The flux profile of a blowing sand cloud:

a wind tunnel investigation

Zhibao Dong *, Xiaoping Liu, Hongtao Wang, Aiguo Zhao, Xunming Wang

Laboratory of Blown Sand Physics and Desert Environments, Cold and Arid Regions Environmental and Engineering Research Institute,

Chinese Academy of Sciences, No. 260, West Donggang Road, Lanzhou, Gansu Province 730000, PR China

Received 25 January 2002; received in revised form 19 March 2002; accepted 27 April 2002

Abstract

The flux profile of a blowing sand cloud, or the variation of blown sand flux with height, is the reflection of blown sand

particles that move in different trajectories, and also the basis for checking drifting sand. Here we report the wind tunnel results

of systematic tests of the flux profiles of different sized sands at different free-stream wind velocities. The results reveal that

within the 60-cm near-surface layer, the decay of blown sand flux with height can be expressed by an exponential function:

qh = aexp(� h/b), where, qh is the blown sand transport rate at height h, a and b are parameters that vary with wind velocity and

sand size. The significance of coefficient a and b in the function is defined: a represents the transport rate in true creep and b

implies the relative decay rate with height of the blown sand transport rate. The true creep fraction, the ratio of the sand

transported on the surface (h = 0) to the total transport varies widely, decreasing with both sand size and wind speed. The flux

profiles are converted to straight lines by plotting sand transport rate, qh, on a log-scale. The slope of the straight lines that

represents the relative decay rate with height of sand transport rate decreases with an increase in free-stream wind velocity and

sand grain size, implying that relatively more of the blown sand is transported to greater heights as grain size and wind speed

increase. The average saltating height represented by the height where 50% of the cumulative flux percentage occurs increases

with both wind speed and grain size, implying that saltation becomes more intense as grain size and/or wind velocity increase.

D 2002 Elsevier Science B.V. All rights reserved.

Keywords: Aeolian transport; Flux profile; Relative decay rate; Average saltation height; Creep fraction

1. Introduction

Study of the transport of blown sand has been of

continuing significance for decades. Humans have

lived with the hazards of blown sand for centuries.

Hurricanes or tornadoes demonstrate the potential

power of the wind, but the destruction of natural

resources by sand-laden wind is more devastating

when the wind erodes loose ground. The eroded

material generates tremendous clouds that may reduce

the atmospheric visibility, impede traffic, damage

crops and electric lines, interfere with communication,

abrade constructions and machines, and degrade val-

uable nonrenewable soil resources. The problem of

blown sand transport becomes more serious as the

climate gets dry and more bare ground is exposed to

the wind by adverse human activities such as land

0169-555X/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved.

PII: S0169 -555X(02 )00170 -8

* Corresponding author. Tel.: +86-931-827-1167; fax: +86-931-

827-3894.

E-mail address: zbdong@ns.lzb.ac.cn (Z. Dong).

www.elsevier.com/locate/geomorph

Geomorphology 49 (2002) 219–230

reclamation and over-grazing, as is evidenced by the

more frequent dust storms in the desertified arid and

semiarid zones.

The problems caused by blown sand are related not

only to the amount transported, but also to the vertical

distribution of the transported material. The flux

profile of a blowing sand cloud, or the variation with

height of blown sand flux, also termed the structure of

a blowing sand cloud, is a reflection of blown sand

particles that move in different trajectories, and also

the basis for checking drifting sand (Wu, 1987).

Though considerable efforts have been devoted to

quantifying the amount of wind-transported material

(Bagnold, 1941; Greeley and Iversen, 1985; Fryrear et

al., 1991) and many theoretical and empirical equa-

tions have been developed (Greeley and Iversen,

1985; Pye and Tsoar, 1990), the flux profile of blow-

ing sand cloud has not been well defined yet. The

variation of blown sand flux with height, in most

cases, used to be described qualitatively (Bagnold,

1936; Chepil, 1945; Sharp, 1964; Wu, 1987).

