Experimental investigation of the concentration profile of a blowing sand cloud

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1 Geomorphology 60 (2004) Experimental investigation of the concentration profile of a blowing sand cloud Xiaoping Liu*, Zhibao Dong The Key Laboratory of Desert and Desertification, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, No. 260, West Donggang Road, Lanzhou, Gansu Province , PR China Received 19 March 2003; received in revised form 3 July 2003; accepted 26 August 2003 Available online 21 November 2003 Abstract Detailed wind tunnel tests were carried out to establish the mean downwind velocity and transport rate of different-sized loose dry sand at different free-stream wind velocities and heights, as well as to investigate the vertical variation in the concentration of blowing sand in a cloud. Particle dynamic analyzer (PDA) technology was used to measure the vertical variation in mean downwind velocity of a sand cloud in a wind tunnel. The results reveal that within the near-surface layer, the decay of blown sand flux with height can be expressed using an exponential function. In general, the mean downwind velocity increases with height and free-stream wind velocity, but decreases with grain size. The vertical variation in mean downwind velocity can be expressed by a power function. The concentration profile of sand within the saltation layer, calculated according to its flux profile and mean downwind profile, can be expressed using the exponential function: c z = ae bz, where c z is the blown sand concentration at height z, and a and bare parameters changing regularly with wind velocity and sand size. The concentration profiles are converted to rays of straight lines by plotting logarithmic concentration values against height. The slope of the straight lines, representing the relative decay rate of concentration with height, decreases with an increase in free-stream wind velocity and grain size, implying that more blown sand is transported to greater heights as grain size and wind speed increase. D 2003 Elsevier B.V. All rights reserved. Keywords: Aeolian processes; Saltation; Blown sand-velocity profile; Sand transport flux profile; Concentration profile 1. Introduction A blowing sand cloud is a special case of gas solid two-phase flow. Blown sands usually move in three modes: creep, saltation and suspension (Bagnold, 1941). Saltation is the predominant mode of motion, accounting for about 75% of the total blown sand flux * Corresponding author. Fax: address: liuxp@ns.lzb.ac.cn (X. Liu). (Bagnold, 1941) and is the most-common subject of blown sand research (Williams, 1964; White, 1985; Wu, 1987; Anderson, 1988; McEwan and Willetts, 1991; White and Mounla, 1991). The formation of all scales of aeolian bed forms, from centimeter-sized ripples to kilometer-sized dunes, is due to the saltation process (Greeley and Iversen, 1985). Erosion by saltating sand is much more effective than by clean wind (Dong et al., 1987; Saleh and Fryrear, 1995), so in many areas, preventing erosion by a saltating sand cloud is the main task in blown sand control X/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi: /j.geomorph

