RETRACTED: The influence of sand bed temperature on lift-off and falling parameters in windblown sand flux

Geomorphology 204 (2014) 477–484

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The influence of sand bed temperature on lift-off and falling parameters in windblown sand flux Tian-Li Bo a,b,⁎, Shao-Zhen Duan a,b, Xiao-Jing Zheng a,b,c, Yi-Rui Liang a,b a b c

Key Laboratory of Mechanics on Disasters and Environment in Western China, Lanzhou University, Lanzhou, 730000, China Department of Mechanics, Lanzhou University, Lanzhou, 730000, China School of Electronical and Mechanical Engineering, Xidian University, Xi'an, 710071, China

a r t i c l e

i n f o

Article history: Received 27 December 2012 Received in revised form 16 August 2013 Accepted 19 August 2013 Available online 31 August 2013 Keywords: Probability distribution Horizontal velocities Vertical velocities Sand bed temperature, windblown sand flux

a b s t r a c t In deserts the temperature of the sand bed can reach up to more than 50 °C, however, existing knowledge on the lift-off and falling velocities and angles of sand particles in windblown sand flux is based mainly on experimental results over a temperature range of 20 °C to 30 °C. Consequently, existing experimental results cannot reflect the actual interaction between saltating sands and the bed. In this study, the influence of the sand bed temperature on the probability distribution of lift-off and falling velocities and angles of sand particles is investigated through an improved Particle Image Velocimetry (PIV) system. Results demonstrate that the distribution shape of lift-off and falling velocities and angles of sand particles is not greatly influenced by the temperature of sand bed, however it has a certain influence on the center of the probability distributions of horizontal velocities, as well as the average, decay constant and amplitude of the distributions of vertical velocities and angles. We present formulas to describe the probability distributions of lift-off and falling velocities and angles with regard to the influence of sand bed temperature. © 2013 Elsevier B.V. All rights reserved.

1. Introduction As a natural phenomenon windblown sand flux is the main reason for the formation of various aeolian landforms and natural disasters. Due to limitations in experimental conditions and methods, detailed and accurate observations of near-bed sand motions are to a large extent prevented (Cheng et al., 2009). Therefore, scientists have divided the process of windblown sand movement into four sub-processes, i.e., the lift-off of sand particles, the saltation of sand particles, the interaction between sand particles and airflow, and the collision between saltating sand particles and the sand bed. Sand particles blown by wind or ejected by falling sand particles are accelerated by airflow and continuously obtain energy from the airflow which is subsequently transferred to the ground surface by collisions between falling sand particles and the bed (Bagnold, 1941; Chepil, 1945; Bisal and Nielsen, 1962; Owen, 1964; White and Schulz, 1977; Mitha et al., 1986; Anderson and Haff, 1988, 1991; Sun and Wang, 2001; Davidson-Arnott et al., 2005; Zheng et al., 2005; Cheng et al., 2006; Zhang et al., 2007). In the process, the lift-off and falling velocities and angles of saltating sand particles and their distributions are of great significance to bridge in bridging microscopic and macroscopic research on the physics of blown sands

⁎ Corresponding author at: Lanzhou University, Department of Mechanics, Lanzhou 730000, China. E-mail address: [email protected] (T.-L. Bo). 0169-555X/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.geomorph.2013.08.026

and are key quantities in determining how the collision processes affect the development of windblown sand flux (Zheng, 2009). As a result, researchers have carried out many studies on the lift-off and falling parameters using theoretical models and experiments in both wind tunnel and field settings (Bagnold, 1941; Owen, 1964; Willetts and Rice, 1986; Anderson and Haff, 1988, 1991; Greeley et al., 1996; Zou et al., 2001; Namikas, 2003; Dong et al., 2004; Wiggs et al., 2004). Since the seminar held at Arhus University in 1985 (Cheng et al., 2006, 2009), great progress has been made on the probability distribution of the lift-off velocities and angles of saltating sand particles by high-speed photographic (HSP), Particle Dynamics Analyzer (PDA) and Particle Image Velocimetry (PIV) etc. (Bagnold, 1941; Bisal and Nielsen, 1962; White and Schulz, 1977; Jensen and Sørensen, 1986; Willetts and Rice, 1986; Werner and Haff, 1988; Anderson and Haff, 1991; Nalpanis et al., 1993; Rice et al., 1995; Greeley et al., 1996). For example, Zou et al. (2001) measured the saltating particles' velocities by HSP and concluded that the probability distribution of saltating sand velocities was a Pearson VII distribution pattern. Greeley et al. (1996) suggested that both of the velocity distributions of ascending and descending sand particles showed a single peak. Rasmussen and Sørensen (2005) showed that the probability distribution of horizontal velocities of sand particles displayed a right skew at 5 mm height. Cheng et al. (2006) argued that the lift-off angles followed a lognormal distribution, whereas the horizontal, vertical, and resultant lift-off velocities followed a Gamma distribution function. Dong et al. (2002, 2004) measured sand particles' velocities by PDA and showed that the probability distribution of sand particles' downwind velocities

