A wind tunnel investigation of the influences of fetch length on the flux profile of a sand cloud...

THE FETCH EFFECT OF A GRAVEL SURFACE ON FLUX PROFILES OF SAND 1613

Copyright © 2004 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms 29, 1613–1626 (2004)

Earth Surface Processes and Landforms

Earth Surf. Process. Landforms 29, 1613–1626 (2004)Published online 11 October 2004 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/esp.1116

* Correspondence to: Z. Dong, Cold and Arid Regions Environmental Research Institute, Chinese Academy of Sciences, No. 260, WestDonggang Road, Lanzhou, Gansu Province 730000, People’s Republic of China. E-mail: [email protected]

A WIND TUNNEL INVESTIGATION OF THE INFLUENCES OF FETCH

LENGTH ON THE FLUX PROFILE OF A SAND CLOUD BLOWING

OVER A GRAVEL SURFACE

ZHIBAO DONG,* HONGTAO WANG, XIAOPING LIU AND XUNMING WANG

Key Laboratory of Desert and Desertification, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese

Academy of Sciences, Lanzhou, China

Received 29 July 2003; Revised 14 March 2004; Accepted 20 April 2004

ABSTRACT

Wind tunnel tests were conducted to examine the fetch effect of a gravel surface on the flux profile of the sand cloud blowingover it using typical dune sand. The results suggest that the flux profile of blown sand over a gravel surface differs fromthat over a sandy surface and is characterized by a peak flux at a height above the surface while that over a sandy surfacedecreases exponentially with height. The flux profile of a sand cloud over a gravel surface can be expressed by a Gaussianpeak function: q = a + b exp (−0·5((h − c)/d)2), where q is the sand transport rate at height h, and a, b, c and d are regressioncoefficients. The significance of the coefficients in the function could be defined in accordance with the fetch length of thegravel surface and wind velocity. Coefficient c represents the peak flux height and increases with both wind velocity andfetch length, implying that the peak flux height is related to the bounce height of the particles in the blowing sand cloud.Coefficient d shows a tendency to increase with both wind velocity and fetch length. The sum of a and b, representing thepeak flux, increases with wind velocity but decreases with fetch length. The average saltation height derived from thecumulative percentage curve shows a tendency to increase with both the fetch length and wind velocity. For any fetch lengthof a gravel surface the sand transport equation is expressed as Q = C(1 − Ut/U)(ρ/g)U3, where Q is the sand transport rate,U is the wind velocity, Ut is the threshold velocity measured at the same height as U, g is the gravitational acceleration, ρis the air density, C is a proportionality coefficient that decreases with the fetch length of the gravel surface. At a given windvelocity, the sand transport rate over a gravel surface is only 52–68 per cent of that over a sandy surface. The flux rate intrue creep over a gravel surface increases with wind velocity but decreases with the fetch length, whereas the creepproportion (the ratio of creep flux to the sand transport rate) decreases with both the wind velocity and fetch length. Two-variable (including fetch length and wind velocity) equations were developed to predict the peak flux height, averagesaltation height and transport rate. Copyright © 2004 John Wiley & Sons, Ltd.

KEY WORDS: aeolian transport; blowing sand cloud; flux profile; transport rate; gravel surface

INTRODUCTION

Aeolian transport is an important geological process as is evident from the extensive distribution of aeolian

deposits such as loess and sand dunes (Liu, 1985; Pye and Tsoar, 1990, Lancaster, 1995; Livingstone and

Warren, 1996). The problems caused by blown sand are determined by the amount transported, the particle

velocity and the spatial distribution of the transported material. The flux profile of a blowing sand cloud, also

termed the structure of blowing sand drift, reflects the movement of blown sand particles in different trajectories,

and is also the basis for checking drifting sand (Wu, 1987). Although considerable efforts have been devoted

to quantifying the amount of wind-transported material (Bagnold, 1941; Greeley and Iversen, 1985; Fryrear

et al., 1991), the flux profile, especially its relation to the variables involved, has not been well defined.

The flux profile of a blowing sand cloud was described qualitatively by Chepil (1945), Sharp (1964), Wu

(1987) and others. Chepil (1945) concluded that 90 per cent of the particles were transported within 0·31 m above

the soil surface, and 60–80 per cent of the eroded materials were transported within the 0·05 m near-surface

layer. Sharp (1964) reported his 11-year observation results of blown sand on a gravel pavement surface in the

1614 Z. DONG ET AL.


Coachella Valley, California. He found that 90 per cent of the blown sand was transported within the 0·87 m

near-surface layer and that the average transport height was about 0·63 m. Wu’s (1987) field observations in

Ulan Buh Sand Land of China indicate that over 90 per cent of the blown sand moves within the 0·30 m layer

and about 80 per cent of it is concentrated within the 0·10 m layer.

