007a), we found that some angles even exceeded π/2,although their probabilities were small. In fact,αmaxwas equal to π when the backward lift-off occurred. Although the function of theories and methods of probability and statistics in the numerical simulation of aeolian process is very limited, the Gaussian distribution, as shown in figure 4, provides a convenient description. Figure 4(a) or equation(1)can be used to compute the transverse effect. For the 630 trajectories we calculated, the absoluteαvalues of 80.9%were larger than π/6.

Figure 4 Distributions of α and

On the basis of present understanding of the aeolian process (Pye and Tsoar, 2009), only three mechanisms could drive the transverse motion of grain: (1) the Magnus effect;(2) grain-bed collisions; and (3) three-dimensional (3-D)turbulent air flow. The general equation for grain motion can be written as:

in whichCd,ρa(bǔ), Ur, and Ωare the drag coefficient, the air density, the relative velocity, and the angle velocity of the grain, respectively. Here we make a rough estimation of the influence of the Magnus force on the transverse motion.Neglecting the drag force term, theycomponent of Equation(3)reduces to:

whereρsis the sand density. Note the 3-D rotation of grain;it is thus reasonable to assume that the three components of angle velocity are in the same scale, Ωx≈ Ωz≈ω. If the streamwise wind speeduis constant, the transverse displacementSyof grain can be estimated via integrating equation(6)twice:

whereH,L, andTare the height, length, and duration of saltation, respectively. For a typical saltation trajectory withH= 0.03 m,L= 0.30 m, andω= 1,000 πrad/s at a wind speed ofu= 7.0 m/s, the transverse displacement is only 0.0105 m. The above estimation indicates that the Magnus effect due to the spin of grain is not a governing factor.

Another possible driving mechanism is the collisions between sand grains and the bed. Either the irregularly shaped sand or the inclined bed could lead to the transverse motion of grain. Although an ideal 3-D grain-bed collision model (which still remains to be proved) predicts that the transverse linear and angular velocities cannot be ignored when the impact velocity is greater than 1.5 m/s (Zhenget al., 2008), it is still difficult to quantify and evaluate the role of this effect. The transverse motion can be observed more clearly if the wind speed becomes greater. Figure 5, in which the moving sand grains concentrated on the central section of the wind tunnel, is an instantaneous image with the frame rate of 125 fps and the thickness on the order of the saltation layer on the strong wind condition. As a disordered or stochastic process, the 3-D grain-bed collision could not lead to such a regular spatial pattern; therefore the transverse motion was finally attributed to the 3-D turbulent air flow. Restricted by the instrumentation, the flow structure could not be measured temporarily. An indirect evidence of the turbulence effect is the fluctuations of grain speed, as shown in figure 6, which reflect the response of sand motion to the unsteady and inhomogeneous variations of the wind.

Figure 5 A spatial pattern of aeolian sand transport

Figure 6 The change of grain speed with time in the transverse direction

4. Conclusions

In conclusion, the transverse motion plays an important role in aeolian sand transport. Both the motion orientation and the time-averaged speed follow Gaussian distributions.The 3-D turbulent air flow, rather than the spin of grain or the grain-bed collisions, controls the transverse motion.

The authors are grateful to Jie Zhang, XiaoZong Ren, and Lei Guo for their help in the wind tunnel experiment. This research was supported by the National Natural Science Foundation of China (Project No. 10904055).

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10.3724/SP.J.1226.2011.00013

9 September 2010 Accepted: 11 November 2010