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Vertical profiles of aeolian sand mass flux
Geomorphology 49 (2002) 205 – 218 www.elsevier.com/locate/geomorph
Vertical profiles of aeolian sand mass flux J.R. Ni a,b,*, Z.S. Li a,b, C. Mendoza c a Department of Environmental Engineering, Peking University, Beijing, 100871, China The Key Laboratory of Water and Sediment Sciences, Ministry of Education, Beijing, 100871, China c Department of Civil Engineering, University of Missouri, Rolla, MO, 65409-0030, USA
b
Received 12 November 2001; received in revised form 10 April 2002; accepted 27 April 2002
Abstract Vertical profiles of the horizontal mass flux of blown sand are investigated experimentally using a passive vertical array in a wind tunnel. Considering lower sampling efficiency of the sand trap in the near-bed region, this investigation is complemented by the measurements of the longitudinal profiles of mass flux made using a horizontal sand trap. The experiments were conducted with two test sands and five different stream velocities.In the upper part of the vertical profile, the measured data exhibit an exponential decay distribution with a positive deviation occurring in the near-bed region. The measured longitudinal profiles are similar to the measured vertical profiles. Linking both profiles and the modes of sand transport, it is possible that saltating sand grains give rise to the well-known exponential decay distribution of mass flux, and that creeping and reptating grains force a deviation from it. A simple equation applicable for both the vertical and the longitudinal sand mass flux variations is introduced and the parameters are estimated from experimental data. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Mass flux profile; Wind tunnel experiment; Sand trap; Trap efficiency
1. Introduction The reliable prediction of vertical profiles of aeolian sand mass flux is crucial for the estimation of sand transport rates, verification of computer models, and understanding of sand-modified wind flows and vertical intensity of aeolian abrasion (Butterfield, 1999). Bagnold (1941) and Chepil (1945) made the first attempts to measure the vertical mass flux profile and discovered that it decreases rapidly with height. Significant progress has resulted from many exper-
imental studies conducted in wind tunnels, field observations, numerical simulations, and theoretical analyses. However, these studies have often yielded different results. Data from many studies such as the wind tunnel data of Williams (1964), White (1982) and Sørensen (1985) and the field data of Sharp (1964), Wu and Ling (1965), Nickling (1978, 1983), Rasmussen et al. (1985), Greeley et al. (1996) and Chen et al. (1996) have revealed an exponential dependence of mass flux with height. This dependence is expressed as qðzÞ ¼ q0 ez=B
ð1Þ
*
Corresponding author. Center for Environmental Sciences, Peking University, Beijing, 100871, China. Tel.: +86-10-62752613; fax: +86-10-6275-1185. E-mail address: [email protected] (J.R. Ni).
where q(z) and q0 are the mass flux at the height z above the bed and at the bed surface (z =0), respectively. According to Nalpanis (1985) and Nalpanis et
0169-555X/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 5 5 5 X ( 0 2 ) 0 0 1 6 9 - 1
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al. (1993), the parameter B=U*2/kg is a length scale that defines the characteristic height of the mass flux profile (U* is the friction velocity, g is the gravitational acceleration constant, and k is a coefficient that may be constant for a single experiment). Other researchers noted significant differences of vertical mass flux distribution in the near-bed region from that predicted by Eq. (1). Kawamura (1951) found a positive deviation (i.e., overestimation) in profiles measured in a wind tunnel and in the field. The fitting of 43 sets of wind tunnel data for five sand grain sizes in the 0.20 –0.715 mm range led Zingg (1953) to propose 1=n a qðzÞ ¼ ð2Þ zþc where a and c are coefficients that may be constants for a single experiment, and n is the exponent. Znamensky (1960), Stout and Zobeck (1996), Sterk and Raats (1996), Rasmussen and Mikkelsen (1998), and Butterfield (1999) suggested similar distributions. Nonetheless, other field data (e.g., Zou et al., 1981; Liu, 1995; Hasi, 1997) displayed marked negative deviations (i.e., underestimation) in the near-bed region, different from those values predicted by the exponential dependency function. From the theoretical analysis of Kawamura (1951), Scott et al. (1995), and Hopwood and Scott (1997) and the numerical simulations by Werner (1990), Anderson and Haff (1991), and McEwan and Willetts (1991) on the vertical distribution of mass flux, it became apparent that the distribution through the saltation layer could not be properly described by the exponential function. More specifically, the results showed a positive deviation in the near-bed region. However, the certainty of this conclusion is still challenged by the diversity of recorded profile patterns reported in the literature. As sand particles in airflow leap forward continuously, the characterization of the sand dynamics may be better described by vertical and longitudinal parameters. The fact that under equilibrium conditions the overall sand mass flux passing through an unitwidth strip perpendicular to the bed is equal to the amount of sand mass flux settling over an unit-width strip of the bed, and that the mean saltation height is proportional to the mean saltation length (e.g., Owen,
1980) suggests the interrelation among the characteristic parameters in both directions. To a certain extent, the vertical mass flux distribution is similar to the longitudinal distribution of sand mass flux; exploitation of this similarity would produce additional information for studying the vertical mass flux profile near the bed. Trying to circumvent the lower efficiency of vertical sand traps, horizontal sand traps are usually deployed for measuring sand transport rates (e.g., Zingg, 1953; Kadib, 1965). Although horizontal array traps have often been used to measure the longitudinal distribution of settling sand mass flux (e.g., Kawamura, 1951; Horikawa and Shen, 1960; Belly, 1964; Greeley et al., 1996), no attempts have been made to analyze the relation between the vertical and longitudinal distributions. The objectives of this research are: (i) to investigate experimentally in a wind tunnel the vertical sand mass flux profile in the near-bed region using a passive array sand trap with a vertical resolution of 1 cm; (ii) to establish the relation between the vertical and longitudinal distributions of sand mass flux below the 1-cm height above the bed surface with measurements from a horizontal sand trap; and (iii) to propose a new mathematical function applicable for both the vertical and longitudinal sand mass flux distributions. The function is evaluated with data in the published reports and this research.
2. Methodology 2.1. The wind tunnel facility The experiments were carried out in a straight-line blowing wind tunnel at the Shapotou Desert Research Station, Lanzhou Institute of Desert Research (Chinese Academy of Sciences). The tunnel body, about 35 m long, is made of 3-mm-thick hard aluminum alloy panels and resting on the lab floor. The seven major parts of the wind tunnel are centrifugal fan, flexible coupling, expanding section, settling section, contraction section, test section, and diffuser section (Fig. 1). The centrifugal fan is capable of producing wind speeds from 3 to 25 m/s. The flexible coupling is 0.65 m long, 1.31 m wide and 1.31 m high. The expanding section is 6.4 m long, 1.31 m wide and 1.31 m high at its entrance, and 2.4 m wide and 1.2 m
J.R. Ni et al. / Geomorphology 49 (2002) 205–218
207
Fig. 1. Schematic diagram of the wind tunnel used for the experiments (dimensions are in mm).
high at the section exit. The settling section, containing a honeycomb filter and two damping screens, is 2.4 m long, 1.2 m wide and 1.5 m high. The contraction section is 2.5 m long, 2.4 m wide and 1.2 m high at its entrance, and 1.2 m wide and 1.2 m high at the exit. The test section is 21 m long, 1.2 m high, and 1.2 m wide. Flow accelerations and the formation of pressure gradients along the test section are controlled by adjustments to the floor slope between 0j and 5j to ensure that the exit crosssection can vary from 1.44 to 1.88 m2. The floor of the test section consists of seven panels, each of which is 3 m long and can be removed to meet specific experiment needs. The diffuser is 3 m long, with the top and the two wing wall panels flared with angles of 1j and 4j, respectively. The inclination of the bottom panel is adjustable.
dinal distribution of sand mass flux. The horizontal trap consists of 300 compartments (each is 101010 cm) made of plywood and is connected to samplecollecting bottles. The trap has 12 compartments in the transverse direction and 25 in the wind flow direction (Fig. 3). 2.4. Wind velocity measurement Instead of the common Pitot tube, wind velocities were measured with a single hack tube connected to a digital pressure meter that, in turn, was controlled by
2.2. Vertical array trap A Liu-type passive vertical array sand trap (Liu, 1995), used to measure the vertical sand mass flux profiles, is 30 cm high and has 30 collection chambers. The aperture of each chamber is 1 cm wide and 1 cm high (Fig. 2). 2.3. Horizontal array trap Because of lower efficiency of vertical array sand traps in the near-bed region, a horizontal trap, similar to the one used by Belly (1964), was adopted for collecting the sand, which vertical array sand traps could hardly collect, and for measuring the longitu-
Fig. 2. Sketch of the vertical sand trap used in the experiments.