Quantitative attempts have also been made to describe the flux profile of a blowing sand cloud through

theoretical analysis and field observation or wind tunnel data. Rouse (1937, quoted by Anderson and Hallet, 1986)

proposed a power law describing the vertical distribution of wind-blown materials. Kawamura (1951) treated the

vertical distribution of a blown sand flux statistically, suggesting that within the saltation layer the blown sand

transport rate decreased exponentially with height. Using natural dune sand in wind tunnel tests, Zingg (1953)

concluded that within the 0·25 m near-surface layer the sand flux decreased with height according to a power

law and the average saltating height increased with grain size and bed shear stress. Chepil and Woodruff (1957)

related the concentration to the height of eroded soil particles within the 0·61 m layer by a power function.

Znamenskii (1960) used systematic wind tunnel tests to investigate the relative sand transport fraction at differ-

ent heights within the 0·10 m near-surface layer at different wind speeds. Williams’ (1964) wind tunnel results

suggested that sand flux decreased with height according to a natural exponential function within the 0·16 m

near-surface layer. Wu and Lin’s (1965) field observations in a dunefield revealed that within the 0·10 m near-

surface layer the transport rate decreased exponentially with height. The results of Gillette et al. (1974) and Gillette

and Walker’s (1977) measurement estimate supported the power-function distribution of blown sand particle

concentration with height, but these findings were with respect to the fine particles transported for long distances

at great heights; the detailed distribution pattern in the near-surface layer where the majority of the blown sand

was transported was generally not well defined. Nickling (1978), in reporting his observations from the Slims River

Valley, Yukon Territory, used a power function to express the variation of sediment transport rate with height.

Differences in the reported results of the flux profiles of blown sand are largely attributable to the complexity

of particle entrainment and transport by wind. Any factors influencing the particle movement will also influence the

flux profile. In a blowing sand cloud the majority (over 75 per cent) of the particles move in saltation (Bagnold,

1941). The particles gain momentum from the wind when they are accelerated in the air and transfer the momentum

to the surface through impact. The underlying surface properties have a profound effect on the impact/entrain-

ment or bounce process that determines the blown particle trajectories, and hence on the flux profile. It has been

reported that the aeolian transport and the flux profiles of blown sand over a gravel surface are different from

those over a sandy surface in its impact-bounce intensity (Bagnold, 1941; Yin, 1989). Bagnold (1941) noticed

that the blown sand particles could jump up to 2 m high over a gravel surface, whereas the maximum saltation

height was only 0·09 m over a sandy surface. The erosion of constructions by blown sand particles in gravel

deserts is found to reach a much great height than that in sandy deserts (Anderson, 1986; Qu et al., 2001).

The gravel in gravel deserts acts as an increased roughness to prevent the in-filling particles from being

entrained and traps the near-surface particles in a sand cloud passing over it. On the other hand, the intense

impact on a gravel surface enables the passing particles to get more momentum from the wind so that the

velocity of a sand cloud over a gravel surface is different from that over a sandy surface. The fetch length

of the underlying surface is also an important variable influencing the development of the flux profile of a

blowing sand cloud (Shao and Raupach, 1992). In earlier papers, the lead author and colleagues have examined

the aerodynamic roughness of gravel surfaces (Dong et al., 2002a) and the velocity profile of a sand cloud

blowing over a gravel surface (Dong et al., 2002b). Here we examine the influence of the fetch length of a gravel

surface on the flux profile of a blowing sand cloud using typical dune sand in a wind tunnel. The objectives are:

(1) to investigate quantitatively the flux profile of a sand cloud blowing over a gravel surface with different fetch

length; (2) to define the relationship between the coefficients in the flux profile function and the fetch length and

wind velocity; (3) to discuss the average saltation height of blown sand and the variables involved; (4) to

examine the sand transport rate and its relationship to the wind velocity and fetch length.