2 372 X. Liu, Z. Dong / Geomorphology 60 (2004) The problems caused by blown sand are related not only to the amount transported, but also to the spatial distribution of the transported material. Two approaches have been used to study the concentration profile of blowing sand clouds: uses of wind tunnels under controlled conditions (Chepil and Woodruff, 1957; Williams, 1964; Gillette and Walker, 1977; Zhu, 1996) and analytical approaches (Owen, 1964; Anderson and Haff, 1988; Sorensen and McEwan, 1996; Wu et al., 2002). Chepil and Woodruff (1957) related the concentration of eroded soil particles near the surface to height using a power function, whereas Zhu (1996) related sand concentration to height using an exponential function. Sorensen and McEwan (1996) calculated the concentration of spherical grains using the saltation model developed by McEwan and Willetts (1991), which also shows that the concentration decreases exponentially with height. Wu et al. (2002) estimated the vertical profiles of particle concentration in the saltation layer based on a probability distribution of vertical liftoff velocities of grains, pointing to the stratified nature of the particle concentration profile. Our knowledge about the quantitative expression of blown sand concentration profile is still insufficient. The determination of the concentration of a blowing sand cloud depends on the measurement of its mass flux and velocity. The mass flux measurement using samplers is relatively easy both in the field and wind tunnels (Goossens et al., 2000). The total transport rate of sand is generally proportional to the cube of wind velocity (Bagnold, 1941; Greeley and Iversen, 1985), and the vertical distribution of blown sand mass flux decreases exponentially with height (Kawamura, 1951; Williams, 1964; Wu and Lin, 1965; Zou et al., 1992; Dong et al., 2002). In contrast, measurement of the velocities of a blowing sand cloud has been problematic. Although theoretical methods have greatly improved our understanding of blown sand movement, they are unable to derive the precise velocities of windblown sand particles due to the stochastic process of particle movement. There are complex mass and energy exchanges among saltating grains, grains on the surface, and the airflow. Moreover, there are processes difficult to consider in theoretical models such as the Magnus effect and Saffman lifting force (White and Schulz, 1977; Zou et al., 2001). Reliable measurement technology is the key to studying the velocity of a blowing sand cloud using an experimental approach. Although high-speed multi-flash photography and photoelectric cell methods have been used to measure movement velocities of individual particles (Zou et al., 1994; Greeley et al., 1996), these methods prove to be only good for fairly large particles (Greeley and Iversen, 1985). It is also difficult from photographic images to interpret the velocity of sand particles at very low heights such as below 0.5 cm where the grains are too crowded, and at higher height, such as over 7 cm, where the moving grains are too few (Zou et al., 2001). Because a blowing sand cloud is group movement composed of a large number of randomly interacting sand particles with various velocities (e.g., White and Schulz, 1977), the statistical average of particle velocities should be obtained using a sufficient number of sand particles. Loose sandy surfaces are most common in desert regions where blown sand is very active. The objectives of this study were: (1) to investigate the flux profile of a blowing sand cloud on a loose sandy bed using detailed wind tunnel tests; (2) to define the vertical variations in the mean downwind velocity of the blowing sand cloud using PDA (particle dynamic analyzer); and (3) to investigate the concentration profile of the blowing sand cloud in the saltation layer. 2. Experimental technique and apparatus The experiments were carried out in a wind tunnel in the Key Laboratory of Desert and Desertification, the Chinese Academy of Sciences. The blow-type non-circulating wind tunnel has a total length of m of which m is the working section. The cross-sectional area of the working section is m. The wind speed can be changed continuously from 1 to 40 m s 1. A DANTEC particle dynamic analyzer (PDA) was used to measure the velocities of a blowing sand cloud. Natural quartz sand from the field was sieved into five size groups according to the diameter (D, in mm): 0.1 < D V 0.2, 0.2 < D V 0.3, 0.3 < D V 0.4, 0.4 < D V 0.5, and 0.5 < D V 0.6. The sieved sand samples were put in a m and 2-cm-deep sand tray. The length of sand tray chosen ensured the

3 X. Liu, Z. Dong / Geomorphology 60 (2004) full development of a saltating sand cloud. During the experiment, the sand tray was set at 9.2 m downwind from the start of working section and exposed to five free-stream wind velocities of 10, 12, 14, 16 and 18 m s 1. It took s for the wind tunnel to reach the required equilibrium free-stream wind velocity. The sand tray was covered with an automatic sliding lid until the required wind velocity was reached. Velocities of the moving sand particles were measured at different heights near the downwind edge of the sand tray to study the vertical variation in the mean velocity of a blowing sand cloud. The measurement principle of PDA is shown in Fig. 1. Glass windows in the flow chamber wall of the wind tunnel provided optical access for the PDA. Parameters applied to the PDA experiments are listed in Table 1. The height of velocity measurement points was precisely adjusted using a computer-controlled traverse system. The final results of the sand cloud velocities are the statistical average of 5000 validated sand particles or a smaller number of validated particles at the measurement point in 30 s, whichever comes first. The computer transfers the velocity data into mean downwind velocity. Measured wind profiles for free-stream speeds of 8to18ms 1, in the wind tunnel at clean state (no sand transport), indicate that the boundary layer Table 1 Properties of the two-component PDA system (DANTEC) used Item Unit Specification Wavelength mm (Green) 488 (Blue) Beam spacing mm 38 Focal length of mm 800 transmitting lens Fringe spacing Am (Green) (Blue) Probe volume Am 390 (Green) diameter 370 (Blue) Frequency shift MHz 40 (Green) 40 (Blue) Gaussian beam mm 1.35 (Green) diameter 1.35 (Blue) Scattering angle deg 159 Receiving lens focal mm 800 length Transmitting angle deg 75.5 Receiving angle deg 60.5 thickness at the working section of the wind tunnel is about 12 cm (Fig. 2). We selected sand-velocity measurement heights within 10 cm above the tunnel floor so that the detected blowing sand cloud is in the boundary layer. Results from field measurements and wind tunnel tests show that a blowing sand cloud is a near-surface phenomenon, 80% occurs within 10 cm Fig. 1. Setup of the experimentation.