T.-L. Bo et al. / Geomorphology 204 (2014) 477–484

followed a Gaussian function, while that of vertical velocities followed a Lorentzian function for fine particles. The measurements of Xie et al. (2006) investigated the probability distribution of lift-off and incident velocities of sand particles and suggested that their vertical components followed Gamma functions with different peak values and shapes and the downwind incident and lift-off horizontal velocities can be described by log-normal and Gamma functions, respectively. The measurements of Kang et al. (2008) suggested a normal function for horizontal lift-off velocities of sand particles and an exponential function for vertical lift-off velocities, whilst the probability distribution of resultant liftoff velocity of saltating particles can be expressed as a log-normal function. Yang et al. (2007) measured particle velocity by PIV which showed that both of the horizontal and vertical velocities of saltating sand particles fitted Gaussian distributions well. At the same time, researchers also carried out investigations of the falling parameters of saltating sand particles (Bagnold, 1941; White and Schulz, 1977; Mitha et al., 1986; Anderson and Haff, 1988; Rice et al., 1995; Dong et al., 2002). For example, Dong et al. (2002) reported that the falling angles increased linearly with increasing lift-off angles, the probability distribution of the falling velocities of saltating sand particles followed a Weibull distribution, and the resultant falling velocities of saltating sand particles followed a modified exponential distribution. Zou et al. (1999) performed a theoretical analysis and suggested a linear relationship between the cotangent of the falling angle and that of the initial lift-off angle. Kang et al. (2008) reported that the probability distributions of the horizontal velocity of ascending and descending particles had a typical peak and were right-skewed at 4 mm height. Cheng et al. (2009) reported that both of the falling angles and vertical velocities followed a gamma distribution and the horizontal and resultant falling velocities followed a Pearson IV distribution. As for the influence of temperature on these distribution phenomena, McKenna Neuman (2003, 2004) studied the influence of the temperature/humidity on the entrainment and transport of sedimentary particles by wind in a wind tunnel. The results suggested that it is easier to entrain particles at low temperature, wherein the critical tractive stress can be as much as 30% lower. For any given wind speed, this factor translates into the entrainment of a particle approximately 40–50% larger in diameter in very cold air as compared to very warm air. Similarly, aeolian transport events at low temperature may be less intermittent than at high temperature, as a result of the reduction in the threshold wind speed. Cold airflows support higher mass transport rates than very warm air, at − 40 °C mass transport rate may be as much as 70% higher than for the equivalent wind speed in hot deserts at air temperatures of 40 °C. The decreased tension of water adsorbed onto particle surfaces at low temperatures is postulated to reduce inter-particle cohesion and, thus, to increase the elasticity of particle impacts on cold beds. From the above-mentioned review of literature, we can see that existing results of lift-off and falling velocities and angles of sand particles are mainly based on experimental results with the temperature of sand bed ranging from 20 °C to 30 °C. However, due to the prolonged exposure to sunshine the temperature of the sand bed in desert regions can reach up to more than 50 °C. Consequently, existing experimental results inaccurately reflect the actual interaction between saltating sands and the sand bed. Therefore it is necessary to conduct more indepth investigations on the influence of bed temperature on the liftoff and falling parameters of sand particles. In this paper, Section 2 gives a description of the methods and materials used in our wind tunnel experiments, including experimental setup and data analysis method; Section 3 presents results and discussions on the influences of the temperature of the sand bed on the probability distribution of lift-off and falling velocities and angles of sand particles, and eventually formulas are given to describe the probability distribution of lift-off and falling velocities and angles of sand particles with regard to the influence of sand bed temperature; Section 4 offers the conclusions of this work.