MATERIAL AND METHODS

The experiments were carried out in the wind tunnel at the Shapotou Desert Experimental Research Station, Key

Laboratory of Desert and Desertification, Chinese Academy of Sciences. The blow-type non-circulating wind



tunnel has a total length of 37 m and is composed of a power section (2·60 m long), an expansion section (6·40 m

long), a stabilization section (1·50 m long), where drag screens and honeycombs are set to reduce large-scale

eddies and establish log-wind profiles in the work section, a compression section (2·50 m long), a working

section (21 m long) and a diffusion section (3 m long). The maximum cross-section of the expansion section is

2·4 m × 1·2 m. The 21 m long working section has a cross-section of 1·2 m × 1·2 m. Wind speed can be changed

continuously from 2 to 30 m s−1. The thickness of the boundary layer can reach 0·4–0·5 m in the working

section.

The sand used for the experiment was typical dune sand from the Shapotou area, southeast of the Tengger

Desert of China. The mean diameter of the dune sand was 2·42 φ (0·18 mm), the standard deviation 0·41 (well

sorted), skewness 0·05, and kurtosis 1·02. The threshold velocity of the sand was 6·2 m s−1, measured at the

centreline of the wind tunnel. The gravel surface was made of one layer of the typical gravel on the Alax Plateau,

northwest China. The gravel was well rounded, and its diameter ranged from 10 mm to 40 mm (Figure 1).

Aeolian transport on a gravel surface is greatly influenced by density and shape of the gravel (Davidson-Arnott

et al., 1997). In the experiments, the gravel was closely distributed (Figure 1).

A WITSEG sampler (segmented sand sampler for wind tunnel test) measured the blown sand flux. The

sampler is 0·60 m tall and sectioned into 60 10 mm × 5 mm openings to collect the blown sand flux at 10 mm

intervals over a total height of 0·6 m (for more details of the sampler refer to Dong et al., 2004). The overall

sampling efficiency is over 90 per cent (Dong et al., 2004).

In the experiment, the sand sample was put in a 3·5 m long, 0·8 m wide and 0·025 m deep sand tray upwind

of the gravel bed. The length of the sand tray was chosen to ensure a significant development of saltating sand

cloud over the sandy and the gravel surfaces. The surfaces of the sand and gravel were levelled to the tunnel

floor. The sampler was set 16 m downwind from the entrance of the working section of the wind tunnel, 50 mm

downwind from the trailing edge of the gravel surface. The bottom of the lowest opening of the sampler was

set flush with the upwind gravel surface and downwind tunnel floor. The sampling time of the sampler ranged

from 30 s to 900 s, depending on the wind velocity (the lower the wind velocity, the longer the sampling time).

The sampler was removed after the experiment and the collected sand measured using an electronic balance

(±1 mg). Because it took about 30 s for the wind to reach a pre-set free-stream speed in the wind tunnel, an

automatic sliding lid covered the sand tray until the required speed was reached, to prevent the sand from being

blown away. Eight free-stream wind velocities (8, 10, 12, 14, 16, 18, 20 and 22 m s−1) were used to measure

the blown sand flux profiles. The free-stream wind velocity was measured by a Pitot-static probe at the centreline

of the wind tunnel, at a height of 0·6 m above the tunnel floor. For each fetch length at each wind velocity, three

repetitions were made to get mean values. Figure 2 illustrates the layout of the test. The experimental data were

Figure 1. Typical gravel distribution and shape in the test

1616 Z. DONG ET AL.


Figure 2. Layout of the test

analysed by a curve-fit method provided by the TableCurveTM 2D, AISN Software, Inc. to develop the flux

profile function and define the corresponding coefficients.

RESULTS AND DISCUSSION

The flux profile

The flux (g cm−2 s−1) of a blowing sand cloud is defined as the mass quantity (g) transported by wind within

a unit flow layer (cm) per unit width (cm) perpendicular to the wind direction per unit time (s).

As a reference for comparison, the flux profile over a loose sandy surface was tested first. Figure 3 shows the

results. On a loose sandy surface the blown sand flux decays exponentially with the height by:

q = k1 exp (−h/k2) (1)

where q is the blown sand transport rate at height h (in g cm−2 s−1), h is the height (in cm), and k1 and k2 are

regression coefficients. Table I indicates that the correlation between transport rate and height is reasonably

good, the squared correlation coefficient R2 being more than 0·95.