4 374 X. Liu, Z. Dong / Geomorphology 60 (2004) Fig. 2. Wind profiles at clean wind conditions for different free-stream speeds (V). above the ground surface (Wu, 1987). Bagnold (1941) suggested that the maximum saltating height of blown sand particles over loose sandy beds was about 9 cm. So the thickness of the boundary layer and the chosen heights of sand-velocity measurement are well representative of the blowing sand cloud, especially the saltating layer. The 19 selected velocity measurement heights were 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 30, 40, 50, 60, 70, 80, 90 and 100 mm. Free-stream wind velocities were measured by a Pitot-static probe at the start of the working section. Blown sand mass flux was measured using a segmented sand sampler (Dong et al., 2002). The sampler is 60 cm tall and sectionalized into sixty cm openings to collect the blown sand at 60 heights at 1-cm intervals. Each opening is connected to a sand chamber that is removed after the test to weigh the collected sand inside using a 1/1000-g electronic balance. The spacer between the openings is made very thin to reduce the measurement error. To minimize the interference of the sand sampler to the airflow, the leading part of the sampler is made wedge-shaped so that the width of the sand chamber is 1.5 cm while the width of openings is only 0.5 cm. A screened vertical vent is connected to each sand chamber to minimize the air pressure in the sand chamber and maximize the collection efficiency. The sampler proved to be good for collecting sands, especially particles over 0.1 mm in diameter whose inter-particle cohesion is not significant, since the overall efficiency was over 90%. In the experiment, the sampler was set 5 cm downwind of the edge of the sand tray (Fig. 1). The bottom of the lowest opening of the sampler was set flush with the tunnel floor. The prepared sand samples were put in the sand tray, the surface leveled to the tunnel floor, then blown by the preset free-stream (centerline, 60 cm above the tunnel floor) wind velocity above the initiation threshold. The wind tunnel was switched off when about 2 cm of the top sand in the tray was blown away. For each sample at each free-stream wind velocity, three repetitions were made to obtain the mean values. 3. Results and discussion 3.1. Variations of the mass flux of blown sand with height The mass flux of blown sand here is described in terms of the transport rate (g cm 2 s 1 ). We

5 X. Liu, Z. Dong / Geomorphology 60 (2004) obtained 25 groups of mass flux data (each group is the mean of three repetitions) under free-stream wind speeds of 10, 12, 14, 16 and 18 m s 1 (Fig. 3). The decay curves of blown sand flux with height are concave for all the grain sizes and wind speeds tested. Regression analysis shows that the Fig. 3. Wind tunnel results of the flux profiles of a blowing sand cloud (1) 0.1 < D V 0.2 mm, (2) 0.2 < D V 0.3 mm, (3) 0.3 < D V 0.4 mm, (4) 0.4 < D V 0.5 mm, (5) 0.5 < D V 0.6 mm, D is the sand grain diameter.