Some researchers have attempted to describe the

flux profile of a blowing sand cloud quantitatively

through theoretical analysis and available field obser-

vation or wind tunnel data (Rouse, 1937, quoted by

Anderson and Hallet, 1986; Karamura, 1951; Zingg,

1953; Chepil and Woodruff, 1957; Znamenskii, 1960;

Williams, 1964; Gillette et al., 1974; Gillette and

Walker, 1977; Nickling, 1978; Takeuchi, 1980; Gree-

ley et al., 1983; Gerety and Slingerland, 1983;

Fryrear, 1987; Vories and Fryrear, 1991; Fryrear

and Saleh, 1993; Chen et al., 1996). In general, two

kinds of functions: power function and exponential

function, have been suggested to describe the flux

profile of a blowing sediment cloud. Blown particles

usually move in three modes: creep, saltation and

suspension (Bagnold, 1941). Factors, such as particle

size, wind, surface properties that influence sediment

particle movement will influence the flux profile. For

example, different functions have been proposed to

describe the flux profiles of different transport modes

in the recent decades (Takeuchi, 1980; Greeley et al.,

1983; Gerety and Slingerland, 1983; Fryrear, 1987;

Vories and Fryrear, 1991; Fryrear and Saleh, 1993;

Chen et al., 1996). Takeuchi (1980) thought that

snow saltation fell off exponentially with height,

whereas suspension profiles fell off by a power

function with height. Greeley et al. (1983) and Gerety

and Slingerland (1983) concluded that the mass flux

in saltation decreased exponentially with height

Fig. 1. The aerodynamic outline of the wind tunnel.

Z. Dong et al. / Geomorphology 49 (2002) 219–230220

above the bed for all their tests. After reanalyzing the

published data, Anderson and Hallet (1986) suggested

an exponential for the saltation flux profile and a

power function for the suspension profile. Though

the conditions are different between a wind tunnel

and the field, the suggested exponential function for

saltation flux and power function for suspension flux

were found to agree well with both the subsequent

field observation and wind tunnel test results (Fryrear,

1987; Vories and Fryrear, 1991; Fryrear and Saleh,

1993). However, Chen et al.’s (1996) results of the

vertical distribution of wind-blown sand flux in the

Taklimakan Desert, China revealed that the saltation

flux profile can be described by neither exponential

function nor power function.

Our knowledge about the quantitative expression

of blown sand flux profile is in need of improvement,

especially the physical significance of the parameters

in the expressions. Systematic tests and field obser-

vation are needed. The existing results suffer the

following limitations: (1) The collected blown sand

samples were not classified with respect to height

enough to get the accurate results. Zingg (1953)

caught mass flux samples at only four heights.

Williams (1964), Gerety and Slingerland (1983),

and Fryrear and Saleh (1993) obtained their results

based only on five sampling heights. The maximum

number of sampling heights of Chen et al. (1996) was

no more than 20 within the 40-cm near-surface layer.

(2) The division of the blown sand transport modes in

practice was arbitrary and it is difficult to describe the

flux profiles of different transport mode respectively.

In many wind tunnel tests and field observations,

suspension and saltation are mixed together though

their relative proportions are different. Recent studies

show that there is no clear distinction between

saltation and creep, creep can be considered as a kind

of saltation with low angle and short trajectory

Fig. 2. The sand sampler used in the test.

Fig. 3. Layout of the test.

Z. Dong et al. / Geomorphology 49 (2002) 219–230 221

Fig. 4. Wind tunnel results of the flux profiles of blowing sand cloud [(1) d= 0.80–1.00 mm, (2) d= 0.63–0.80 mm, (3) d= 0.56–0.63 mm, (4) d= 0.50–0.56 mm, (5) d= 0.40–0.50

mm, (6) d= 0.25–0.40 mm, (7) d= 0.20–0.25 mm, (8) d= 0.15–0.20 mm, (9) d= 0.10–0.15 mm].

Z.Donget

al./Geomorphology49(2002)219–230

222

(Lancaster, 1995; Livingstone and Warren, 1996). (3)

Although many quantitative functions have been

suggested for the flux profile of a blowing sand

cloud, the significance of the key parameters in the

function has not been defined. This limits the further

extension of these functions. (4) The flux profile of a

blowing sand cloud is greatly influenced by surface

conditions, the existing results are obtained from

different surface conditions so that they are difficult

to be compared.

A loose sandy surface is the most common surface

in desert regions where blown sand is very active. We

have measured the blown sand flux at different

heights in a wind tunnel. Here we report a part of

the study: (1) to investigate the flux profile of a

blowing sand cloud on loose sandy bed; (2) to define

the physical significance of the parameters in flux

profiles and their relationship to grain size and wind

velocity; (3) to discuss the average saltation height of

blown sand and the influencing factors.