Equation 1 is in the same form as the exponential decay function proposed by Williams (1964) for the 0·16 m

near-surface layer based on wind tunnel tests. Our earlier review showed that most published results suggest that

the blown sand transport rate in saltation decays with height by a natural exponential law. The coefficients k1

Figure 3. The flux profiles of the sand cloud over a loose sandy surface (U is the wind velocity)



Table I. The flux profile of a sand cloud blowing over a loose sandy surface

U (m s−1) Q (g cm−1 s−1) k1 k2 R2

8 0·37 0·0956 4·5645 0·9610 0·94 0·2185 4·9935 0·9912 1·88 0·3637 5·9080 0·9914 2·75 0·5919 6·4562 0·9716 4·70 0·9681 6·5895 0·9918 6·41 1·1873 6·9384 0·9920 9·62 1·3023 8·1960 0·9822 12·70 1·5667 8·9514 0·99

The fitted function q = k1 exp(−h/k2) is q with the sand transport rate at height h. U is thewind velocity, Q is the total transport rate, R2 is the squared correlation coefficient at the0·05 significance level.

and k2 show a regular relationship with wind velocity. The coefficient k1 represents the transport in true creep

on the surface (at zero height) and increases with wind speed. The creep proportion (the ratio of creep transport

rate to total transport rate) ranges from 12 to 25 per cent, decreasing with the wind velocity. The average creep

proportion (20 per cent) is close to the 25 per cent estimated by Bagnold (1941). The coefficient k2 characterizes

the relative decay rate of the sand transport rate and increases with the wind speed.

Figure 4 shows the measured flux profiles over different fetch lengths of gravel surface. At low wind velocities

(8 m s−1 and 10 m s−1), the decay curves of the flux with height are generally similar to those over a sandy surface.

As the wind speed increases the curves gradually deviate from those over a sandy surface. A peak flux appears

at a certain height above the surface. Above the peak the flux decreases with height, while below the peak the

sand flux increases with height. Figure 4 shows that the peak flux height increases with both the wind speed and

fetch length. The flux profile over a gravel surface can be fitted by a Gaussian peak function:

q = a + b exp (−0·5((h − c)/d )2) (2)

where q is the blown sand flux at height h (in g cm−2 s−1), h is the height (in cm), and a, b, c and d are regression

coefficients. Table II indicates that the relation between Equation 2 and experimental results is very good, the

squared correlation coefficient R2 being over 0·97.

Table II also indicates that all the regression coefficients in Equation 2 can be defined in accordance with the

wind velocity and fetch length. Coefficient c characterizes the peak flux height hp. The values of c for the flux

profile at 8 m s−1 and 10 m s−1 are generally negative, characterizing a meaningless peak flux height. In fact

the peak flux occurs at the lowest level (on the surface) in these conditions. When the wind speed exceeds

10 m s−1, coefficient c increases with both the wind speed and the fetch length of the gravel surface. For the

0·5 m long gravel surface, the peak flux height is 17 mm at 12 m s−1. It reaches 170 mm for the 12 m long gravel

surface at 22 m s−1. Regression analysis reveals that:

hp = c = f(U)L0·5

f(U) = −3·09 + 0·39U

R2 = 0·96 (3)

where L is the fetch length (in m), and U is the wind velocity (in m s−1). Equation 3 indicates that the peak

flux height is proportional to the square root of the fetch length and increases linearly with the wind velocity.

It is worth emphasizing that Equation 3 is valid for the total range of wind speed and fetch length tested.

However, due to the limited size of the wind tunnel test section it was not possible to investigate the total

range of validity. Figure 5 shows that Equation 3 is a good predictor of hp at the tested wind speeds and fetch

lengths.

1618 Z. DONG ET AL.


Figure 4. The flux profiles of the sand cloud over a gravel surface with different fetch (L is the fetch length of the gravel surface, U is thewind velocity)



Table II. The curve-fit results of the Gaussian distribution function of the variation with height of blown sand flux

U Serial L Q a b c d R2

(m s−1) No. (m) (g cm−1 s−1)

8 01 0·5 0·072 0·000155 0·015457 2·18951 2·00334 0·9702 2 0·153 9·208e-5 0·02682 −4·68192 8·27600 0·9903 4 0·083 0·000114 0·01212 −2·93554 7·68610 0·9704 6 0·124 3·733e-5 0·02457 −16·1114 15·0312 1·0005 8 0·154 −1·523e-6 0·02607 −15·5770 15·6015 1·0006 10 0·171 1·870e-5 0·03159 −14·5783 14·4537 1·0007 12 0·098 5·240e-6 0·01134 −8·50793 13·5927 0·99