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Fig. 3. Sketch of the horizontal sand trap used in the experiments. (Dimensions are in mm).
an IBM PC. The hack tube is routinely used in fluidized bed experiments (Zheng and Lu, 1980), but not yet in blown-sand transport research. Properly designed hack tubes can avoid sand grains entering the tube apertures. A single hack tube consists of two alloy tubes (3 mm outer diameter, 2.4 mm inner diameter) soldered together; one end of each is hacked at a 50j angle. The hack tube was calibrated with a Pitot tube in clean airflow in the wind tunnel (Fig. 4). During the experiments, its dynamic and static pressure ports were oriented in the windward and leeward directions, respectively. The Chinese made digital pressure meter, BPY-I, has an accuracy rate within 0.15%.
Fig. 4. Pressure differences measured with the hack tube and Pitot tube.
2.5. Experimental procedures Thirty experiments, covering measurements of wind velocity profiles (run nos. 1 to 10) and vertical (run nos. 11 to 20) and longitudinal (run nos. 21 to 30) sand mass flux distributions, were conducted with two types of sand of different grain size compositions and under five free-stream wind velocities. A summary of the experimental conditions is given in Table 1. The two test sands were obtained from a dune field near the Shapotou Station located at the southeast edge of the Tengger Desert in China. The mean grain diameter, d and the sorting r of finer sand (Sand A) is 0.17 mm and 0.35, and those of the coarser one (Sand B) is 0.35 mm and 0.60 (Fig. 5), respectively. The five freestream wind velocities tested were 8.5, 11.5, 13.5, 16.5, and 22.5 m/s; measured at the centerline of the test section entrance (x =0); and their associated friction velocities ranged from about 45 to 240 cm/s. During the experimental runs, after many equipment calibrations and adjustments, the wind tunnel floor was covered with a sand bed, 6 cm thick and 23 m long, that extended from x =1 m to the end of the diffuser section. The sand bed was leveled with a scrapper before the start of each run. The vertical sand traps were positioned at x =13.5 m. Owing to the fact that the vertical sand mass flux distribution reaches equilibrium before about x =10 m, the wind velocity profiles were measured at x =13.5 m and from 0.25, 0.5, 0.75, 1.0, 2.0, 3.5, 5.0, 10.0, 20.0, 35.0, and 60.0 cm above the sand surface. The velocity data for the lower six heights were acquired with a single hack tube that moved
J.R. Ni et al. / Geomorphology 49 (2002) 205–218 Table 1 Summary of experimental conditions Run no.
Sand grain mean diameter (mm)
Free stream velocity at x =0 m (m/s)
Friction velocity at x =13.5 m (m/s)
Sampling duration (min)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
0.17 0.17 0.17 0.17 0.17 0.35 0.35 0.35 0.35 0.35 0.17 0.17 0.17 0.17 0.17 0.35 0.35 0.35 0.35 0.35 0.17 0.17 0.17 0.17 0.17 0.35 0.35 0.35 0.35 0.35
8.5 11.5 13.5 16.5 22.5 8.5 11.5 13.5 16.5 22.5 8.5 11.5 13.5 16.5 22.5 8.5 11.5 13.5 16.5 22.5 8.5 11.5 13.5 16.5 22.5 8.5 11.5 13.5 16.5 22.5
0.61 0.86 1.18 1.64 2.36 0.47 0.77 1.11 1.53 2.31 0.61 0.86 1.18 1.64 2.36 0.47 0.77 1.11 1.53 2.31 0.61 0.86 1.18 1.64 2.36 0.47 0.77 1.11 1.53 2.31
– – – – – – – – – – 3 2 1 1/2 1/3 3 2 1 1/2 1/3 3 2 1 1/2 1/3 3 2 1 1/2 1/3
vertically, whereas the velocity data at each of the remaining five points were obtained with an array of five fixed-hack tubes. The wind velocity was first measured simultaneously at the five pre-established higher points and sequentially at the lower six remaining points. Each pressure reading was recorded at 1-s interval. About 15 pressure readings were averaged to yield one data point of the wind velocity profile. The vertical sand trap was placed at the centerline of the x =13.5 m cross-section. The bottom of the lowest compartment was set flush with the local surface of sand bed. The sampling durations to measure the vertical mass flux distribution were 3, 2, 1, 1/2 and 1/3 min for the corresponding wind velocities of 8.5, 11.5, 13.5, 16.5, and 22.5 m/s. After
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each experiment, the samples were weighted with an electronic scale of high accuracy and the sand trap compartments cleaned. For the experiments to measure the longitudinal distribution of settling sand grains, first a 30 cm deep trench was excavated to place the horizontal sand trap, between x =13.5 m to x =16 m, then, the trap was set down and leveled with respect to the tunnel sand bed surface. Only the sand collected by the two central compartments of each row of the horizontal trap was used for analysis; the data reported are their average. The sampling durations to measure the settling sand mass flux were 3, 2, 1, 1/2 and 1/3 min for the corresponding wind velocities of 8.5, 11.5, 13.5, 16.5, and 22.5 m/s. As with the vertical sand trap array, after each experiment the samples were weighted with an electronic scale of high accuracy and the sand trap compartments cleaned. No reentrainment of sand deposited in the compartments occurred when measuring the longitudinal sand transport. Measurements of settling sand mass flux were intended to complement the data on vertical sand flux profile. In fact, the central compartments of the first row of the horizontal trap immediately downwind from x =13.5 m can collect effectively the sand in
Fig. 5. Particle size distributions of the test sands.
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the near-bed region that cannot enter properly the lowest chamber of the vertical array trap. To guarantee the independence of the results, the sand bed was remixed and leveled after each run.
3. Results 3.1. Vertical profiles of wind velocity The results of velocity measurements for the two test sands are plotted conventionally against the logarithmic height in Fig. 6. The friction velocity, U*, was estimated from a semi-logarithmic regression fit to the measured velocity data taken above the 3-cm elevation to remove the effect of the sand particle motion on the wind flow. The results demonstrate that for the same value of the free stream velocity, the friction velocities in Sand A experiments are higher than those in Sand B experiments; the difference between the friction velocities in Sand A experiments and those in Sand B experiments decreases when increasing the stream velocity. This indicates that the effect of the vertical distribution of sand on the wind speed is, for the same value of the free stream velocity, more pronounced for the finer sand than for the coarser one. 3.2. Vertical profile of sand mass flux The measured sand mass flux profiles are shown in Fig. 7. The flux measured with the lowest compartment of the trap array is not reliable since traps distort the flow field near the bed and, consequently. Fig. 7 reveals an exponential dependence of the mass flux on height above the surface, except in the near-bed region, in agreement with the findings of many other investigators (e.g., Kawamura, 1951; Butterfield, 1999). The extension of the region where the exponential mass flux distribution applies (hereafter, the exponential decay region) increases with increments of the wind friction velocity, whereas the thickness of the near-bed region decreases. For a given stream velocity, the near-bed region in experiments with Sand A is thicker than that with Sand B, suggesting that the region where there is a deviation from the exponential distribution expands as the grain size increases. The straight lines in Fig. 7 are the
Fig. 6. Measured wind velocity profiles.
linear-exponential regression fit to the mass flux data. The height at which the vertical distributions of mass flux starts to deviate from the exponential distribution is about 4 – 8 and 2– 4 cm above the bed for Sand A and Sand B, respectively. The thickness of the region with appreciable deviation from the exponential distribution decreases with increasing the sand grain size. It increases first and then decreases with further increment of the wind friction velocity (Fig. 8).