2. Experimental methods

The experiment was carried out in the wind tunnel

at the Shapotou Desert Experimental Research Sta-

tion, Institute of Desert Research, Chinese Academy

of Sciences. The blow-type non-circulating wind

tunnel (Fig. 1) has a total length of 37 m and is

composed of a power section (2.60 m long), expan-

sion section (6.40 m long), stabilization section (1.50

m long, where drag screens and honeycombs are set to

reduce large-scale eddying), compression section

(2.50 m long), work section (21 m long) and diffusion

section (3 m long) (Fig. 1). The maximum cross-

sectional area at the expansion section is 2.4 m� 1.2

m. The 21-m-long working section has a cross-sec-

tional area of 1.2 m� 1.2 m. Wind speed can be

changed continuously from 2 to 30 m s � 1. The

stability coefficient of air flow, g < 3.0%, uniformity

coefficient of wind speed du < 2.0%, average turbu-

lence e = 0.6%, the axial static pressure gradient AdCp/

dxA = 0.01 m � 1. The depth of boundary layer can

reach 40–50 cm in the work section.

The main purpose of this experiment is to measure

the flux profile of a blowing sand cloud with different

sizes at different wind velocities. Natural sand from

the field was sifted into nine size groups for tests:

0.10–0.15, 0.15–0.20, 0.20–0.25, 0.25–0.40, 0.40–

0.50, 0.50–0.56, 0.56–0.63, 0.63–0.80 and 0.80–

1.00 mm.

Blown sand flux was measured by a segmented

sand sampler (Fig. 2). The sampler is 60 cm tall and

sectionalized into sixty 1� 0.5-cm openings to collect

the blown sand at 60 heights at 1 cm intervals. Each

opening is connected to a sand chamber that is

removed after the test to weigh the collected sand

inside using a 1/1000 g electronic balance. The spacer

between the openings is made very thin to reduce the

measurement error. To minimize the interference of the

sand sampler to the airflow, the leading part of the

sampler is made wedge-shaped so that the width of the

sand chamber is 1.5 cm while the width of openings is

only 0.5 cm. A screened vertical vent is connected to

each sand chamber to minimize the air pressure in the

sand chamber and maximize the collection efficiency.

The sampler that was evaluated in a wind tunnel before

use proved to be good for collecting aeolian sands,

especially particles over 0.1 mm in diameter whose

inter-particle cohesion is not significant, the overall

efficiency is over 90%.

In the experiment, the sampler was set 16 m down-

wind from the entrance of the work section of the wind

tunnel, 5 cm apart from the sand tray upwind. The

bottom of the lowest opening of the sampler was set

flush with the tunnel floor. The sand tray upwind of the

sand sampler is 4 m long, 0.8 m wide and 2.5 cm deep.

The chosen length of the sand tray ensured the full

development of the saltation cloud. The prepared sand

samples were put in the sand tray, and the surface was

leveled to the tunnel floor, then blown by the required

free-stream (centerline, 60 cm above the tunnel floor)

Table 1

The measured threshold shear velocity of the tested sandsa

d (mm) 0.80–1.00 0.63–0.80 0.56–0.63 0.50–0.56 0.40–0.50 0.25–0.40 0.20–0.25 0.15–0.20 0.10–0.15

V * t (cm s� 1) 50.99 50.01 48.58 47.31 44.45 40.33 39.14 36.89 35.29

Vt (m s� 1) 12.15 11.35 9.90 9.06 8.21 7.59 7.11 5.56 4.73

a d is the sand grain diameter, V * t is the threshold shear velocity, Vt is the threshold velocity measured at centerline height.