10 08 0·5 0·184 0·00028 0·03074 2·31146 2·97328 0·9809 1 0·237 0·00021 0·04356 −1·0119 5·29493 0·9910 2 0·463 8·097e-5 0·05492 −4·1767 10·2656 1·0011 4 0·421 −3·704e-7 0·06236 −15·9433 16·6506 1·0012 6 0·355 0·00013 0·02064 −0·07465 13·8788 1·0013 8 0·482 0·00030 0·02682 0·17115 14·0685 0·9914 10 0·421 0·00022 0·02462 −0·0044 13·6552 1·0015 12 0·265 7·742e-5 0·01528 −0·2158 14·1784 1·00

12 16 0·5 0·533 0·00037 0·07785 1·70098 4·29789 0·9817 1 0·723 0·00032 0·09704 −0·28786 6·40995 0·9918 2 0·914 0·00036 0·06890 1·66867 9·40084 0·9919 4 1·006 0·00051 0·05821 1·21713 12·8057 0·9920 6 0·897 0·00070 0·04300 3·98323 13·1146 1·0021 8 0·999 0·00089 0·04387 4·10090 14·3520 1·0022 10 1·038 0·00126 0·04387 4·14624 14·6254 1·0023 12 0·833 0·00094 0·03221 6·04771 14·9081 1·00

14 24 0·5 1·373 0·00180 0·17842 3·37567 3·73152 1·9925 1 1·469 0·00145 0·15651 4·00439 4·50552 0·9826 2 1·828 0·00073 0·13780 1·66867 9·40084 0·9927 4 1·875 0·00120 0·09388 4·19976 12·4139 1·0028 6 1·867 0·00194 0·08211 5·23182 13·3122 1·0029 8 1·664 0·00195 0·06153 6·03362 15·7334 1·0030 10 1·845 0·00210 0·06700 6·17920 16·0340 1·0031 12 1·570 0·00250 0·05076 8·98972 15·8756 1·00

16 32 0·5 2·618 0·00162 0·31143 3·21682 4·416575 1·0033 1 2·690 0·00107 0·27109 2·72874 5·98864 0·9934 2 3·049 0·00229 0·21036 4·93666 7·68982 0·9935 4 3·245 0·00257 0·14613 6·08792 12·5573 1·0036 6 3·055 0·00350 0·12448 7·40100 12·9796 1·0037 8 2·897 0·00646 0·09397 9·31310 14·6842 0·9938 10 2·658 0·00466 0·08518 9·07776 15·7845 1·0039 12 2·443 0·00476 0·06995 10·5971 17·0569 1·00

18 40 0·5 4·621 0·00244 0·51028 2·54374 5·40152 0·9841 1 4·203 0·00146 0·39059 3·14567 6·17858 1·0042 2 5·013 0·00175 0·32925 4·98972 8·65821 1·0043 4 4·661 0·00403 0·19700 8·87297 11·7405 1·0044 6 4·701 0·00626 0·17591 9·35046 13·0601 1·0045 8 4·212 0·00826 0·12599 11·0973 15·7085 0·9946 10 4·163 0·00796 0·11243 11·5680 16·9079 0·9947 12 3·790 0·00894 0·09714 13·2281 17·5149 0·99

20 48 0·5 6·542 0·00488 0·64216 3·86157 5·25100 1·0049 1 5·481 0·00376 0·46846 5·18968 5·60085 0·9950 2 6·707 0·00311 0·40073 7·42067 8·06667 1·0051 4 6·361 0·00399 0·25515 9·35998 12·6124 1·00

(continued overleaf )

1620 Z. DONG ET AL.


Coefficient d increases with both wind velocity and fetch length. The sum of coefficients a and b, representing

the peak flux corresponding to the peak height, increases with wind velocity but decreases with peak height

(Figure 6).

Natural gobi deserts have sufficient fetches for the full development of a blowing sand cloud. Therefore, the

flux profile of a blowing sand cloud over gravel deserts should be characterized by a Gaussian peak function,

as is evidenced by Yin’s (1989) field observations. Yin (1989) measured the blown sand flux at different heights

on the gravel desert in Turpan, Xingjing, northwest China, during strong wind events. His observed that the flux

profile after three years exhibited a peak flux at about 0·50 m from the surface at an average wind speed of

36 m s−1. Below 0·50 m the sand flux increased linearly with height, while above 0·50 m the sand flux decayed

exponentially. The peak flux height in his observed results was several times greater than the maximum value

we measured (0·17 m for a 12 m long gravel fetch at 22 m s−1 wind velocity). This is probably because the wind

velocity in his observations was much greater than in our tests and because the natural desert had a much longer

gravel fetch. He also concluded that the peak flux height increased with the wind speed. Detailed data on the

flux profile over gravel surfaces are scarce, especially the fetch effect, so that a more detailed comparison

between previous results and ours is difficult.