2. Methods and materials 2.1. Wind tunnel experiment The experiments were performed at the multi-function environmental wind tunnel of the Key Laboratory of Mechanics on Disasters and Environment in western China, the Ministry of Education of China, Lanzhou University, P. R. China. The working section of the wind tunnel is 20 m long with a cross-section that is 1.3 m wide and 1.45 m high (Tong and Huang, 2012). The wind velocity along 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 of the working section ensure that saltation occurs within the boundary layer of the steady turbulence flow (Tong and Huang, 2012). The main purpose of the experiment is to measure the lift-off and falling velocities and angles of saltating particles. Natural sands were taken from the Badain Jaran Desert with an average sand diameter of 0.3 mm; the probability distribution of particle size is shown in Fig. 1. Prepared sand samples were laid in an 18 m-long and 1 m-wide sand tray where the depth of sand bed was 0.05 m so that a fully developed saltation flow could be developed. Since the sand bed was long enough, this ensured that the distance between the CCD camera and the leading edge of the sand bed was larger than the saturation length of sand transport, therefore, the measured data in this study correspond to saturated sand flux. In experiments, the sand bed was exposed to free-stream wind which had a friction velocity 0.45 m/s. An automatic sliding lid was used to cover the sand bed until the wind velocity was satisfied, so that the sand samples in the sand bed were not blown away before starting any measurements. The velocities of particles were measured by a PIV system, an optical glass window in the wind tunnel flow chamber wall provided an optical access for the PIV system. The velocity vectors were derived from subsections of the target area of the particle-seeded flow by measuring the movement of particles between two light pulses, i.e. Vp = Δx/Δt, where Vp is the particle velocity, and Δx is the displacement of particles between two light pulses with time interval Δt (delay time) (for more details of the measurement principle, please refer to Stanislas et al., 2000.). The PIV system had five key components: a double pulsed laser (two laser pulses that illuminate the saltating particles with a short time difference), light sheet optics (optics that transform the laser light into a thin light plane that is guided into the saltating cloud), a charge-coupled device (CCD) camera (fast frame-transfer CCD that captures two frames exposed by laser pulses), a synchronizer (timing controller that uses highly accurate electronics to control the

18 16

Probability distribution(%)

478

14 12 10 data

8 6 4 2 0 0.01

0.1

Partical Size (mm) Fig. 1. The probability distribution of sand grain diameter.

1

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Fig. 2. Layout of the experimentation.

laser and camera), and operational software (Yang et al., 2007). Fig. 2 illustrates the setup of the experiment. In the experiments, the CCD camera was set 0.65 m from the light sheet, resulting in a target area of about 108 mm wide × 108 mm high (The image size was 2048 pixels wide × 2048 pixels high with an amplification factor of 0.05 that converted the pixels to millimeters). The image acquisition rate was set as 20 frames per second where the delay time was 0.002 s. Each experiment was repeated three times, and the duration of each run was 2 min after the saltation flow became steady. The final particle velocity represented the average value over 10 s (i.e., 200 frames), which was selected from the data obtained in 6 min and ensured the analysis results were consistent with those when the sampling duration was longer than 10 s. Every two frames yielded one velocity sample, so the final particles' velocities were obtained from 100 samples, and the number of sand particles used for analysis was O (107). Free-stream wind velocities were measured by a Pitot-static probe at the front edge of the working section (Fig. 2). It should be noted that our laser incident setup of the PIV system is different from existing PIV experiments. The incident laser is not from the top (Yang et al., 2007) but from the side edge of the wind tunnel, and then the laser was refracted into the flow direction by a mirror whose size is 10 cm × 10 cm. The distance between the mirror and the target area of CCD camera was about 5 m, which guarantees that the mirror does not affect the flow field and the motions of particles within the target area, as shown in Fig. 2. This improvement reduces the influence of the laser reflection from the ground surface on the identification of saltating sand particles, especially the near-bed sand particles, thereby the track of sand particle motion close to the sand surface can be achieved. In the experiments, heating of the sand bed was achieved by a heating device which was laid under the sand bed. The heating device consists of iron sheets and electric heater coils, that is electric heater

coils were tightly arranged between two iron sheets where the distance between two electric heater coils was 1 cm, which guarantees that the sand particles are uniformly heated.

2.2. Data analysis In order to obtain the spatial distribution, velocity distribution and particle size information of sand particles in the windblown sand flux, Insight 3G software was used to analyze the PIV images (Mizushima et al., 2009; Volino et al., 2009). The analysis consists of four steps. 1) Determining the position of sand particles: we separate sand particles from the PIV original gray images (Fig. 3) based on global gray-scale threshold (Gonzalez, 2003), and then determine the centroid of a sand particle according to the pixels it occupies (Tapia et al., 2006); 2) Obtaining sand grain diameter: we determine the sand grain diameter according to the number of the pixels occupied by a sand particle, i.e., the cross-sectional area of a spherical sand particle is equal to the sum area of the pixels; 3) Particle-pair identification: image pairs are processed using the crosscorrelation technique of the Insight 3G software package (Stockman et al., 2009). It should be noted that the area of the query window was generally taken as 32 32 or 64 64 (Adrian, 1991), however we changed it into 64 32 considering that the horizontal velocities of sand particles are much larger than their vertical components. Such treatment not only reduces computations, but also ensures the accuracy of the matching; 4) Particle velocity calculation: based on the distance between matching sand particles in two successive frames, we can calculate a sand particle's velocity (Tapia et al., 2006).

Fig. 3. A pair of the original PIV image.

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Fig. 4. (a) and (b) are two PIV original images, for observation we select only the zone below 1.3 cm, (c) is the velocity vector of the sand particle obtained from (a) and (b), where circles indicate sand particles and arrows denote the velocity vector of sand particles; sand size is represented by circle's diameter.