Z. Dong et al. / Geomorphology 49 (2002) 219–230 223

Table 2

Correlation between sand transport rate qh and height ha

Serial no. d (mm) V (m s� 1) Q (g cm� 1 s� 1) a b Fc (%) r

01 0.80–1.00 16 0.3832 0.0147 31.1251 3.84 0.98

02 18 1.4935 0.0580 30.5419 3.88 0.99

03 20 2.0827 0.0807 30.6729 3.87 0.99

04 22 3.0997 0.1194 30.7366 3.85 0.99

05 0.63–0.80 14 0.4056 0.0151 32.7815 3.72 0.95

06 16 1.2208 0.0501 28.4767 4.10 0.97

07 18 1.8764 0.0784 27.6389 4.18 0.98

08 20 2.9355 0.1227 27.4525 4.18 0.98

09 22 3.7415 0.1575 27.1834 4.21 0.99

10 0.56–0.63 12 0.4583 0.0223 23.8086 4.87 0.97

11 14 0.9669 0.0464 23.7482 4.80 0.99

12 16 1.6135 0.0705 26.0752 4.37 0.97

13 18 2.6877 0.1127 27.4474 4.19 0.98

14 20 4.1030 0.1668 28.5742 4.07 0.98

15 22 4.7338 0.1764 32.3941 3.73 0.98

16 0.50–0.56 12 0.6662 0.0375 19.6763 5.63 0.97

17 14 1.1711 0.0617 20.9452 5.27 0.98

18 16 1.9087 0.0919 23.1787 4.81 0.97

19 18 3.0668 0.1499 22.9950 4.89 0.99

20 20 4.2487 0.1853 26.0780 4.36 0.98

21 22 5.9335 0.2608 26.2289 4.40 0.99

22 0.40–0.50 10 0.4010 0.0308 14.4596 7.68 0.96

23 12 0.8579 0.0561 16.6121 6.54 0.98

24 14 1.5247 0.0947 17.4381 6.21 0.99

25 16 2.4957 0.1468 18.3973 5.88 0.98

26 18 3.8313 0.2042 20.4737 5.33 0.98

27 20 5.4672 0.2726 22.1643 4.99 0.97

28 22 7.0897 0.3409 23.1531 4.81 0.98

29 0.25–0.40 10 0.4730 0.0400 13.1419 8.46 0.97

30 12 0.9101 0.0658 15.1427 7.23 0.98

31 14 1.7061 0.1167 15.8239 6.84 0.98

32 16 2.9323 0.1896 16.7179 6.47 0.98

33 18 4.3294 0.2740 17.0195 6.34 0.98

34 20 6.6399 0.4145 17.1527 6.24 0.99

35 22 10.2167 0.5868 18.8683 5.74 0.98

36 0.20–0.25 10 0.4980 0.0530 10.5471 10.64 0.97

37 12 1.1600 0.1017 12.1586 8.77 0.98

38 14 2.2143 0.1863 12.8547 8.41 0.98

39 16 3.6147 0.3005 12.8907 8.31 0.99

40 18 5.1172 0.3865 14.2713 7.55 0.99

41 20 7.4094 0.5558 14.3217 7.50 0.98

42 22 10.7381 0.7630 15.2148 7.11 0.97

43 0.15–0.20 8 0.2848 0.0625 5.3181 21.95 0.98

44 10 0.5531 0.0918 6.8561 16.60 0.98

45 12 1.2598 0.1761 8.0171 13.99 0.98

46 14 2.6500 0.3661 8.0319 13.82 0.98

47 16 4.3800 0.5793 8.4012 13.23 0.97

48 18 6.4103 0.8013 8.8679 12.50 0.96

49 20 9.3378 1.0581 9.8392 11.33 0.92

50 22 13.1656 1.4412 10.2181 10.95 0.92

51 0.10–0.15 8 0.2327 0.0686 4.21540 29.48 0.91

52 10 0.4996 0.1059 5.6935 21.20 0.92

53 12 1.1392 0.2145 6.2862 18.83 0.92

Z. Dong et al. / Geomorphology 49 (2002) 219–230224

wind velocity above the initiation threshold. Because it

took some time for the wind tunnel to reach a pre-set

free-stream wind speed, an automatic sliding lid cov-

ered the sand tray until the required wind speed was

reached so that the sand was not blown away. The

wind tunnel was powered off when about 2 cm of the

top sand in the tray was blown away. For each sample

at each free-stream wind velocity, three repetitions

were made to get the mean values. Fig. 3 illustrates

the layout of the sand tray and sampler.

3. Analysis of the results

The maximum free-stream wind speed tested was

22 m s� 1. We obtained 58 groups of mass flux data

(each group is the mean of three repetitions) for

analysis (Fig. 4). The coarser the sand, the fewer the

wind speeds tested because the initiation threshold

velocity changes with grain size (Table 1). The decay

curves of blown sand flux with height are similar for

all the grain sizes and wind speeds tested. The total

transport rate increases with wind speed but decreases

with grain size. Fig. 4 indicates that the increase in the

total transport rate results in an increase in the trans-

port rate at every layer.