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Fig. 7. Effects of the stream velocity and grain size on the vertical mass flux profiles. Note: The solid lines and dot lines correspond to the exponential decay function and Eq. (3), respectively.
What occurs in the near bed region can be described with a ratio defined as [Measured value with a compartmentPredicted value with the exponential distribution]/[Measured value with the compartment of the vertical sand trap]. This ratio is an indicator of the deviation of the measured mass flux profile from the exponential distribution (Fig. 9). The ratio is about 0.2 –0.4 and 0.4 – 0.9 for Sand A and Sand B, respectively. As in Fig. 8, the ratio increases first and then decreases with increments of the wind friction velocity. Sand grain size and fluid friction velocity have a marked effect on the vertical gradient of the measured mass flux. For a selected stream velocity, the vertical gradient of sand flux measured with Sand A is larger than that measured with Sand B, the difference between them decreases when the free stream velocity increases (see Fig. 7). In addition, the difference in mass flux at a given height in experiments with Sands A and B increases with height above the bed, suggesting that the effect of the sand size on mass flux increases with height as well.
The formation of wind-induced local scour around the trap base was easily detected during the experiments. Some of the creeping and saltating sand grains were not collected, resulting in the measured mass flux being smaller than the actual mass flux in the near-bed region. This coincides with Rasmussen and Mikkelsen (1998), who found that the efficiency of the Ames, Aarhus and Aberdeen traps were from 50% to 70% lower below the 1.5-cm height, and with Butterfield (1999) who reported that below an elevation of 1.9 cm, an Aarhus trap underestimated the sand mass flux by 37% when compared with measurements made with an optical sensor. Distortions of this nature led Sørensen (1985) to circumvent direct measurements of the sand mass flux in the near-bed region by extrapolating the mass flux distribution curve estimated for points outside of it. Obviously, this extrapolation is valid only when the exponential decay of mass flux with height is well established in the entire saltation layer. Because of the possibility of occurrence of several types of mass flux profiles,
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Fig. 8. The height at which the vertical distributions of mass flux begin to deviate from the exponential distribution.
extrapolation can only be considered as an approximation. In the present investigation, a horizontal trap was used to acquire crucial information on sand mass flux below the 1 cm height for an attempt to explain several types of sand mass flux profiles already identified in the Introduction, and in particular, to answer the question of why the vertical profiles of mass flux in the near-bed region deviate from the exponential distribution for different grain size and stream velocity conditions.
which the longitudinal distributions of mass flux begin to depart from the exponential distribution is about 25 –50 and 20 –30 cm for the experiments with Sand A and Sand B, respectively (Fig. 11), indicating that this region decreases for larger grain sizes. Generally, the length of this region also decreases with increasing wind friction velocities. For the lower free-stream velocities, i.e. 8.5 and 11.5 m/s, the longitudinal gradients of mass flux measured in the experiments with Sand A are greater than those in the runs with Sand B, whereas for higher free-stream velocities, i.e. 13.5, 16.5 and 22.5 m/s, the difference between the longitudinal gradients measured for the two sands experiments is smaller. The influence of sand grain size on the longitudinal distributions of mass flux decreases with increasing free stream velocities. The sand collected in the compartments of the first row of the horizontal trap comprises the creep, reptation and saltation grains, while the sand gathered in the rest of compartments does not include the creep grain. To gain additional insight into the influence of the flow friction velocity and sand grain size on the longitudinal distribution, a comparison was made between the values of mass flux measured in the first row compartments and the corresponding values pre-
3.3. Longitudinal profile of settling sand mass flux Fig. 10 depicts the longitudinal profiles of settling sand mass flux measured along the horizontal trap (upwind edge of the trap is at the x =13.5 m crosssection) for two sand grain sizes and several friction velocities. The data for the experiments with Sands A and B reveal an exponential decay, except near the upwind edge where the mass flux deviates. The deviation from the exponential decay curve decreases in the downwind direction. Similar to the vertical profiles of sand mass flux, the longitudinal profiles are also affected by the wind friction velocity and sand grain size. The distance at
Fig. 9. Deviation of the vertical profiles from the exponential distribution.
J.R. Ni et al. / Geomorphology 49 (2002) 205–218
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Fig. 10. Variation of sand mass flux along the horizontal trap.
dicated using the exponential function derived from the longitudinal distribution data shown in Fig. 12 for the five wind velocities and the two test sands. The ratio (MeasuredPredicted)/Measured is always less than 1.0 and decreases with increasing the friction velocity. For Sand A, the ratio decreases sharply with increasing friction velocity for values of U*V1.2 m/s
and for Sand B, the ratio decreases gently with increasing values of the friction velocity. Evidently, there are remarkable similarities and some differences between the measurements made with the horizontal and the vertical sand traps. The vertical and the longitudinal sand mass flux distributions agree with the exponential decay distribution
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Fig. 11. Distances at which the mass flux longitudinal variations begin to deviate from the exponential distribution.
through most of the flow and deviate from it near the bed for the vertical case, and near the leading edge of the horizontal trap for the longitudinal case. However,
Fig. 12. Comparisons of calculated and trapped sand at first row compartments of the horizontal trap.
the degree of deviation is different. Considering that the vertical and longitudinal distributions of sand mass flux are only two aspects of the aeolian sand transport, the similarity between the two distributions should be closely related to the modes of sand transport. In fact, both the vertical and longitudinal distributions of sand mass flux are closely related to the modes of sand transport. Butterfield (1999) indicated that an exponential decline in mass flux with height far from the bed probably stems from a grain population in a state of successive saltation. It is equally probable then that the mass flux associated with saltating sand grains has an exponential decay with height and that the deviation occurring near the bed arises from the creeping and reptating grain population. Similarly, wind tunnel data by Kawamura (1951), Horikawa and Shen (1960) and Belly (1964) demonstrated that the longitudinal distribution of settling mass flux agrees well with the exponential decay distribution except near the upwind edge of the horizontal trap (Fig. 13). In a field study, Greeley et al. (1996) found that the sand grains trapped in the first compartments were coarser, and attributed it to creeping and reptating sand grains. Thus, creeping and reptating grains probably induce the deviation from the exponential decay
Fig. 13. Measured longitudinal sand mass flux profiles.
J.R. Ni et al. / Geomorphology 49 (2002) 205–218
pattern of the longitudinal distribution of sand mass flux near the leading edge of the trap and the saltating sand grain mass accounts for the well-documented exponential decay with distance.
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4. Function for mass flux profiles Except the measurement with the lowest compartment of the trap array, the other data of vertical
Fig. 14. Comparison of vertical mass flux profiles measured with single-tube traps and Eq. (3).