Through above 4 steps we can identify the diameters, locations and velocities of moving sand particles from successive frames, as shown in Fig. 4. Another improvement of this study is the identification of the ground surface in data analysis. In previous experiments, the sand bed was always deemed as a flat bed (Nalpanis et al., 1993; Rice et al., 1995; Zhang et al., 2007; Cheng et al., 2009), which did not consider the change of the elevation of sand surface (which could be several millimeters) during the development of the windblown sand flux. Since it is difficult to measure the ground surface during an experimental run, Werner (1990) assumed that the fluctuation of the sand bed is not larger than one sand grain diameter. This assumption has been accepted up to now, but it doesn't match the actual situation in windblown sand flux. Therefore, we determine the exact position of the sand bed surface based on the area occupied by sand particles in PIV images, i.e., the area which has over 95% sand grain cover is deemed as a part of sand bed surface. Such a treatment has not been considered in previous algorithms. 3. Results and discussion Following the procedure demonstrated in the previous section, we measured the lift-off and falling velocities and angles of sand particles in the wind tunnel when the friction wind velocity is 0.45 m/s, the sand bed (T) temperatures are 25 °C, 38 °C, 50 °C, 55 °C and 65 °C. It should be noted that the lift-off and falling angles are, respectively, determined by counterclockwise and clockwise. Fig. 5 displays the probability distribution of horizontal and vertical falling velocities of sand particles for various temperatures of sand bed. From Fig. 5 it is apparent that the distribution shape of falling velocities is not greatly influenced by the temperature of the sand bed, that is, the probability distribution of horizontal falling velocities of sand parti2

f uf −ðx−xc Þ =2w2f cles follows a normal distribution (R N 0.99), i.e., yuf , 0 þA e f which is consistent with the results of Kang et al. (2008); here, yuf 0 , xc, wf and Auf are the offset, center, width and area of the normal distribution,

respectively. The probability distribution of the vertical falling velocities of sand particles also follows a negative exponential distribution wf −x=t (R N 0.94), i.e., ywf , which is also consistent with the results 0 þA e f wf are the offset, decay constant of Kang et al. (2008), where ywf 0 , t and A and amplitude of the negative exponential distribution, respectively. However, there are some quantitative differences for various bed temperatures, that is, with increasing bed temperatures the center of the probability distribution of the horizontal falling velocities increases linearly by about 45% (i.e., a progressively right-shifted trend as the temperature of the sand bed increases), the average of the probability distribution of the vertical falling velocities decreases exponentially (by 23%), the decay constant of the probability distribution of the vertical falling velocities decreases linearly, and the amplitude of the probability distribution of vertical falling velocities increases exponentially, as shown in Fig. 5c. Therefore, the probability distribution of the falling velocities can be described by the following equation, f

8
 2 2 > < f u f jT ¼ 34e−ðu f −0:3−0:004T Þ =2ð0:35Þ
 > : f v jT ¼ 40ð2 þ 0:01T Þe−v f =ð0:4−0:001T Þ f

ð1Þ

Here, T is the temperature of the bed, and uf and vf are the horizontal and vertical falling velocities of sand particles, respectively. From Fig. 5 the horizontal falling velocity is seen to be smaller than the results of Kang et al. (2008) and Cheng et al. (2009), as shown in Table 1. This difference may be caused by the following reasons: 1) the sand particles whose horizontal velocities are negative (when sand particles move along streamwise the horizontal velocities of sand particles are positive) were ignored in the previous studies (Cheng et al., 2009); 2) the friction wind velocity is less than in previous studies (Table 1), while the horizontal falling velocity increases with wind velocity (Kang et al., 2008); and 3) sampling height is less than in previous studies (Table 1). Due to the wind velocity and the drag force acting on the sand particles increasing with height, these cause the horizontal

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105 wf

A of vf;R=0.93

c

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0.4 95 0.3

Awf

xcf/average/tf

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f

xc of uf ;R=0.91

0.2

90

average of vf ;R=0.99 f

t of vf ;R=0.95

0.1

85 30

40

50

60

Temperature (OC) Fig. 5. The change of falling velocities with the increase of temperature. (a) and (b) show the probability distributions of horizontal and vertical falling velocities, respectively, in different cases of sand bed temperature; (c) shows the variations of xfc, tf, Awf and average with increasing temperature, respectively. Here, xfc is the center of the probability distribution of horizontal falling velocities; the average, tf and Awf are the averaged value, decay constant and amplitude of the probability distribution of vertical fall velocities, respectively.

falling velocities to increase with height. The impact of a fast particle naturally results in two populations of particles, a fast rebounding particle and many ejected particles, where the ejected particles typically reach saltation heights of the order of 10 times the mean diameter. However, most of the sampling heights in existing experiments are greater than the saltation heights, so a considerable number of grains transported with low trajectories were lost in previous studies (Jensen and Sørensen, 1986; Dong et al., 2002; Andreotti, 2004; Lammel et al., 2012; Pähtz et al., 2012). As a fourth consideration, the sampling number of previous studies (Table 1) is relatively small, it is therefore insufficient to reflect the actual movement of sand particles. Fig. 6 displays the probability distribution of horizontal and vertical lift-off velocities of sand particles for various bed temperatures. It reveals that the distribution shape of lift-off velocities of sand particles is not greatly influenced by the temperature of sand bed, that is, the Table 1 The experiment details and results of previous studies and this paper (h is sampling height; xc is the mean horizontal fall velocity; u* is friction wind velocity; N is the sampling number; HSP is high-speed photographic method; PDA is Particle Dynamics Analysis method; PIV is Particle Image Velocimetry method).