6 376 X. Liu, Z. Dong / Geomorphology 60 (2004) curves can be approximated by the exponential function: q z ¼ Ae z=b ð1þ where z is height (cm), q z is the blown sand transport rate at height z (g cm 2 s 1 ), and A and B are regression coefficients. R 2 values greater than 0.95 (Table 2) show that Eq. (1) fits well to the observed data for all the cases. Like Eq. (1), most published results suggest that the blown sand transport rate in saltation decays exponentially with height (Williams, 1964; Takeuchi, 1980; Greeley et al., 1983; Gerety and Slingerland, 1983; Anderson and Hallet, 1986; Wu, 1987; Fryrear et al., 1991; Fryrear and Saleh, 1993). Our results focus on sands greater than 0.1 mm in diameter and Table 2 Results of regression between the sand transport rate and height D (mm) V (m s 1 ) A B R < D V < D V < D V < D V < D V Fitted function: q z = Ae z/b, where q z is the sand transport rate (g cm 2 s 1 ) and z is height (cm). D is the sand grain diameter (mm), V is free-stream wind velocity (m s 1 ) and R 2 is the squared correlation coefficient. consequently, the effect of true suspension is negligible, as in many sand transport models (Bagnold, 1941; Greeley and Iversen, 1985). We can therefore confirm that the flux profile of a blowing sand cloud in saltation obeys the law of natural exponential decay with height Variations of the mean downwind velocity of a blowing sand cloud with height Fig. 4 shows the vertical variation in mean downwind velocities within a blowing sand cloud, comprising sediments of different sizes at different free-stream wind velocities. In general, the mean downwind velocity increases with height and freestream velocity, but decreases with the grain size. The greater the grain size, the more complex is the variation of the mean downwind velocity with height because coarse particles collide more strongly. The ratio of the mean downwind velocity of a blowing sand cloud to the clean wind velocity decreases with an increasing grain size and decreasing height (Table 3). This is because finer particles are more easily accelerated by wind and those particles at greater heights have more time of acceleration by wind. Comparison between mean downwind velocity and the actual wind velocity is difficult because we did not measure the wind velocity that is modified by the blowing sand cloud due to the Owen effect. The absolute value of downwind velocity of some particles can reach 230% of the clean wind velocity (e.g., sand with 0.3 < D V 0.4 mm at 1-cm height and 12-m s 1 free-stream wind velocity), implying that the inter-particle collision in the air or the initial impact on the bed also plays an important role in downwind velocity of the grains. Because existing literature about the mean velocity of a blowing sand cloud is scarce, we can only make a rough comparison between the results reported previously and ours reported here. Measurements of particle velocity by a photoelectric cell method at pressures corresponding to those on Earth, Mars and Venus have been made in the MARSWIT wind tunnel (Greeley and Iversen, 1985). The results show that the speeds of fairly large particles with a mean diameter of mm are 10 20% of the wind tunnel free-stream speed at Martian atmospher-

7 X. Liu, Z. Dong / Geomorphology 60 (2004) Fig. 4. Vertical variation of the mean downwind velocity of a blowing sand cloud within the saltation layer (1) 0.1 < D V 0.2 mm, (2) 0.2 < D V 0.3 mm, (3) 0.3 < D V 0.4 mm, (4) 0.4 < D V 0.5 mm, (5) 0.5 < D V 0.6 mm, D is the sand grain diameter. ic pressure, 50 60% at Earth atmospheric pressure, and nearly 100% at Venus atmosphere pressure. Detailed comparison and discussion are difficult because experimental conditions, tested particle size, measurement height and the free-stream wind velocity employed are different. Regression by the least squares method indicates that the change in mean downwind velocity of a

8 378 X. Liu, Z. Dong / Geomorphology 60 (2004) Table 3 Examples of the percentage (P) of the mean downwind velocities of a blowing sand cloud to the clean wind velocity D (mm) V (m s 1 ) z (cm) P (%) 0.1 < D V < D V < D V < D V < D V D is the sand grain diameter (mm), V is free-stream wind velocity (m s 1 ) and z is height (cm). blowing sand cloud with height can be expressed by the power function u z ¼ jz k ð2þ where z is height (cm), u z is the mean downwind velocity at height z (cm s 1 ), and j and k are regression coefficients. Table 4 indicates that except sand with 0.5 < D V 0.6 mm at 10-m s 1 free-stream wind velocity, Eq. (2) fits well to the observed data with R 2 z Wind tunnel experiments by Zou et al. (2001) also show that the increase in the velocity of windblown sand particles with height can be expressed by a power function. The difference between their results and ours is that their results focus on resultant particle velocity, whereas ours concern mean downwind velocity Variation of the concentration of saltating sand grains with height Given the vertical profiles of the mass flux ( q z ) and the mean horizontal particle velocity (u z ), the particle volume concentration (c z ) becomes q z c z ¼ q p u z ð3þ where q p is the sand density (2.65 g/cm 3 ). The measured values q z and u z for z V 10 cm were put into Eq. (3) to compute c z. Fig. 5 shows how the derived c z for different heights and particle sizes Table 4 Results of regression between the mean downwind velocity and height D (mm) V (m s 1 ) j k R < D V < D V < D V < D V < D V Fitted function: u z = jz k, where u z is the mean downwind velocity (cm s 1 ) and z is height (cm). D is the sand grain diameter (mm), V is free-stream wind velocity (m s 1 ) and R 2 is the squared correlation coefficient.