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Table 2 Values of a and n in Eq. (3) (U*, H, and d from measurements) Source
d (mm)
Authors Authors Authors Authors Authors Authors Authors Authors Authors Authors Kawamura (1951) Kawamura (1951) Gerety and Slingerland (1983) Gerety and Slingerland (1983) Gerety and Slingerland (1983) Gerety and Slingerland (1983) Rasmussen and Mikkelsen (1998) Rasmussen and Mikkelsen (1998) Rasmussen and Mikkelsen (1998)
0.17 0.17 0.17 0.17 0.17 0.35 0.35 0.35 0.35 0.35 0.25 0.25 0.18
U* (m/s)
a
H
n
0.61 0.86 1.18 1.64 2.36 0.47 0.77 1.11 1.53 2.31 48.8 73.2 20
0.0444 0.1818 0.9413 1.907 5.2529 0.0473 0.1887 0.5404 1.2670 2.8191 0.11 0.34 0.0234
19 29 33 33.5 35 31 33 35 38 41 14 20 15
2.02 1.72 1.39 1.28 1.03 0.67 0.68 0.71 0.70 0.65 1.08 0.87 1.42
0.18
40
0.0414
30
1.05
0.18
52
0.1599
35
1.52
0.18
110
0.3762
48
1.48
0.20
27
0.0036
8.5
0.73
0.20
49
0.038
9
0.92
0.20
63
0.199
10
0.83
distribution of sand mass flux is well represented by an equation of the form:
1 1 qðzÞ ¼ a z H
n ;
z>0
ð3Þ
where a is a coefficient, H is the maximum height of the saltation layer, and n is the exponent (Fig. 7). The sand flux data collected with single-tube traps may be used for analysis of the vertical profile since their efficiency is the highest among the sand traps investigated (Li and Ni, submitted for publication). As shown in Figs. 7 and 14, Eq. (3) fits the data well with the estimated values of a and n given in Table 2. Also, the functional form of Eq. (3) can be used to describe the longitudinal distribution of settling sand mass flux when rewritten as
1 1 qðxÞ ¼ b x L
m ;
x>0
ð4Þ
Fig. 15. Comparison of Kawamura’s (1951) and Horikawa and Shen’s (1960) data on longitudinal mass flux variation and Eq. (4).
where b is a coefficient, L is the maximum length of the sand grain jumps, and m an exponent. The curves in Figs. 10 and 15 indicate the good fit of Eq. (4) to the authors’, Kawamura’s (1951), and Horikawa and Shen’s (1960) data. The estimated values of b and m are given in Table 3. The values of a, b, n, and m in Eqs. (3) and (4) depend on the wind friction velocity and the sand grain diameter. The values of a and b correspond to Table 3 Values of b and m in Eq. (4) (U*, L, and d from measurements) Source
d (mm)
U* (m/s)
b
L
m
Authors Authors Authors Authors Authors Authors Authors Authors Authors Authors Kawamura (1951) Horikawa and Shen (1960)
0.17 0.17 0.17 0.17 0.17 0.35 0.35 0.35 0.35 0.35 0.25 0.20
0.61 0.86 1.18 1.64 2.36 0.47 0.77 1.11 1.53 2.31 0.41 0.76
1.73 2.40 3.18 5.29 10.03 0.54 1.28 3.03 6.27 11.01 0.35 0.22
450 500 525 550 580 280 350 470 580 680 110 220
1.47 1.10 0.79 0.70 0.61 0.81 0.79 0.78 0.73 0.64 0.89 1.01
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the horizontal mass flux at z =H/(H+1) and the vertical mass flux at x =L/(L+1), respectively. The exponents n and m embody variation of the distribution-gradient, which could be regarded as ‘‘saltation – diffusion’’ parameters that reflect both the characteristics of the ejection after the grains collide with the bed and the diffusive nature of sand grains in airflow. The values of the parameters H and L correspond to the maximum in the vertical and longitudinal distribution mass flux, respectively; they are associated with the average maximum saltating height and saltating length of the sand grains.
5. Conclusions Several conclusions are drawn from this study regarding the vertical and longitudinal sand mass flux distributions and the efficiency of sand traps. First, a novel combination of accurate measurements of the longitudinal sand mass flux distribution and those for a vertical profile is introduced. Thirty wind tunnel runs with two test sands and five stream wind velocities were conducted. The longitudinal distribution measured with a horizontal sand trap complemented effectively the uncertain measurements made by the lowest compartment of a Liu-type passive vertical array sand trap used. The two distributions are similar in shape. By connecting both the two distributions and the modes of sand transport, it is found that saltating sand grains give rise to the well-known exponential decay distribution of mass flux, and that creeping and reptating grains force a deviation from it. Second, the measurements confirmed that the upper part of the vertical mass flux profile followed quite well the exponential decay function, but not in the near-bed region where a positive deviation from it was observed. The range of deviation decreases with increasing friction velocity or sand grain size. Third, the longitudinal sand mass flux distribution follows an exponential decay away from the leading edge of the horizontal trap; however, the data on sand flux measured by the first few compartments show a deviation from it. The analysis of mode of transport and the measurements indicate that the creeping and reptating grains are responsible for the deviation of the mass flux profile from the exponential decay.
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Finally, both the vertical and the longitudinal sand mass flux variation are well represented by Eqs. (3) and (4), respectively.
Acknowledgements The project was supported by the National Natural Science Foundation of China under the Grant No. 49625101. The authors are especially grateful to Prof. X.W. Liu, Prof. T. Wang, Prof. H.L. Xiao and Mr. P.X. Gao at Lanzhou Institute of Desert Research, Chinese Academy of Sciences, for their help in the wind tunnel experiment. Also, sincere thanks are due to Mr. S.L. Wu at Peking University for his assistance in the experiment.
References Anderson, R.S., Haff, P.K., 1991. Wind modification and bed response during saltation of sand in air. Acta Mech. Suppl. 1, 21 – 52. Bagnold, R.A., 1941. The Physics of Blown Sand and Desert Dunes. Methuen, London, 265 pp. Belly, P.Y., 1964. Sand movement by wind (with Addendum II by A Kadib). U.S. Army Corps of Engineers, Coastal Engineering Research Center, Tech. Memo No. 1. Butterfield, G.R., 1999. Near-bed mass flux profiles in aeolian sand transport, high-resolution measurements in a wind tunnel. Earth Surf. Process. Landf. 24, 393 – 412. Chen, W., Yang, Z., Dong, Z., 1996. Vertical distribution of windblown sand flux in the surface layer during sand storms in the Taklamakan Desert, Central Asia. Phys. Geogr. 17, 193 – 218. Chepil, W.S., 1945. Dynamics of wind erosion: I. Nature of movement of soil by wind. Soil Sci. 60, 305 – 320. Gerety, K.M., Slingerland, R., 1983. Nature of the saltating population in wind tunnel experiments with heterogeneous size-density sands. In: Brookfield, M.E., Ahlbrandt, T.S. (Eds.), Eolian Sediments and Processes. Elsevier, Amsterdam, pp. 115 – 131. Greeley, R., Blumberg, D.G., Williams, S.H., 1996. Field measurements of the flux and speed of wind-blown sand. Sedimentology 43, 41 – 52. Hasi, 1997. Preliminary study on the vertical distributions of wind dust over Bashang Plateau, Hebei Province. J. Desert Res. 17, 9 – 14 (in Chinese with English abstract). Hopwood, J.M., Scott, W.D., 1997. A mathematical model of saltation. Acta Mech. 124, 199 – 211. Horikawa, K., Shen, H.W., 1960. Sand movement by wind action. U.S. Army Corps of Engineers, Beach Erosion Board, Tech, Memo 119. Kadib, A.A., 1965. A function of sand movement by wind. Univ. Calif., Berkeley, Tech. Rep. HEL-2-12.