This paper Kang et al. (2008) Cheng et al. (2009)

Method

xc (m/s)

h(mm)

u*(m/s)

N

PIV PDA HSP

0.43–0.6 1.0 1.1

b1 N4 N5

0.45 0.72 0.67

N107 3000–4000 340

probability distribution of the horizontal lift-off velocities follows a norl 2 2 mal distribution (R N 0.99), i.e., yul þ Aul e−ðx−xc Þ =2wl , where, yul, xl , w 0

0

c

l

and Aul are the offset, center, width and area of the normal distribution, respectively. The probability distribution of the vertical lift-off velocities of sand particles follows a negative exponential distribution (R N 0.99), wl −x=t l wl i.e., ywl , where ywl are the offset, decay constant 0 , t and A 0 þA e and amplitude of the negative exponential distribution, respectively. It is consistent with the distribution shape of the falling velocities. However, there are some quantitative differences for various sand bed temperatures, that is, with increasing bed temperature the center of the probability distribution of the horizontal lift-off velocities increases linearly by about 55% (i.e., a progressively right-shifted trend as the temperature of the sand bed increases), the average of the probability distribution of the vertical lift-off velocities decreases exponentially (by 64%), the decay constant of the probability distribution of the vertical lift-off velocities decreases exponentially, and the amplitude of the probability distribution of vertical lift-off velocities increases exponentially, as shown in Fig. 6c. Therefore, the probability distribution of the lift-off velocities of sand particles can be described by the following equation, l

8 < f ðu jT Þ ¼ 34e−ðul −0:25−0:005T Þ2 =2ð0:35Þ2 l
 −T=72 : f ðvl jT Þ ¼ 140 1−2e−T=20 e−vl =0:6e

ð2Þ

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O

25 C O 38 C O 50 C O 55 C O 65 C

20

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probability distribution(%)

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0.8 wl

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A of vl;R=0.99

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xcl/average/tl

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xc of ul;R=0.97 0.4

90

average of vl;R=0.99 l

80

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70 25

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O

Temperature( C) Fig. 6. The change of lift-off velocities with the increase of temperature. (a) and (b) show the probability distributions of horizontal and vertical lift-off velocities, respectively, in different cases of sand bed temperature; (c) shows the variations of xlc, tl, Awl and average with increasing temperature, respectively. Here, xlc is the center of the probability distribution of horizontal lift-off velocities; the average, tl and Awl are the averaged value, decay constant and amplitude of the probability distribution of vertical lift-off velocities, respectively.

where, ul and vl are the horizontal and vertical lift-off velocities of sand particles respectively. Actually, the variation of the lift-off and falling velocities of sand particles with the temperature of sand bed can be explained by the variation of the air density (ρ), the relative humidity, the upward and streamwise wind velocities, i.e., with increasing bed temperature the air density and the relative humidity decrease, the upward and streamwise wind velocities increase (McKenna Neuman, 2003, 2004; Yue and Zheng, 2006; Yahaya and Frangi, 2009). With the increase of the streamwise wind velocity, the drag force F D ¼ 18 πC D ρD2s ju−ud jðu−ud Þ (where CD is the aerodynamic drag coefficient, Ds is sand grain diameter, u and ud are wind and particle velocities, respectively) increases, which therefore results in an increase in the horizontal lift-off and falling velocities of sand particles. With the increase of the upward wind velocity the drag force increases, and then the vertical falling velocities of sand particles decrease. Due to the decrease in relative humidity, the increased surface tension of water adsorbed onto particles at high temperatures is postulated to increase inter-particle cohesion and thus to decrease the elasticity of particles impacting on the bed. Accordingly, the vertical lift-off velocity decreases. In addition, with increasing horizontal falling velocity and decreasing vertical falling velocity, the lift-off angle decreases after the particle–bed collision, and then the horizontal and vertical lift-off velocities increase and decrease, respectively. It should be noted that though the decrease in air density makes the drag force decrease, it is relatively small compared with the action of wind velocity.