Regression analyses show that for all grain sizes

and wind speeds, the transport rate decreases expo-

nentially with height

qh ¼ aexpð�h=bÞ ð1Þ

where, qh is the blown sand transport rate at height h,

in grams per centimeter per second, h is height, in

centimeters, a and b are regressive coefficients. Table

Serial no. d (mm) V (m s� 1) Q (g cm� 1 s� 1) a b Fc (%) r

54 14 2.4702 0.5009 5.7398 20.28 0.95

55 16 4.4214 0.8653 5.8603 19.57 0.95

56 18 7.0073 1.2067 6.6695 17.22 0.89

57 20 10.7681 1.8452 6.52048 17.14 0.96

58 22 15.6736 2.4033 7.2367 15.33 0.95

a Fittet function: qh= aexp(� h/b), qh is in grams per centimeter per second, h is in centimeters, d is the sand grain diameter, V is free-stream

wind velocity, Q is the total sand transport rate, Fc is the creep fraction, r is the squared correlation coefficient.

Fig. 5. The transport fraction in true creep at different wind speeds for different sand sizes.

Table 2 (continued )

Z. Dong et al. / Geomorphology 49 (2002) 219–230 225

2 indicates that the correlation between transport rate

and height is reasonably good. In over 90% of the

cases, the correlation coefficient R2 is over 0.95.

Here, the sand transported on the surface (h in Eq.

(1) is zero) is defined as the creep, the ratio of true

creep flux to total sand flux is defined as creep frac-

tion or creep proportion. So, coefficient a in Eq. (1)

represents the transport rate in creep. Table 2 reveals

that the creep transport rate increases with wind

speed, but decreases with grain size while the creep

fraction within the 60-cm layer varies widely, ranging

from about 4% to 29%. Because the maximum

Fig. 6. Change of K value with sand size and wind speed.

Fig. 7. The selected cumulative percentage diagram illustrating the characteristic heights.

Z. Dong et al. / Geomorphology 49 (2002) 219–230226

percentage of the transport rate at the top flow layer

(60 cm high) is only 0.58% (0.80–1.00 mm sand at

22 m s� 1 free-stream wind velocity), the total trans-

port rate in the 60-cm measured layer approximately

represents the whole blown sand flux and the creep

fraction can be regarded as the creep fraction out of

the whole blown sand flow. The creep fraction

generally decreases with grain size, and also shows

the tendency of decreasing with wind speed when the

sand size is less than 0.56 mm (Fig. 5), in accordance

with the decrease of relative decay rate with grain

size. The creep fraction is about 4% at all free-stream

wind speeds for 0.80–1.00 and 0.63–0.80 mm

sands, and 4.5% for 0.56–0.63 mm sand. The creep

fraction for 0.10–0.15 sand decreases from 29% at 8

m s� 1 to 15% at 22 m s� 1. On average, the creep

fraction is about 9%.

Coefficient b in Eq. (1), representing the relative

rate of decrease with height above the surface of the

sand transport rate, decreases with both sand size and

wind speed. The slope of the straight lines in Fig. 4

represents the relative decrease rate and can be

derived by:

k ¼ ðlnq2 � lnq1Þ=ðh2 � h1Þ ¼ �1=b ð2Þ

where, k is the inclination, q1 and q2 are the transport

rate at height h1 and h2, h1 and h2 are two different

heights.

So the slope k is the negative reciprocal of coef-

ficient b in Eq. (1). The negative values of k indicate

that the blown sand transport rate decreases with an

increase in height while the absolute value K =AkAimplies the relative decrease rate. Fig. 6 indicates that

K decreases with both increases in sand size and free-

stream wind speed except the 0.80–1.00 and 0.63–

0.80 mm sands.

Fig. 8. The characteristic heights of blown sand flux profile [(a) h25, (b) h50, (c) h75, (d) h90].