Table II. (continued )

U Serial L Q a b c d R2

(m s−1) No. (m) (g cm−1 s−1)

52 6 6·313 0·00793 0·21923 10·5925 13·8545 1·0053 8 5·374 0·01163 0·15629 13·3428 14·7999 0·9954 10 5·290 0·01268 0·13614 14·2481 16·7877 0·9955 12 4·927 0·01236 0·11778 15·4307 17·8957 0·99

22 56 0·5 8·512 0·00524 0·75348 4·11573 5·96042 1·0057 1 8·078 0·00417 0·63567 5·01430 6·49142 1·0058 2 8·282 0·00314 0·46639 8·21316 8·44731 1·0059 4 7·599 0·00641 0·28996 12·0302 11·9068 1·0060 6 7·702 0·01009 0·25234 12·7125 13·8322 1·0061 8 7·678 0·01325 0·21372 14·2846 15·9802 1·0062 10 6·491 0·01318 0·15919 15·5857 18·0286 0·9963 12 6·552 0·01760 0·15114 17·0336 17·7565 0·99

The fitted Gaussian function q = a + b exp (−0·5((h − c)/d)2) is q with the sand flux at height h. U is the wind velocity, Q is the sand transportrate, L is the fetch length of the gravel surface. R2 is the squared correlation coefficient at the 0·05 significance level.

Figure 5. Comparison of the predicted and measured peak flux height



Figure 6. Variation of the peak flux with wind velocity and peak flux height (U is the wind velocity)

Aeolian sand transport in gravel deserts thus shows differences compared to sandy deserts. This also explains

why wind-eroded landforms in gravel deserts often display a maximum of abrasion at a considerable height

above the surface (Greeley and Iversen, 1985; Anderson, 1986; Qu et al., 2001).

The difference between the flux profile of a blowing sand cloud over a gravel surface and that over a sandy

surface is attributable to the difference in grain–bed interaction. The flux profile of a blowing sand cloud is

related to the particle trajectories (Anderson and Haff, 1988). The key factors determining a particle trajectory

include the particle’s lift-off velocity and angle (Anderson, 1987). There are four types of trajectories: the low

velocity and low angle type; low velocity and high angle type; high velocity and low angle type; and high velocity

and high angle type (Lancaster, 1995). The higher the lift-off angle and velocity the greater the height the

particles can reach. The trajectory type is greatly dependent on the initiation mechanism of a blown sand particle.

On a gravel surface where there is little sand supply, the particle–bed interaction is dominated by an impact/

bounce process in which the impacting particles are rebounded at a relatively high velocity and angle. Dong

et al. (2002b), using particle dynamic analyser (PDA) measurement technology in a wind tunnel, found that both

the impact and rebounded particles on a gravel surface had much greater initial angles than those entrained on

a sandy surface. Consequently, the saltating particles reach greater heights, resulting in a higher peak flux height.

The increase of peak flux height with wind velocity is due to the more intensive impact and rebound resulting

from the greater particle velocity. A long fetch of gravel provides the moving particles with more impact/bounce

repetitions so that more particles reach greater heights, resulting in an increase of the peak flux height. On a

loose sandy bed where there is a rich sand supply, particles may be entrained by wind drag and/or ejected by

impacting particles. Particles entrained by the wind usually have relatively low impact angles (Dong et al.,

2002b). The interaction between an impacting particle and a loose sandy surface is characterized by an impact/

entrainment process in which the momentum of the impacting particle is lost in emitting more particles. Conse-

quently, individually entrained particles obtain less momentum than impacting particles (McEwan et al., 1992).

A particle with a relatively low initial velocity and angle reaches a lower height, resulting in a lower peak flux

height. In fact, Figure 3 shows that the peak flux occurs at the lowest level (on the surface) over a sandy substrate.

Four characteristic heights (h25, h50, h75 and h90 corresponding to 25, 50, 75 and 90 per cent of the cumulative

percentage) are derived from the ‘percentage-smaller’ diagram (Figure 7). Figure 7 indicates that all four of the

characteristic heights show a tendency to increase with both the wind velocity and fetch length. Over the sandy

surface at a 22 m s−1 wind speed, 90 per cent of the blown sand is within 0·18 m, while over the 12 m long gravel

cover at a 22 m s−1 wind speed, 90 per cent of the blown sand is within 0·45 m. So it is important to specify

the surface properties and wind speed when discussing the cumulative percentage of the blown sand flux and

the flux profile. This is the main reason why the reported results disagree with respect to the qualitative

description of the flux profile of blowing sand clouds, as mentioned in the Introduction.