Fig. 7 displays the probability distribution of the lift-off and falling angles of sand particles for various bed temperatures. The distribution shape of lift-off and falling angles of sand particles appears not to be significantly influenced by the temperature of sand bed, that is, both of the probability distribution of lift-off and falling angles of sand particles follows a negative exponential distribution (R N 0.93). However, there are some quantitative differences for different bed temperatures, that is, with increasing sand bed temperature the average of the lift-off and falling angles decreases exponentially by about 51% and 39%, respectively, over the 25–65 °C temperature range; the amplitudes of the probability distribution of the lift-off and falling angles increase linearly; and the decay constants of the probability distribution of the lift-off and falling angles decrease exponentially, as shown in Fig. 7c and d. Therefore, the probability distribution of the lift-off and falling angles of sand particles can be described by the following equation, (

−α=ð158e−T=33 Þ

f ðαjT Þ ¼ ð1:5 þ 0:6T Þe

f ðβjT Þ ¼ ð18:4 þ 0:4T Þe

−β=ð48e−T=97 Þ

ð3Þ

where, α and β are the respective lift-off and falling angles of the sand particles. In addition, we analyzed the variation of the ratios between lift-off and falling quantities (velocities and angles) of sand particles with bed temperature, as shown in Fig. 8. It can be found that with increasing

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30

probability distribution(%)

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25 O

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lift-off angle;R=0.97 incident angle;R=0.97

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tl of lift-off angle;R=0.99 Af of incident angle;R=0.98

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Fig. 7. The change of lift-off and incident angle with the increase of temperature. (a) and (b) show the probability distributions of lift-off and incident angles, respectively, in different cases of sand bed temperature; (c) shows the variations of averaged lift-off and incident angles with increasing temperature; (d) gives the variations of Al, Af, tl and tf with bed temperature. Here, Al and Af are the amplitude of the probability distribution of lift-off and falling angles, respectively; tl and tf are the decay constant of the probability distribution of lift-off and fall angles.

4. Conclusions In this study, we achieved measurements of the lift-off and falling velocities and angles of saltating sand particles close to bed surface in a wind tunnel with different temperatures of sand bed using an improved

lift-off parameters/incident parameters

bed temperature the ratio between horizontal lift-off velocity and horizontal falling velocity decreases (by 11%), the ratio between vertical lift-off velocity and vertical falling velocity increases (by up to 54%) and the ratio between lift-off angle and falling angle decreases (by 21%). Finally, the influence of bed temperature on aeolian saltation characteristics was analyzed. With increasing bed temperature the vertical lift-off velocities of sand particles decrease, and the saltating height or the height of saltating layer decreases accordingly. With increasing bed temperature the horizontal lift-off velocities of sand particles increase, and then the saltating length increases. Existing studies show that steady state flux can be written as qs = ρsus, where the saturated density, ρs = 2γρa(u2* − u2* t)/g, us is the steady state velocity, ρa is the air density, u*t is the threshold friction wind velocity and y is the model parameter proposed by Sauermann et al. (2001). Therefore with increasing sand bed temperature the vertical lift-off velocity decreases and the threshold friction wind velocity increases, and then the ρs decreases. With increasing temperature the horizontal velocity increases, and then us increases. That is, the increasing temperature of the sand bed makes the number of sand particles in the windblown sand flow decrease, but the velocity of sand particles increase. This agrees with the results of McKenna Neuman (2004) which show that with increasing bed temperature the mass transport rate decreases, since ρs(T2)/ρs(T1) is larger than us(T1)/us(T2), where, T1 and T2 are the temperatures of the sand bed and T2 N T1.

2.0

1.8

Angle Horizontal velocity Vertical velocity

1.6

1.4

1.2

1.0

0.8 0.3

0.4

0.5

0.6

Temperature(OC) Fig. 8. The variation of the ratio between lift-off velocities and angles of sand particles and falling velocities and angles of sand particles with sand bed temperature.