Z. Dong et al. / Geomorphology 49 (2002) 219–230 227

Four characteristic heights h25, h50, h75 and h90corresponding to the 25%, 50%, 75% and 90% of the

cumulative percentage out of the total transport rate

are derived from the ‘percentage-smaller’ diagram

(Fig. 7). Except for the 0.80–1.00 and 0.63–0.80

mm sands, all the four characteristic heights show the

tendency of increasing with both grain size and wind

speed (Fig. 8). Usually the characteristic height h50,

the height representing the 50% cumulative percent-

age, is defined as the average saltation height ha(Zingg, 1953; Wu, 1987). Zingg (1953) proposed

the empirical relationship between the average salta-

tion height and grain size:

ha ¼ 7:7d3=2s1=4 ð3Þ

where, ha is the average saltation height, in inches, d is

sand grain size, in millimeters, s is the shear stress on

the ground surface, in pound per square inch.

To develop the relationship between average sal-

tation height and sand grain size, we obtained for each

grain size the mean value of the average saltation

height for all wind speeds together in Fig. 8. The

mean average saltation height increases linearly with

the log of sand size.

ham ¼ 184:03þ 71:18lnd R2 ¼ 0:98 ð4Þ

where, ham is the mean average saltation height, in

millimeters, d is the mean grain size, in millimeters.

4. Discussion

The function we got for the blown sand flux profile

(Eq. (1)) is in the same form as the exponential decay

function proposed by Williams (1964) for the 16-cm

near-surface layer based on wind tunnel tests. Most

published results suggest that the blown sand transport

rate in saltation decays with height by a natural

exponential law (Williams, 1964; Takeuchi, 1980;

Greeley et al., 1983; Gerety and Slingerland, 1983;

Anderson and Hallet, 1986; Wu, 1987; Fryrear et al.,

1991; Fryrear and Saleh, 1993). According to Bag-

nold (1941), particles less than 0.08 mm in diameter

are defined as dust and usually move in suspension.

Our results are for sands greater than 0.1 mm in

diameter so that the transport in true suspension is

negligible. So the natural exponential function proves

to be a good descriptor for saltation flux. In the finest

wind-blown sands, the predominant diameter is never

less than 0.08 mm (Bagnold, 1941). Usual values of

blown sand, depending on the locality, lie between

0.15 and 0.3 mm (Bagnold, 1941). In fact, in many

sand transport models, the fraction in true suspension

was neglected (Bagnold, 1941; Greeley and Iversen,

1985). Neglecting the suspension fraction which,

except perhaps in the case of very dusty sand, appears

to be very small indeed, we can therefore think that

the flux profile of a blowing sand cloud obeys the law

of natural exponential decay with height.

The blown sand transport in creep is usually

difficult to measure in both the field and wind tunnel.

The sand movement in true creep at zero height is

sensitive to the surface disturbance such as lowering

the surface level once the erosion occurs. Crude

estimate of the surface creep used to be included in

the blown sand transport model (Bagnold, 1941). Any

ground trap for surface creep such as that used by

Bagnold (1941) is not able to distinguish the blown

sands in true creep and saltation, and the creep

fraction is inevitably overestimated. Bagnold’s

(1941) measurements both in the wind tunnel and in

the open indicated that the surface creep was approx-

imately equal to a quarter of the whole sand flow,

greater than that we suggested above. Our results

suggest that the creep fraction is a function of wind

speed and sand size, which are two important factors

influencing particle movement. Estimating the creep

fraction must specify sand size and wind speed.

The relative decay rate and creep fraction are

closely related. Particles that move between different

layers change the relative decay rate on one hand and

creep fraction on the other hand. Both the variations

of the relative decay rate and creep fraction with wind

speed and grain size imply that relatively more sands

are transported to higher levels as sand grain size and

wind speed increase. This is qualitatively in agree-

ment with some previously reported results (Znamen-

skii, 1960; Wu and Lin, 1965; Chen et al., 1996).