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Kawamura, R., 1951. Study of sand movement by wind. Univ. Tokyo, Rep. Inst. Sci. Technol. 5, 95 – 112 (in Japanese). Li, Z.S., Ni, J.R., 2002. Sampling efficiency of vertical array aeolian-sand traps. Geomorphology (submitted for publication). Liu, X.W., 1995. Experimental Physics and Engineering of Blown Sand. Science Press, Beijing, 210 pp. (in Chinese with English abstract). McEwan, I.K., Willetts, B.B., 1991. Numerical model of the saltation cloud. Acta Mech. Suppl. 1, 53 – 66. Nalpanis, P., 1985. Saltating and suspended particles over flat and sloping surfaces: II. Experiments and numerical simulations. In: Barndorff-Nielsen, O.E., Møller, J.T., Rasmussen, K.R., Willetts, B.B. (Eds.), Proceedings of International Workshop on the Physics of Blown Sand. Aarhus University, Denmark, pp. 37-66. Nalpanis, P., Hunt, J.C.R., Barrett, C.F., 1993. Saltating particles over flat beds. J. Fluid Mech. 251, 661 – 685. Nickling, W.G., 1978. Eolian sediment transport during dust storms: Slims River Valley, Yukon Territory. Can. J. Earth Sci. 15, 1069 – 1084. Nickling, W.G., 1983. Grain-size characteristics of sediment transported during dust storms. J. Sediment. Petrol. 53, 1011 – 1024. Owen, P.R., 1980. The physics of sand movement. Lecture Notes, Workshop on Physics of Flow in Desert. International Centre for Theoretical Physics, Trieste. Rasmussen, K.R., Mikkelsen, H.E., 1998. On the efficiency of vertical array aeolian field traps. Sedimentology 45, 789 – 800. Rasmussen, K.R., Sørensen, M., Willetts, B.B., 1985. Measurements of saltation and wind strength on beaches. In: Barndorff-Nielsen, O.E., Møller, J.T., Rasmussen, K.R., Willetts, B.B. (Eds.), Proceedings of International Workshop on the Physics of Blown Sand. Aarhus University, Denmark, pp. 301-325. Scott, W.D., Hopwood, K.M., Summers, K.J., 1995. A mathematical model of suspension with saltation. Acta Mech. 108, 1 – 22.
Sharp, R.P., 1964. Wind-driven sand in Coachella Valley, California. Geol. Soc. Am. Bull. 75, 785 – 804. Sørensen, M., 1985. Estimation of some aeolian saltation transport parameters from transport rate profiles. In: Barndorff-Nielsen, O.E., Møller, J.T., Rasmussen, K.R., Willetts, B.B. (Eds.), Proceedings of International Workshop on the Physics of Blown Sand. Aarhus University, Denmark, pp. 141-190. Sterk, G., Raats, P.A.C., 1996. Comparison of models describing the vertical distribution of wind-eroded sediment. J. Soil Sci. Soc. Am. 60, 1914 – 1919. Stout, J.E., Zobeck, T.M., 1996. The Wolfforth field experiment: a wind erosion study. Soil Sci. 161, 616 – 632. Werner, B.T., 1990. A steady-state model of wind-blown sand transport. J. Geol. 98, 1 – 17. White, B.R., 1982. Two-phase measurements of saltating turbulent boundary layer flow. Int. J. Multiphase Flow 8, 459 – 473. Williams, G., 1964. Some aspects of the eolian saltation load. Sedimentology 3, 257 – 287. Wu, Z., Ling, Y.Q., 1965. A preliminary study of wind-blown sand movement and sand disaster prevention. Res. Sand Disaster Prev. 7, 7 – 14 (in Chinese). Zheng, Q.S., Lu, Z.Q., 1980. Fluid Mechanics. Mechanical Industry Press, Beijing, 414 pp. (in Chinese). Zingg, A.W., 1953. Wind tunnel studies of the movement of sedimentary material. Proc. 5th Hydraulic Conf. Inst. of Hydraulics, Iowa City, pp. 111 – 135. Znamensky, A.I., 1960. Experimental Research of Wind Erosion on Sands and Questions of Protection Against Sand Drifts. Science Press, Beijing, 120 pp. (in Chinese). Zou, B.G., Cong, Z.L., Liu, S.J., 1981. A preliminary observation of the basic characteristics of sand – carrying current and effects of the measures adopted in its prevention and control. J. Desert Res. 1, 33 – 39 (in Chinese with English abstract).
Vertical profiles of aeolian sand mass flux J.R. Ni a,b,*, Z.S. Li a,b, C. Mendoza c a Department of Environmental Engineering, Peking University, Beijing, 100871, China The Key Laboratory of Water and Sediment Sciences, Ministry of Education, Beijing, 100871, China c Department of Civil Engineering, University of Missouri, Rolla, MO, 65409-0030, USA
b
Received 12 November 2001; received in revised form 10 April 2002; accepted 27 April 2002
Abstract Vertical profiles of the horizontal mass flux of blown sand are investigated experimentally using a passive vertical array in a wind tunnel. Considering lower sampling efficiency of the sand trap in the near-bed region, this investigation is complemented by the measurements of the longitudinal profiles of mass flux made using a horizontal sand trap. The experiments were conducted with two test sands and five different stream velocities.In the upper part of the vertical profile, the measured data exhibit an exponential decay distribution with a positive deviation occurring in the near-bed region. The measured longitudinal profiles are similar to the measured vertical profiles. Linking both profiles and the modes of sand transport, it is possible that saltating sand grains give rise to the well-known exponential decay distribution of mass flux, and that creeping and reptating grains force a deviation from it. A simple equation applicable for both the vertical and the longitudinal sand mass flux variations is introduced and the parameters are estimated from experimental data. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Mass flux profile; Wind tunnel experiment; Sand trap; Trap efficiency
1. Introduction The reliable prediction of vertical profiles of aeolian sand mass flux is crucial for the estimation of sand transport rates, verification of computer models, and understanding of sand-modified wind flows and vertical intensity of aeolian abrasion (Butterfield, 1999). Bagnold (1941) and Chepil (1945) made the first attempts to measure the vertical mass flux profile and discovered that it decreases rapidly with height. Significant progress has resulted from many exper-
imental studies conducted in wind tunnels, field observations, numerical simulations, and theoretical analyses. However, these studies have often yielded different results. Data from many studies such as the wind tunnel data of Williams (1964), White (1982) and Sørensen (1985) and the field data of Sharp (1964), Wu and Ling (1965), Nickling (1978, 1983), Rasmussen et al. (1985), Greeley et al. (1996) and Chen et al. (1996) have revealed an exponential dependence of mass flux with height. This dependence is expressed as qðzÞ ¼ q0 ez=B
ð1Þ
*
Corresponding author. Center for Environmental Sciences, Peking University, Beijing, 100871, China. Tel.: +86-10-62752613; fax: +86-10-6275-1185. E-mail address: [email protected] (J.R. Ni).
where q(z) and q0 are the mass flux at the height z above the bed and at the bed surface (z =0), respectively. According to Nalpanis (1985) and Nalpanis et
0169-555X/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 5 5 5 X ( 0 2 ) 0 0 1 6 9 - 1
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al. (1993), the parameter B=U*2/kg is a length scale that defines the characteristic height of the mass flux profile (U* is the friction velocity, g is the gravitational acceleration constant, and k is a coefficient that may be constant for a single experiment). Other researchers noted significant differences of vertical mass flux distribution in the near-bed region from that predicted by Eq. (1). Kawamura (1951) found a positive deviation (i.e., overestimation) in profiles measured in a wind tunnel and in the field. The fitting of 43 sets of wind tunnel data for five sand grain sizes in the 0.20 –0.715 mm range led Zingg (1953) to propose 1=n a qðzÞ ¼ ð2Þ zþc where a and c are coefficients that may be constants for a single experiment, and n is the exponent. Znamensky (1960), Stout and Zobeck (1996), Sterk and Raats (1996), Rasmussen and Mikkelsen (1998), and Butterfield (1999) suggested similar distributions. Nonetheless, other field data (e.g., Zou et al., 1981; Liu, 1995; Hasi, 1997) displayed marked negative deviations (i.e., underestimation) in the near-bed region, different from those values predicted by the exponential dependency function. From the theoretical analysis of Kawamura (1951), Scott et al. (1995), and Hopwood and Scott (1997) and the numerical simulations by Werner (1990), Anderson and Haff (1991), and McEwan and Willetts (1991) on the vertical distribution of mass flux, it became apparent that the distribution through the saltation layer could not be properly described by the exponential function. More specifically, the results showed a positive deviation in the near-bed region. However, the certainty of this conclusion is still challenged by the diversity of recorded profile patterns reported in the literature. As sand particles in airflow leap forward continuously, the characterization of the sand dynamics may be better described by vertical and longitudinal parameters. The fact that under equilibrium conditions the overall sand mass flux passing through an unitwidth strip perpendicular to the bed is equal to the amount of sand mass flux settling over an unit-width strip of the bed, and that the mean saltation height is proportional to the mean saltation length (e.g., Owen,
1980) suggests the interrelation among the characteristic parameters in both directions. To a certain extent, the vertical mass flux distribution is similar to the longitudinal distribution of sand mass flux; exploitation of this similarity would produce additional information for studying the vertical mass flux profile near the bed. Trying to circumvent the lower efficiency of vertical sand traps, horizontal sand traps are usually deployed for measuring sand transport rates (e.g., Zingg, 1953; Kadib, 1965). Although horizontal array traps have often been used to measure the longitudinal distribution of settling sand mass flux (e.g., Kawamura, 1951; Horikawa and Shen, 1960; Belly, 1964; Greeley et al., 1996), no attempts have been made to analyze the relation between the vertical and longitudinal distributions. The objectives of this research are: (i) to investigate experimentally in a wind tunnel the vertical sand mass flux profile in the near-bed region using a passive array sand trap with a vertical resolution of 1 cm; (ii) to establish the relation between the vertical and longitudinal distributions of sand mass flux below the 1-cm height above the bed surface with measurements from a horizontal sand trap; and (iii) to propose a new mathematical function applicable for both the vertical and longitudinal sand mass flux distributions. The function is evaluated with data in the published reports and this research.