1622 Z. DONG ET AL.


Figure 7. Variation of the characteristic heights (see text) with wind velocity and fetch length (U is the wind velocity)

Usually the characteristic height h50, the height representing the 50 per cent cumulative percentage, is defined

as the average saltation height ha (Zingg, 1953; Wu, 1987). The average saltation height (ha or h50) increases

with the fetch length L according to:

ha = f1(U) + f2(U)L0·5

f1(U) = 1·63 + 2·93 × 10−10eU

f2(U) = 8·18 − 57·11/U (4)

Figure 8 shows that the average saltation height predicted by Equation 4 fits the measured values reasonably

well.

Sand transport rate

Analyzing the data in Table I reveals that the sand transport rate on a sandy surface varies with the wind

velocity according to:

Q = 0·00134(1 − Ut/U)(ρ/g)U3, R2 = 0·99 (5)

where Q is the total sand transport rate (in g cm−1 s−1), U is the wind velocity (in cm s−1), Ut is the threshold

velocity measured at the same height as U(Ut = 6·2 m s−1), ρ is the density of air (1·22 kg m−3) and, g is the

acceleration due to gravity (9·81 m s−2). Equation 5 is in the same form as the sand transport equation suggested

by Dymin (1954, quoted by Greeley and Iversen, 1985). Dymin’s equation is:



Figure 8. Comparison of the predicted and measured average saltation height

Q = C(1 − Ru)(ρ/g)U3 (6)

where C is a proportionality coefficient, Ru = Ut /U.

We have not attempted to relate the sand transport rate to friction wind velocity because the near-surface air

layer with a blowing sand cloud is not a constant shear stress layer (Gillette, 1999).

Tables I and II show that at a given wind velocity, the sand transport rate over a gravel surface is generally

less than that over the sandy surface. This is because the loose sandy surface has more than enough sand for

entrainment, while the gravel may trap sand particles moving at low level, especially those in ‘creep’. The

transport rate over gravel surfaces varies widely with fetch length, the variation range generally decreasing with

wind velocity. At 8, 10, 12, 14, 16, 18, 20 and 22 m s−1, the variation range (the ratio of the maximum to the

minimum) is 239, 182, 195, 137, 133, 132, 136 and 131 per cent, respectively. At high wind velocities (18, 20

and 22 m s−1), the total flux decreases with fetch length, while at low wind velocities it increases first and then

decreases with fetch length. The maximum transport rate occurs with a fetch length of 4 m, at wind velocity of

16 m s−1, 4–6 m at 14 m s−1, and 8–10 m at 12, 10 and 8 m s−1.

The trapping effect of the surface and the saltation height of particles influence the sand transport rate

collected by the sampler over a gravel surface. The gravel surface may have a profound trapping effect on the

creeping sand. The transport rate in true creep can be obtained by Equation 2 when h = 0. Figure 9 shows that

on a gravel surface the creep transport rate, in general, increases with wind velocity but decreases with fetch

length, while the creep proportion (the ratio of flux in creep to the transport rate) decreases with an increase

in both the wind velocity and fetch length (Figure 10). The creep proportion, ranging from 1·7 to 18·0 per cent,

averages 11·8, 7·2, 5·0, 4·4, 3·61, 3·2, 2·64 and 2·3 per cent for the 0·5, 1, 2, 4, 6, 8, 10 and 12 m fetch lengths

respectively, all much less than that on the sandy surface. This implies that the sand is more susceptible to being

trapped in the gravel at shorter fetch and at lower wind velocities. This is because the gravel surface near the

sampler has some random properties such as the arrangement pattern and shapes of the gravel that can greatly

change the collected transport rate. When the fetch is longer, a greater proportion of particles move in the high

layer so that the random properties of the gravel near the sampler have less influence. This explains why the

sand transport rate has wide variations at low wind velocities. The decreasing transport rate with a decrease

in fetch length at wind velocities less than 18 m s−1 is also largely attributable to the trapping effect of the

gravel.

When the wind velocity is great enough or the fetch long enough, another effect is dominant. A higher

proportion of particles move in the upper layer over the sampler as the wind velocity and fetch increase, resulting

in less collected flux. The collected transport rate at high wind velocities thus decreases with the fetch length.