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PIV system. Based on the experimental data, we analyzed the influence of the bed temperature on the probability distribution of lift-off and falling velocities and angles of sand particles, which can improve our understanding of the collision process between falling sand grains and bed sands and the evolution of windblown sand flux. It is of potential benefit for modeling sediment transport and morphodynamics of desert and coastal aeolian landscapes under different physical conditions (Baas, 2002; Parteli et al., 2011; Luna et al., 2011). Results show that 1) the distribution shapes of the lift-off and falling parameters are not greatly influenced by the bed temperature, i.e., the probability distribution of the horizontal velocities follows a normal distribution, both of the probability distributions of the vertical velocities and angles follow a negative exponential distribution; 2) with increasing bed temperature the mean of the horizontal velocities increases linearly, the mean of the vertical velocities decreases, the decay constant and amplitude of the probability distribution of the vertical velocities decrease and increase, respectively; 3) with increasing temperature both the means of the lift-off and falling angles decrease exponentially, and the amplitude and decay constant of the probability distribution of the lift-off and falling angles increase and decrease, respectively; and 4) with increasing bed temperature the ratio between the horizontal lift-off velocity and falling velocity decreases, the ratio between the vertical lift-off and falling velocities increases, and the ratio between the lift-off and falling angles decreases. In addition, we presented formulas to describe the probability distribution of the lift-off and falling velocities and angles which considered the influence of bed temperature. The variation of the lift-off and falling parameters with sand bed temperature can be explained by the variation of the air density, the relative humidity and wind velocity (with increasing temperature the air density and the relative humidity decrease, upward wind velocity and streamwise wind velocity increase), that is, due to the increase of upward and streamwise wind velocities the drag force of sand particles increase, and then the horizontal velocities of sand particles increase but the vertical falling velocities decrease. Due to the decrease in relative humidity, the elasticity of particles impacting on the bed decreases, and then the vertical lift-off velocities decrease. Accordingly, the liftoff and falling angles of sand particles decrease. Acknowledgments This research was supported by a grant from the National Natural Science Foundation of China (Nos. 11072097, 11232006, 11202088 and 11121202), National Key Technology R&D Program (2013BAC07B01), the Science Foundation of Ministry of Education of China (No. 308022), Fundamental Research Funds for the Central Universities (lzujbky-2009k01) and the Project of the Ministry of Science and Technology of China (No. 2009CB421304). The authors express their sincere appreciation for this support. References Adrian, R.J., 1991. Particle-imaging techniques for experimental fluid mechanics. Ann. Rev. Fluid Mech. 23, 261–304. Anderson, R.S., Haff, P.K., 1988. Simulation of eolian saltation. Science 241, 820–823. Anderson, R.S., Haff, P.K., 1991. Wind modification and bed response during saltation of sand in air. Acta Mech. 1, 21–51 (Suppl.). Andreotti, B., 2004. A two-species model of aeolian sand transport. J. Fluid Mech. 510, 47–70. Bagnold, R.A., 1941. The Physics of Blown Sand and Desert Dunes. William Morrowand Co, New York. Baas, A.C.W., 2002. Chaos, fractals and self-organization in coastal geomorphology: simulating dune landscapes in vegetated environments. Geomorphology 48, 309–328. Bisal, F., Nielsen, K.F., 1962. Movement of soil particles in saltation. Can. J. Soil Sci. 42, 81–86. Cheng, H., Zou, X.Y., Zhang, C.L., 2006. Probability distribution functions for the initial liftoff velocities of saltating sand grains in air. J. Geophys. Res. 111, D22205. Cheng, H., Zou, X.Y., Zhang, C.L., Quan, Z.J., 2009. Fall velocities of saltating sand grains in air and their distribution laws. Powder Technol. 192, 99–104.