Znamenskii’s (1960) wind tunnel results showed that

within the 10-cm near-surface blown sand flow layer,

the percentage in 0–1 cm layer decreased with wind

speed, that in 1–4 cm layer independent of wind

speed, while those in the layers above 4 cm increased

with wind speed. These imply that blown sand is

transported higher as wind speed increases, similar to

Z. Dong et al. / Geomorphology 49 (2002) 219–230228

Bagnold’s (1941) conclusion. Wu and Lin’s (1965)

field observation in the shifting dunefield in Xinjiang,

China indicated that the log of blown sand transport

rate was linearly related to height at all the observed

wind speeds and total sand transport rates. An

increase in wind speed results in a decrease in the

relative percentage of the sand flow in the lower

layers, but an increase in the higher layers. At a given

wind speed, the percentage of the sand flow in the

lower layers increased, but that in the higher layers

decreased as the total transport rate increased. In our

tests, the total transport rate increases with a decrease

in sand size, implying that for the smaller sized sands

that have higher total transport rate, relatively more is

transported in the lower layers, similar to Wu and

Lin’s results. Chen et al.’s (1996) wind tunnel tests

and field observation with respect to the dune sands in

the Taklimakan Desert of China demonstrated that as

wind speed increased, the higher flow layer experi-

enced more rapid increase in mass flux rate.

Our results also imply that saltation plays a

primary role in determining the flux profile of the

blowing sand cloud. For the sand size range we

tested, the primary mechanism for the blown sand

particles to move in vertical direction is the impact

on the bed by saltating particles. The saltation

process becomes more significant as particle size

and wind strength increase. This explains why the

average saltation height increases with both wind

speed and sand size. Saltation that is also partly

dependent on the bed properties is more intense on

hard surfaces than on loose surfaces. This explains

why Bagnold (1936) found that the maximum sal-

tation over desert pavement could reach 2 m, while

only 9 cm over loose sandy surfaces. The difference

between Sharp’s (1964) results for the blown sand

profile on desert pavements and those of Chepil

(1945) on soil surfaces and Wu and Lin (1965) on

a shifting dunefield are also attributable to the

saltation process.

5. Conclusions

The flux profile of the blowing sand cloud has

been established by detailed wind tunnel investigation

using different sized sand at different free-stream

wind speeds. The sand sampler that is sectionalized

into 60 heights with 1 cm interval is reasonably good

for demonstrating the variation of blown sand flux

with height. The derived exponential decay function

of blown sand transport rate with height within the

60-cm measurement near-surface layer agrees well

with the exponential decay law proposed by some

previous researchers for the sand transport rate in

saltation. Considering the fact that the transport

fraction in the top blown sand flow layer (60 cm)

in our tests is so small (less than 0.58% of the total

transport rate) that the sand transport above 60 cm

can be neglected, the exponential decay law should

be a good descriptor for the flux profile of a blowing

sand cloud in which saltation of the primary mode of

particle movement. Whether the law of exponential

decay with height holds good for fine material such

as dust that moves in suspension needs further study.

The conditions in a wind tunnel are different from

those in the field. The flux profiles of a blowing sand

cloud should be evaluated using detailed measure-

ment in the field.

The two coefficients in the exponential decay

function and their change imply the influence of sand

size and wind speed on the flux profile of a blowing

sand cloud. Coefficient a represents the transport rate

by creep defined as the blown sand movement on the

surface or at zero height. The relative proportion of

sand transport rate in true creep to the total transport

varies widely, changing with both wind speed and

sand size. The fixed creep fraction included in sand

transport models such as Bagnold’s model is not

appropriate. Typically, Bagnold’s estimate that surface

creep is approximately equal to a quarter of the whole

sand flow is generally overestimated. Coefficient b

represents the relative decay rate of the blown sand

flux with height. The greater the coefficient b, the less

is the decay rate. Relatively more sands are trans-

ported at higher levels as wind speed and grain size

increase, implying that saltation that gets more intense

with grain size and wind speed is the primary trans-

port mode responsible for the flux profile of a blowing

sand cloud.

Saltation is related not only to sand size and wind

speed, but also to the surface properties. For example,

saltation is much more intense over desert pavements

than on loose sandy surfaces. The influence of surface

properties on the flux profile of a blowing sand cloud

is in need of further study.

Z. Dong et al. / Geomorphology 49 (2002) 219–230 229

Acknowledgements

We gratefully acknowledge the funding from the

National Key Project for Basic Research

(2000048702), Hundred Talents Project and the

Knowledge Innovation Project of the Chinese Acad-

emy of Sciences (KZCX2-304), and the Natural

Science Foundation of China (NSFC40001005). We

wish to thank Mr. G. Wang for his help in wind tunnel

experiment, and Dr. G. Wu and Mr. B. He for

preparing the illustrations. Profs. N. Lancaster and D.

Goossens’s valuable comments improving the manu-

script are especially acknowledged.

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