9 X. Liu, Z. Dong / Geomorphology 60 (2004) Fig. 5. Vertical variation of the concentration of a blowing sand cloud within the saltation layer (1) 0.1 < D V 0.2 mm, (2) 0.2 < D V 0.3 mm, (3) 0.3 < D V 0.4 mm, (4) 0.4 < D V 0.5 mm, (5) 0.5 < D V 0.6 mm, D is the sand grain diameter. varies according to free-stream wind velocities. The decay curves of blown sand concentration with height are concave for all the grain sizes and wind speeds tested. Regression analysis shows that at all grain sizes and wind speeds, the particle volume concentration decreases exponentially with height: c z ¼ ae bz ð4þ

10 380 X. Liu, Z. Dong / Geomorphology 60 (2004) where z is height (cm), c z is the particle volume concentration at height z, and a and b are regression coefficients. As shown in Table 5, Eq. (4) fits well to the observed data with R 2 z Sorensen and McEwan (1996) also proposed an equation similar to Eq. (4) for 2-cm near-surface layer, based on the work of McEwan and Willetts (1991) saltation model for six shear velocities. Some other published results also suggest that the blown sand concentration in saltation decays exponentially with height (Zou et al., 1992; Zhu, 1996). Because we used sands greater than 0.1 mm, the effect of true suspension is negligible. Thus, our results confirm that the natural exponential function is a good descriptor for saltation concentration. Coefficient a, representing the concentration at zero height, increases with wind speed, but decreases with grain size (Table 5). The curves in Fig. 5 are converted to straight lines if we plot concentration c z on a log scale against Table 5 Results of regression between concentration and height D (mm) V (m s 1 ) a b R < D V e e e e e < D V e e e e e < D V e e e e e < D V e e e e e < D V e e e e Fitted function: c z= ae bz, where c z is particle volume concentration and z is height (cm). D is the sand grain diameter (mm), V is free-stream wind velocity (m s 1 ) and R 2 is the squared correlation coefficient. height, and coefficient b in Eq. (4) corresponds to the slope of the straight lines. Differences in the coefficient b in Table 5 indicate that more sand is transported to higher levels as sand grain size and wind speed increase. 4. Conclusions The concentration profile of a blowing sand cloud has been established by detailed wind tunnel investigation using different-sized sand at different freestream wind speeds. The sand sampler that is sectionalized into 60 heights with 1-cm interval is reasonably good for demonstrating the variation of blown sand flux with height. The mean downwind velocities of a blowing sand cloud were measured using PDA. The velocity of a sand cloud was mainly influenced by clean wind velocity and was of the same order of magnitude as the wind velocities, although initial impacts on the sand bed and inter-particle collisions in the air may have caused sand movement opposite to the wind direction. The mean downwind velocities of fine sands at greater heights are particularly close to the clean wind velocity. The obtained exponential-decay function of blown sand concentration with height within the near-surface layer agrees well with previous research results regarding the concentration of sand in saltation, pointing to wide applicability of such a function. The conditions in a wind tunnel, however, are different from those in the field where the wind direction and speed are highly variable. Therefore, the concentration profiles of a blowing sand cloud should also be evaluated using detailed measurement in the field. Moreover, saltation is related not only to sand size and wind speed but also to surface properties. For example, saltation is much more intense over desert pavements than on loose sandy surfaces (Bagnold, 1941). The influence of surface properties on the sand concentration profile is also in need of further study. Acknowledgements The National Key Project for Basic Research (G ) and the Knowledge Innovation Project of the Chinese Academy of Sciences