Chepil, W.S., 1945. Dynamics of Wind Erosion (Part I to II). Soil Sci. 60, 305–320. Davidson-Arnott, R.G.D., MacQuarrie, K., Aagaard, T., 2005. The effect of wind gusts, moisture content and fetch length on sand transport on a beach. Geomorphology 68, 115–129. Dong, Z.B., Liu, X.P., Li, F., Wang, H.T., Zhao, A.G., 2002. Impact-entrainment relationship in a saltation cloud. Earth Surf. Process. Landforms 27, 641–658. Dong, Z.B., Liu, X.P., Wang, X.M., Li, F., Zhao, A.G., 2004. Experimental investigation of the velocity of a sand cloud blowing over a sandy surface. Earth Surf. Process. Landforms 29, 343–358. Gonzalez, R.C., 2003. Digital Image Processing, Second ed. Publishing House of Electronics Industry. Greeley, R., Blumberg, D.G., Williams, S.H., 1996. Field measurement of the flux and speed of wind-blown sand. Sedimentology 43, 41–52. Jensen, J.L., Sørensen, M., 1986. Estimation of some aeolian transport parameters: a reanalysis of Williams' data. Sedimentology 33, 547–558. Kang, L.Q., Guo, L.J., Gu, Z.M., Liu, D.Y., 2008. Wind tunnel experimental investigation of sand velocity in aeolian sand transport. Geomorphology 97, 438–450. Lammel, M.L., Rings, D., Kroy, K., 2012. A two-species continuum model for Aeolian sand transport. New J. Phys. 14, 093037. Luna, M.C.M.M., Parteli, E.J.R., Durán, O., Herrmann, H.J., 2011. Model for the genesis of coastal dune fields with vegetation. Geomorphology 129, 215–224. Mitha, S., Tran, M.Q., Werner, B.T., Haff, P.K., 1986. The grain-bed impact process in Aeolian saltation. Acta Mech. 63, 267–278. Mizushima, J., Sugihara, G., Miura, T., 2009. Two modes of oscillatory instability in the flow between a pair of corotating disks. Phys Fluids 21, 014101. McKenna Neuman, C., 2003. Effects of temperature and humidity upon the entrainment of sedimentary particles by wind. Boun-Lay Meteorol. 108, 61–89. McKenna Neuman, C., 2004. Effects of temperature and humidity upon the transport of sedimentary particles by wind. Sedimentology 51, 1–17. Nalpanis, P.J., Hunt, C.R., Barrett, C.F., 1993. Saltating particles over flat beds. J. Fluid Mech. 251, 661–685. Namikas, S.L., 2003. Field measurement and numerical modelling of aeolian mass flux distributions on a sandy beach. Sedimentology 50, 303–326. Owen, P.R., 1964. Saltation of uniform grains in air. J. Fluid Mech. 20, 225–242. Pähtz, T., Kok, J.F., Herrmann, H.J., 2012. The apparent roughness of a sand surface blown by wind from an analytical model of saltation. New J. Phys. 14, 043035. Parteli, E.J.R., Andrade, J.S., Herrmann, H.J., 2011. Transverse instability of dunes. Phys. Rev. Lett. 107, 18801. Rasmussen, K.R., Sørensen, M., 2005. Dynamics of particles in Aeolian saltation. Powder Grains 2, 967–972. Rice, M.A., Willetts, B.B., McEwan, I.K., 1995. An experimental study of multiple grain-size ejecta produced by collisions of saltating grains with a flat bed. Sedimentology 42, 695–706. Sauermann, G., Kroy, K., Herrmann, H., 2001. A continuum saltation model for sand dunes. Phys. Rev. E 64, 31305. Stanislas, M., Kompenhas, J., Westerweel, J., 2000. Particle Image Velocimetry: Progress Towards Industrial Application. Kluwer Academic Publishers, Dordrecht, The Netherlands. Sun, Q.C., Wang, G.Q., 2001. Simulation of dynamic behavior of saltation grains from loose sedimentary beds. J. Desert Res. 21, 17–21 (Suppl., in Chinese, with English Abstract). Tapia, H.S., Aragón, J.A.G., Hernandez, D.M., Garcia, B.B., 2006. Particle tracking velocimetry (PTV) algorithm for non-uniform and non-spherical particles. Electron. Robot. Automot. Mech. Conf. 2, 325–330. Tong, D., Huang, N., 2012. Numerical simulation of saltating particles in atmospheric boundary layer over flat bed and sand ripples. J. Geophys. Res. 117, D16205. Volino, R.J., Schultz, M.P., Flack, K.A., 2009. Turbulence structure in a boundary layer with two-dimensional roughness. J. Fluid Mech. 635, 75–101. Werner, B.T., 1990. A steady-state model of wind-blown sand transport. J. Geol. 98, 1–17. Werner, B.T., Haff, P.K., 1988. The impact process in Aeolian saltation: two-dimensional simulations. Sedimentology 35, 189–196. White, B.R., Schulz, J.C., 1977. Magnus effect in saltation. J. Fluid Mech. 81, 497–512. Wiggs, G.F.S., Baird, A.J., Atherton, R.J., 2004. The dynamic effects of moisture on the entrainment and transport of sand by wind. Geomorphology 59, 13–30. Willetts, B.B., Rice, M.A., 1986. Collisions in aeolian saltation. Acta Mech. 63, 255–265. Xie, L., Dong, Z.B., Zheng, X.J., 2006. Experimental analysis of sand particles' lift-off and incident velocities in wind-blown sand flux. Acta Mech. Sin. 21, 564–573. Yahaya, S., Frangi, J.P., 2009. Profile of the horizontal wind variance near the ground in near neutral flow - K-theory and the transport of the turbulent kinetic energy. Ann. Geophys. 27, 1843–1859. Yang, P., Dong, Z.B., Qian, G.Q., Luo, W.Y., Wang, H.T., 2007. Height profile of the mean velocity of an Aeolian saltating cloud: wind tunnel measurements by Particle Image Velocimetry. Geomorphology 89, 320–334. Yue, G.W., Zheng, X.J., 2006. Electric field in windblown sand flux with thermal diffusion. J. Geophys. Res. 111. Zhang, W., Kang, J.H., Lee, S.J., 2007. Visualization of saltating sand particle movement near a flat ground surface. J. Vis. 10, 39–46. Zheng, X.J., 2009. Mechanics of Wind-blown Sand Movement. Springer, German. Zheng, X.J., Xie, L., Zhou, Y.H., 2005. Exploration of probability distribution of velocities of saltating sand particles based on the stochastic particle-bed collisions. Phys. Lett. A 341, 107–118. Zou, X.Y., Hao, Q.Z., Zhang, C.L., Yang, B., Liu, Y.Z., Dong, G.R., Zhou, S.X., 1999. Parameters analysis of trajectory of saltating sand in wind-sand current. Chin. Sci. Bull. 44, 1084–1088. Zou, X.Y., Wang, Z.L., Hao, Q.Z., Zhang, C.L., Liu, Y.Z., Dong, G.R., 2001. The distribution of velocity and energy of saltating sand grains in a wind tunnel. Geomorphology 36, 155–165.