2. Methodology 2.1. The wind tunnel facility The experiments were carried out in a straight-line blowing wind tunnel at the Shapotou Desert Research Station, Lanzhou Institute of Desert Research (Chinese Academy of Sciences). The tunnel body, about 35 m long, is made of 3-mm-thick hard aluminum alloy panels and resting on the lab floor. The seven major parts of the wind tunnel are centrifugal fan, flexible coupling, expanding section, settling section, contraction section, test section, and diffuser section (Fig. 1). The centrifugal fan is capable of producing wind speeds from 3 to 25 m/s. The flexible coupling is 0.65 m long, 1.31 m wide and 1.31 m high. The expanding section is 6.4 m long, 1.31 m wide and 1.31 m high at its entrance, and 2.4 m wide and 1.2 m
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207
Fig. 1. Schematic diagram of the wind tunnel used for the experiments (dimensions are in mm).
high at the section exit. The settling section, containing a honeycomb filter and two damping screens, is 2.4 m long, 1.2 m wide and 1.5 m high. The contraction section is 2.5 m long, 2.4 m wide and 1.2 m high at its entrance, and 1.2 m wide and 1.2 m high at the exit. The test section is 21 m long, 1.2 m high, and 1.2 m wide. Flow accelerations and the formation of pressure gradients along the test section are controlled by adjustments to the floor slope between 0j and 5j to ensure that the exit crosssection can vary from 1.44 to 1.88 m2. The floor of the test section consists of seven panels, each of which is 3 m long and can be removed to meet specific experiment needs. The diffuser is 3 m long, with the top and the two wing wall panels flared with angles of 1j and 4j, respectively. The inclination of the bottom panel is adjustable.
dinal distribution of sand mass flux. The horizontal trap consists of 300 compartments (each is 101010 cm) made of plywood and is connected to samplecollecting bottles. The trap has 12 compartments in the transverse direction and 25 in the wind flow direction (Fig. 3). 2.4. Wind velocity measurement Instead of the common Pitot tube, wind velocities were measured with a single hack tube connected to a digital pressure meter that, in turn, was controlled by
2.2. Vertical array trap A Liu-type passive vertical array sand trap (Liu, 1995), used to measure the vertical sand mass flux profiles, is 30 cm high and has 30 collection chambers. The aperture of each chamber is 1 cm wide and 1 cm high (Fig. 2). 2.3. Horizontal array trap Because of lower efficiency of vertical array sand traps in the near-bed region, a horizontal trap, similar to the one used by Belly (1964), was adopted for collecting the sand, which vertical array sand traps could hardly collect, and for measuring the longitu-
Fig. 2. Sketch of the vertical sand trap used in the experiments.
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Fig. 3. Sketch of the horizontal sand trap used in the experiments. (Dimensions are in mm).
an IBM PC. The hack tube is routinely used in fluidized bed experiments (Zheng and Lu, 1980), but not yet in blown-sand transport research. Properly designed hack tubes can avoid sand grains entering the tube apertures. A single hack tube consists of two alloy tubes (3 mm outer diameter, 2.4 mm inner diameter) soldered together; one end of each is hacked at a 50j angle. The hack tube was calibrated with a Pitot tube in clean airflow in the wind tunnel (Fig. 4). During the experiments, its dynamic and static pressure ports were oriented in the windward and leeward directions, respectively. The Chinese made digital pressure meter, BPY-I, has an accuracy rate within 0.15%.
Fig. 4. Pressure differences measured with the hack tube and Pitot tube.
2.5. Experimental procedures Thirty experiments, covering measurements of wind velocity profiles (run nos. 1 to 10) and vertical (run nos. 11 to 20) and longitudinal (run nos. 21 to 30) sand mass flux distributions, were conducted with two types of sand of different grain size compositions and under five free-stream wind velocities. A summary of the experimental conditions is given in Table 1. The two test sands were obtained from a dune field near the Shapotou Station located at the southeast edge of the Tengger Desert in China. The mean grain diameter, d and the sorting r of finer sand (Sand A) is 0.17 mm and 0.35, and those of the coarser one (Sand B) is 0.35 mm and 0.60 (Fig. 5), respectively. The five freestream wind velocities tested were 8.5, 11.5, 13.5, 16.5, and 22.5 m/s; measured at the centerline of the test section entrance (x =0); and their associated friction velocities ranged from about 45 to 240 cm/s. During the experimental runs, after many equipment calibrations and adjustments, the wind tunnel floor was covered with a sand bed, 6 cm thick and 23 m long, that extended from x =1 m to the end of the diffuser section. The sand bed was leveled with a scrapper before the start of each run. The vertical sand traps were positioned at x =13.5 m. Owing to the fact that the vertical sand mass flux distribution reaches equilibrium before about x =10 m, the wind velocity profiles were measured at x =13.5 m and from 0.25, 0.5, 0.75, 1.0, 2.0, 3.5, 5.0, 10.0, 20.0, 35.0, and 60.0 cm above the sand surface. The velocity data for the lower six heights were acquired with a single hack tube that moved
J.R. Ni et al. / Geomorphology 49 (2002) 205–218 Table 1 Summary of experimental conditions Run no.
Sand grain mean diameter (mm)
Free stream velocity at x =0 m (m/s)
Friction velocity at x =13.5 m (m/s)
Sampling duration (min)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
0.17 0.17 0.17 0.17 0.17 0.35 0.35 0.35 0.35 0.35 0.17 0.17 0.17 0.17 0.17 0.35 0.35 0.35 0.35 0.35 0.17 0.17 0.17 0.17 0.17 0.35 0.35 0.35 0.35 0.35
8.5 11.5 13.5 16.5 22.5 8.5 11.5 13.5 16.5 22.5 8.5 11.5 13.5 16.5 22.5 8.5 11.5 13.5 16.5 22.5 8.5 11.5 13.5 16.5 22.5 8.5 11.5 13.5 16.5 22.5
0.61 0.86 1.18 1.64 2.36 0.47 0.77 1.11 1.53 2.31 0.61 0.86 1.18 1.64 2.36 0.47 0.77 1.11 1.53 2.31 0.61 0.86 1.18 1.64 2.36 0.47 0.77 1.11 1.53 2.31
– – – – – – – – – – 3 2 1 1/2 1/3 3 2 1 1/2 1/3 3 2 1 1/2 1/3 3 2 1 1/2 1/3
vertically, whereas the velocity data at each of the remaining five points were obtained with an array of five fixed-hack tubes. The wind velocity was first measured simultaneously at the five pre-established higher points and sequentially at the lower six remaining points. Each pressure reading was recorded at 1-s interval. About 15 pressure readings were averaged to yield one data point of the wind velocity profile. The vertical sand trap was placed at the centerline of the x =13.5 m cross-section. The bottom of the lowest compartment was set flush with the local surface of sand bed. The sampling durations to measure the vertical mass flux distribution were 3, 2, 1, 1/2 and 1/3 min for the corresponding wind velocities of 8.5, 11.5, 13.5, 16.5, and 22.5 m/s. After
209
each experiment, the samples were weighted with an electronic scale of high accuracy and the sand trap compartments cleaned. For the experiments to measure the longitudinal distribution of settling sand grains, first a 30 cm deep trench was excavated to place the horizontal sand trap, between x =13.5 m to x =16 m, then, the trap was set down and leveled with respect to the tunnel sand bed surface. Only the sand collected by the two central compartments of each row of the horizontal trap was used for analysis; the data reported are their average. The sampling durations to measure the settling sand mass flux were 3, 2, 1, 1/2 and 1/3 min for the corresponding wind velocities of 8.5, 11.5, 13.5, 16.5, and 22.5 m/s. As with the vertical sand trap array, after each experiment the samples were weighted with an electronic scale of high accuracy and the sand trap compartments cleaned. No reentrainment of sand deposited in the compartments occurred when measuring the longitudinal sand transport. Measurements of settling sand mass flux were intended to complement the data on vertical sand flux profile. In fact, the central compartments of the first row of the horizontal trap immediately downwind from x =13.5 m can collect effectively the sand in
Fig. 5. Particle size distributions of the test sands.