At low wind velocities the transport rate also begins to decrease with the fetch when the gravel surface reaches

1624 Z. DONG ET AL.


Figure 9. Variation of the creep flux with wind velocity and fetch length (U is the wind velocity)

a certain length. The variation with fetch length of the transport rate is largely due to the balance of the trapping

effect of the gravel and the saltation height of the sand particles, although their quantitative significance is still

unknown.

As for the sand transport rate over the sandy surface, the relationship between the transport rate and wind

velocity for different gravel fetches can be expressed in the form of Equation 6. The coefficient C for the gravel

surface is 52–68 per cent of that for the sandy surface (Table III), decreasing with an increase in fetch length

according to:

C = 0·000877 − 1·276 × 10−6L2 (7)

So the sand transport equation for the gravel surface is:

Q = (0·000877 − 1·276 × 10−6L2)(1 − Ut/U)(ρ/g)U3, R2 = 0·98 (8)

Figure 11 shows that the total flux predicted by Equation 8 is in good agreement with the measured values.

Figure 10. Variation of the creep proportion with wind velocity and fetch length (U is the wind velocity)



CONCLUSIONS

Flux profiles of a sand cloud blowing over a gravel surface with different fetch lengths were examined in a wind

tunnel. The following conclusions were reached.

The flux profile of a sand cloud blowing over a gravel surface is different from that over a sandy surface.

Previous research and the results we obtained show that the blown sand flux over a loose sandy surface decays

exponentially with height, with the maximum flux at the lowest level (on the surface). The blown sand flux

profile over a gravel surface is generally characterized by a Gaussian peak function that has a peak flux at a

certain height above the surface, although it shares some similarities with that over a loose sandy surface at low

wind velocities (less than 12 m s−1 in this test). The coefficients in the Gaussian peak function can be defined

in accordance with the fetch length and wind velocity. Empirical equations were developed to relate the peak

flux height and average saltation height to fetch length and wind velocity. Results obtained by this study show

that the damage by aeolian processes in gravel deserts has a pattern that differs from that in sandy deserts.

At any given wind velocity the transport rate of a sand cloud passing over a gravel surface is generally smaller

than that over a sandy surface. The sand transport rate also varies with the fetch length. At high wind velocities

(over 16 m s−1) the sand transport rate shows a regular decrease with fetch length, but the relationship is more

complex at low wind velocities (less than 16 m s−1). The random properties of the gravel near the sand sampler

have great influence on the collected sand transport rate. The equation relating sand transport rate over a gravel

surface to wind velocity is in the same form as that over a sandy surface, but the proportionality coefficient is

different and decreases with the fetch length. The transport rate over a gravel surface can be predicted based

on wind velocity and fetch length.

In this paper we have presented some preliminary results and provided some basic data on the fetch effect

of a gravel surface on the flux profile of a blowing sand cloud. However, the empirical relationships we obtained

Table III. The coefficient C in the total sand transport equation for different fetch length of gravel surface

L (m) 0·5 1 2 4 6 8 10 12

C 0·00089 0·00082 0·00091 0·00085 0·00085 0·00080 0·00073 0·00070R2 0·99 1·00 0·99 0·98 0·98 0·99 0·98 0·99

The total sand transport equation is Q = C(1 − Ut/U)U3(ρ/g), Q is the sand transport rate (in g cm−1s−1), U is the wind velocity (in cm s−1),Ut is the threshold velocity measured at the same height as U(Ut = 6·2 m s−1), ρ is the density of air (1·22 kg m−3), g is the acceleration dueto gravity (9·81 m s−2), L is the fetch length of the gravel surface, R2 is the squared correlation coefficient at the 0·05 significance level.

Figure 11. Comparison of the predicted and measured sand transport rate

1626 Z. DONG ET AL.


should be valid only for a certain range of fetch length and wind velocity. To define the fetch effect based on

a sound physical basis requires clarifying the physics of the successive impact/bounce processes over a gravel

surface. This is a subject in need of our further study. It is also impossible to simulate the full development of

a sand cloud blowing over a gravel surface within the limited size of a wind tunnel. Field observations are

important to validate and extend the results obtained in wind tunnel tests.

ACKNOWLEDGEMENTS

We gratefully acknowledge the funding from the National Science Fund for Distinguished Young Scholars

of the Natural Science Foundation of China (40225003), the Knowledge Innovation Project of the Chinese

Academy of Sciences (KZCX3-SW-324). Professor A. Warren’s valuable comments on improving the manu-

script are especially appreciated.

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A wind tunnel investigation of the influences of fetch length on the flux profile of a sand cloud...

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