11 X. Liu, Z. Dong / Geomorphology 60 (2004) (KZCX3-SW-324) fund this research. Their financial support is gratefully acknowledged. We wish to thank Mr. Z. Yang and Mr. H. Xia for their help in wind tunnel experiment; Dr. G. Wu and Mr. B. He for preparing the illustrations. Prof. T. Wang and Prof. J. Qu s encouragement and Prof. X. Zou s constructive suggestions are specially appreciated. References Anderson, R.S., Erosion profiles due to particles entrained by wind: application of aeolian sediment-transport model. Geological Society of America Bulletin 97, Anderson, R.R., Haff, P.K., Simulation of aeolian saltation. Science 241, Anderson, R.S., Hallet, B., Sediment transport by wind: toward a general model. Geological Society of America Bulletin 97, Bagnold, R.A., The Physics of Blown Sand and Desert Dunes. Methuen, London. 265 pp. Chepil, W.S., Woodruff, N.P., Sedimentary characteristics of dust storms: II. Visibility and dust concentration. American Journal of Science 255, Dong, G.R., Li, C.Z., Jin, J., Gao, S.Y., Wu, D., Some results of soil erosion by wind from wind tunnel tests. Chinese Science Bulletin 32 (4), (in Chinese). Dong, Z.B., Liu, X., Wang, H.T., The flux profile of a blowing sand cloud: a wind tunnel investigation. Geomorphology 49, Fryrear, D.W., Saleh, A., Field wind erosion: vertical distribution. Soil Science 155, Fryrear, D.W., Stout, J.E., Hagen, L.J., Vories, E.D., Wind erosion: field measurement and analysis. Transactions of the ASAE 34, Gerety, K.M., Slingerland, R., Nature of saltation population in wind tunnel experiments with heterogeneous size-density sands. In: Brookfield, M.E., Ahlbrand, T.S. (Eds.), Eolian Sediments and Progresses: Developments in Sedimentology. Elsevier, Amsterdam, pp Gillette, D.A., Walker, T.R., Characteristics of airborne particles produced by wind erosion of sandy soil, high plains of west Texas. Soil Science 123, Goossens, D., Offer, Z., London, G., Wind tunnel and field calibration of five aeolian sand traps. Geomorphology 35, Greeley, R., Iversen, J.I., Wind as a Geological Process. Cambridge Univ. Press, Cambridge. 333 pp. Greeley, R., Williams, S.H., Marshall, J.R., Velocities of wind-blown particles in saltation: preliminary laboratory and field measurements. In: Brookfield, M.E., Ahlbrandt, T.S. (Eds.), Eolian Sediments and Progresses: Developments in Sedimentology. Elsevier, Amsterdam, pp Greeley, R., Blumberg, D.G., Williams, S.H., Field measurement of the flux and speed of wind-blown sand. Sedimentology 43, Kawamura, R., Study on sand movement by wind. Report, vol. 5. Institute of Science and Technology, Tokyo, pp McEwan, I.K., Willetts, B.B., Numerical model of the saltation cloud. Acta Mechnica 1, (Suppl.). Owen, P.R., Saltation of uniform sand grains in air. Journal of Fluid Mechanics 20, Saleh, A., Fryrear, D.W., Threshold wind velocities of wet soils as affected by wind blown sand. Soil Science 160, Sorensen, M., McEwan, I.K., On the effect of mid-air collisions on aeolian saltation. Sedimentology 43, Takeuchi, M., Vertical profile and horizontal increase of driftsnow transport. Journal of Glaciology 26, White, B.R., The dynamics of particle motion in saltation. In: Barndorff-Nielsen, O.E (Ed.), International Workshop on the Physics of Blown Sand. I. Modeling Concepts, vol. 1. Department of Theoretical Statistics, Institute of Mathematics, University of Aarhus, Aarhus, pp White, B.R., Mounla, H., An experimental study of Froude number effect on wind tunnel saltation. Acta Mechanica 1, (Suppl.). White, B.R., Schulz, J.C., Magunus effect on saltation. Journal of Fluid Mechanics 81, Williams, G., Some aspects of aeolian transport load. Sedimentology 3, Wu, Z., Aeolian Geomorphology. Science Press, Beijing, p. 316 (in Chinese). Wu, Z., Lin, Y., A preliminary study on blown sand movement and its control. Blown Sand Control Research 7, 7 14 (in Chinese). Wu, J.J, He, L.H., Zheng, X.J., A study on the characteristics of the concentration profile in saltating layer. Journal of LanZhou University (Natural Science) 38, Zhu J.J., Theory and Experiment Research on Gas-Particle Turbulent Flow in a Boundary Layer. Ph.D thesis. Department of Civil Engineering Mechanics, Xi an Jiaotong University, p. 28 Zou, X.Y., Zhu, J.J., Dong, G.R., Liu, Y.Z., Wu, D., Distribution function of the vertical eject velocities of the saltating sand particles in blowing sand cloud. Chinese Science Bulletin 37 (23), (in Chinese). Zou, X.Y., Liu, Y.Z., Dong, G.R., Tentative calculation of wind sand current energy. Chinese Science Bulletin 39 (12), Zou, X.Y., Wang, Z.L., Hao, Q.Z., Zhang, C.L., Liu, Y.Z., Dong, G.R., The distribution of velocity and energy of saltating sand grains in a wind tunnel. Geomorphology 36,