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the near-bed region that cannot enter properly the lowest chamber of the vertical array trap. To guarantee the independence of the results, the sand bed was remixed and leveled after each run.
3. Results 3.1. Vertical profiles of wind velocity The results of velocity measurements for the two test sands are plotted conventionally against the logarithmic height in Fig. 6. The friction velocity, U*, was estimated from a semi-logarithmic regression fit to the measured velocity data taken above the 3-cm elevation to remove the effect of the sand particle motion on the wind flow. The results demonstrate that for the same value of the free stream velocity, the friction velocities in Sand A experiments are higher than those in Sand B experiments; the difference between the friction velocities in Sand A experiments and those in Sand B experiments decreases when increasing the stream velocity. This indicates that the effect of the vertical distribution of sand on the wind speed is, for the same value of the free stream velocity, more pronounced for the finer sand than for the coarser one. 3.2. Vertical profile of sand mass flux The measured sand mass flux profiles are shown in Fig. 7. The flux measured with the lowest compartment of the trap array is not reliable since traps distort the flow field near the bed and, consequently. Fig. 7 reveals an exponential dependence of the mass flux on height above the surface, except in the near-bed region, in agreement with the findings of many other investigators (e.g., Kawamura, 1951; Butterfield, 1999). The extension of the region where the exponential mass flux distribution applies (hereafter, the exponential decay region) increases with increments of the wind friction velocity, whereas the thickness of the near-bed region decreases. For a given stream velocity, the near-bed region in experiments with Sand A is thicker than that with Sand B, suggesting that the region where there is a deviation from the exponential distribution expands as the grain size increases. The straight lines in Fig. 7 are the
Fig. 6. Measured wind velocity profiles.
linear-exponential regression fit to the mass flux data. The height at which the vertical distributions of mass flux starts to deviate from the exponential distribution is about 4 – 8 and 2– 4 cm above the bed for Sand A and Sand B, respectively. The thickness of the region with appreciable deviation from the exponential distribution decreases with increasing the sand grain size. It increases first and then decreases with further increment of the wind friction velocity (Fig. 8).
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Fig. 7. Effects of the stream velocity and grain size on the vertical mass flux profiles. Note: The solid lines and dot lines correspond to the exponential decay function and Eq. (3), respectively.
What occurs in the near bed region can be described with a ratio defined as [Measured value with a compartmentPredicted value with the exponential distribution]/[Measured value with the compartment of the vertical sand trap]. This ratio is an indicator of the deviation of the measured mass flux profile from the exponential distribution (Fig. 9). The ratio is about 0.2 –0.4 and 0.4 – 0.9 for Sand A and Sand B, respectively. As in Fig. 8, the ratio increases first and then decreases with increments of the wind friction velocity. Sand grain size and fluid friction velocity have a marked effect on the vertical gradient of the measured mass flux. For a selected stream velocity, the vertical gradient of sand flux measured with Sand A is larger than that measured with Sand B, the difference between them decreases when the free stream velocity increases (see Fig. 7). In addition, the difference in mass flux at a given height in experiments with Sands A and B increases with height above the bed, suggesting that the effect of the sand size on mass flux increases with height as well.
The formation of wind-induced local scour around the trap base was easily detected during the experiments. Some of the creeping and saltating sand grains were not collected, resulting in the measured mass flux being smaller than the actual mass flux in the near-bed region. This coincides with Rasmussen and Mikkelsen (1998), who found that the efficiency of the Ames, Aarhus and Aberdeen traps were from 50% to 70% lower below the 1.5-cm height, and with Butterfield (1999) who reported that below an elevation of 1.9 cm, an Aarhus trap underestimated the sand mass flux by 37% when compared with measurements made with an optical sensor. Distortions of this nature led Sørensen (1985) to circumvent direct measurements of the sand mass flux in the near-bed region by extrapolating the mass flux distribution curve estimated for points outside of it. Obviously, this extrapolation is valid only when the exponential decay of mass flux with height is well established in the entire saltation layer. Because of the possibility of occurrence of several types of mass flux profiles,
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Fig. 8. The height at which the vertical distributions of mass flux begin to deviate from the exponential distribution.
extrapolation can only be considered as an approximation. In the present investigation, a horizontal trap was used to acquire crucial information on sand mass flux below the 1 cm height for an attempt to explain several types of sand mass flux profiles already identified in the Introduction, and in particular, to answer the question of why the vertical profiles of mass flux in the near-bed region deviate from the exponential distribution for different grain size and stream velocity conditions.
which the longitudinal distributions of mass flux begin to depart from the exponential distribution is about 25 –50 and 20 –30 cm for the experiments with Sand A and Sand B, respectively (Fig. 11), indicating that this region decreases for larger grain sizes. Generally, the length of this region also decreases with increasing wind friction velocities. For the lower free-stream velocities, i.e. 8.5 and 11.5 m/s, the longitudinal gradients of mass flux measured in the experiments with Sand A are greater than those in the runs with Sand B, whereas for higher free-stream velocities, i.e. 13.5, 16.5 and 22.5 m/s, the difference between the longitudinal gradients measured for the two sands experiments is smaller. The influence of sand grain size on the longitudinal distributions of mass flux decreases with increasing free stream velocities. The sand collected in the compartments of the first row of the horizontal trap comprises the creep, reptation and saltation grains, while the sand gathered in the rest of compartments does not include the creep grain. To gain additional insight into the influence of the flow friction velocity and sand grain size on the longitudinal distribution, a comparison was made between the values of mass flux measured in the first row compartments and the corresponding values pre-
3.3. Longitudinal profile of settling sand mass flux Fig. 10 depicts the longitudinal profiles of settling sand mass flux measured along the horizontal trap (upwind edge of the trap is at the x =13.5 m crosssection) for two sand grain sizes and several friction velocities. The data for the experiments with Sands A and B reveal an exponential decay, except near the upwind edge where the mass flux deviates. The deviation from the exponential decay curve decreases in the downwind direction. Similar to the vertical profiles of sand mass flux, the longitudinal profiles are also affected by the wind friction velocity and sand grain size. The distance at
Fig. 9. Deviation of the vertical profiles from the exponential distribution.
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213
Fig. 10. Variation of sand mass flux along the horizontal trap.
dicated using the exponential function derived from the longitudinal distribution data shown in Fig. 12 for the five wind velocities and the two test sands. The ratio (MeasuredPredicted)/Measured is always less than 1.0 and decreases with increasing the friction velocity. For Sand A, the ratio decreases sharply with increasing friction velocity for values of U*V1.2 m/s
and for Sand B, the ratio decreases gently with increasing values of the friction velocity. Evidently, there are remarkable similarities and some differences between the measurements made with the horizontal and the vertical sand traps. The vertical and the longitudinal sand mass flux distributions agree with the exponential decay distribution
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Fig. 11. Distances at which the mass flux longitudinal variations begin to deviate from the exponential distribution.
through most of the flow and deviate from it near the bed for the vertical case, and near the leading edge of the horizontal trap for the longitudinal case. However,
Fig. 12. Comparisons of calculated and trapped sand at first row compartments of the horizontal trap.
the degree of deviation is different. Considering that the vertical and longitudinal distributions of sand mass flux are only two aspects of the aeolian sand transport, the similarity between the two distributions should be closely related to the modes of sand transport. In fact, both the vertical and longitudinal distributions of sand mass flux are closely related to the modes of sand transport. Butterfield (1999) indicated that an exponential decline in mass flux with height far from the bed probably stems from a grain population in a state of successive saltation. It is equally probable then that the mass flux associated with saltating sand grains has an exponential decay with height and that the deviation occurring near the bed arises from the creeping and reptating grain population. Similarly, wind tunnel data by Kawamura (1951), Horikawa and Shen (1960) and Belly (1964) demonstrated that the longitudinal distribution of settling mass flux agrees well with the exponential decay distribution except near the upwind edge of the horizontal trap (Fig. 13). In a field study, Greeley et al. (1996) found that the sand grains trapped in the first compartments were coarser, and attributed it to creeping and reptating sand grains. Thus, creeping and reptating grains probably induce the deviation from the exponential decay
Fig. 13. Measured longitudinal sand mass flux profiles.
J.R. Ni et al. / Geomorphology 49 (2002) 205–218
pattern of the longitudinal distribution of sand mass flux near the leading edge of the trap and the saltating sand grain mass accounts for the well-documented exponential decay with distance.
215
4. Function for mass flux profiles Except the measurement with the lowest compartment of the trap array, the other data of vertical
Fig. 14. Comparison of vertical mass flux profiles measured with single-tube traps and Eq. (3).
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Table 2 Values of a and n in Eq. (3) (U*, H, and d from measurements) Source
d (mm)
Authors Authors Authors Authors Authors Authors Authors Authors Authors Authors Kawamura (1951) Kawamura (1951) Gerety and Slingerland (1983) Gerety and Slingerland (1983) Gerety and Slingerland (1983) Gerety and Slingerland (1983) Rasmussen and Mikkelsen (1998) Rasmussen and Mikkelsen (1998) Rasmussen and Mikkelsen (1998)
0.17 0.17 0.17 0.17 0.17 0.35 0.35 0.35 0.35 0.35 0.25 0.25 0.18
U* (m/s)
a
H
n
0.61 0.86 1.18 1.64 2.36 0.47 0.77 1.11 1.53 2.31 48.8 73.2 20
0.0444 0.1818 0.9413 1.907 5.2529 0.0473 0.1887 0.5404 1.2670 2.8191 0.11 0.34 0.0234
19 29 33 33.5 35 31 33 35 38 41 14 20 15
2.02 1.72 1.39 1.28 1.03 0.67 0.68 0.71 0.70 0.65 1.08 0.87 1.42
0.18
40
0.0414
30
1.05
0.18
52
0.1599
35
1.52
0.18
110
0.3762
48
1.48
0.20
27
0.0036
8.5
0.73
0.20
49
0.038
9
0.92
0.20
63
0.199
10
0.83
distribution of sand mass flux is well represented by an equation of the form:
1 1 qðzÞ ¼ a z H
n ;
z>0
ð3Þ
where a is a coefficient, H is the maximum height of the saltation layer, and n is the exponent (Fig. 7). The sand flux data collected with single-tube traps may be used for analysis of the vertical profile since their efficiency is the highest among the sand traps investigated (Li and Ni, submitted for publication). As shown in Figs. 7 and 14, Eq. (3) fits the data well with the estimated values of a and n given in Table 2. Also, the functional form of Eq. (3) can be used to describe the longitudinal distribution of settling sand mass flux when rewritten as
1 1 qðxÞ ¼ b x L
m ;
x>0
ð4Þ
Fig. 15. Comparison of Kawamura’s (1951) and Horikawa and Shen’s (1960) data on longitudinal mass flux variation and Eq. (4).
where b is a coefficient, L is the maximum length of the sand grain jumps, and m an exponent. The curves in Figs. 10 and 15 indicate the good fit of Eq. (4) to the authors’, Kawamura’s (1951), and Horikawa and Shen’s (1960) data. The estimated values of b and m are given in Table 3. The values of a, b, n, and m in Eqs. (3) and (4) depend on the wind friction velocity and the sand grain diameter. The values of a and b correspond to Table 3 Values of b and m in Eq. (4) (U*, L, and d from measurements) Source
d (mm)
U* (m/s)
b
L
m
Authors Authors Authors Authors Authors Authors Authors Authors Authors Authors Kawamura (1951) Horikawa and Shen (1960)
0.17 0.17 0.17 0.17 0.17 0.35 0.35 0.35 0.35 0.35 0.25 0.20
0.61 0.86 1.18 1.64 2.36 0.47 0.77 1.11 1.53 2.31 0.41 0.76
1.73 2.40 3.18 5.29 10.03 0.54 1.28 3.03 6.27 11.01 0.35 0.22
450 500 525 550 580 280 350 470 580 680 110 220
1.47 1.10 0.79 0.70 0.61 0.81 0.79 0.78 0.73 0.64 0.89 1.01
J.R. Ni et al. / Geomorphology 49 (2002) 205–218
the horizontal mass flux at z =H/(H+1) and the vertical mass flux at x =L/(L+1), respectively. The exponents n and m embody variation of the distribution-gradient, which could be regarded as ‘‘saltation – diffusion’’ parameters that reflect both the characteristics of the ejection after the grains collide with the bed and the diffusive nature of sand grains in airflow. The values of the parameters H and L correspond to the maximum in the vertical and longitudinal distribution mass flux, respectively; they are associated with the average maximum saltating height and saltating length of the sand grains.
5. Conclusions Several conclusions are drawn from this study regarding the vertical and longitudinal sand mass flux distributions and the efficiency of sand traps. First, a novel combination of accurate measurements of the longitudinal sand mass flux distribution and those for a vertical profile is introduced. Thirty wind tunnel runs with two test sands and five stream wind velocities were conducted. The longitudinal distribution measured with a horizontal sand trap complemented effectively the uncertain measurements made by the lowest compartment of a Liu-type passive vertical array sand trap used. The two distributions are similar in shape. By connecting both the two distributions and the modes of sand transport, it is found that saltating sand grains give rise to the well-known exponential decay distribution of mass flux, and that creeping and reptating grains force a deviation from it. Second, the measurements confirmed that the upper part of the vertical mass flux profile followed quite well the exponential decay function, but not in the near-bed region where a positive deviation from it was observed. The range of deviation decreases with increasing friction velocity or sand grain size. Third, the longitudinal sand mass flux distribution follows an exponential decay away from the leading edge of the horizontal trap; however, the data on sand flux measured by the first few compartments show a deviation from it. The analysis of mode of transport and the measurements indicate that the creeping and reptating grains are responsible for the deviation of the mass flux profile from the exponential decay.
217
Finally, both the vertical and the longitudinal sand mass flux variation are well represented by Eqs. (3) and (4), respectively.
Acknowledgements The project was supported by the National Natural Science Foundation of China under the Grant No. 49625101. The authors are especially grateful to Prof. X.W. Liu, Prof. T. Wang, Prof. H.L. Xiao and Mr. P.X. Gao at Lanzhou Institute of Desert Research, Chinese Academy of Sciences, for their help in the wind tunnel experiment. Also, sincere thanks are due to Mr. S.L. Wu at Peking University for his assistance in the experiment.
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