JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 98, NO. D7, PAGES 12,719-12,726, JULY 20, 1993
Effect of SaltationBombardmenton the Entrainmentof Dust by Wind
Y. SHAO AND M. R. RAUPACH
Centre.p•r EnvironmentalMechanics,CommonwealthScientificand Industrial ResearchOrganization,Canberra, Australia
P. A. FINDLATER
WesternAustralianDepartmentof Agriculture, Geraldton,Australia
Saltationis the wind-driven,hoppingmotionof sand-sizedparticlesacrossan erodiblesurface.This mode
of motion not only transportssand and similar materialsin its own right but can also initiate (through
bombardmentof the surface) the entrainmentand subsequenttransport by suspensionof smaller dust
particles.In this paper, we report a wind tunnel study of the effect of saltationbombardmenton dust
entrainment.The techniqueis to allow sandgrainsto saltatefrom an upwind sandsourceonto a bed of dust
particles.The experimentconfirmsthat the ejectionof dustparticlesby saltationbombardment
(as opposedto
detachmentof dustparticlesby aerodynamicforces)is the principalmechanismfor the naturalentrainmentof
dust by wind. The data are used to examinethe dependenceof the dust emissionflux Fa (massper unit
groundarea per unit time) upon the friction velocity u,; it is found that Fa is closelyproportionalto the
streamwise
flux of saltating
sandgrains,whichin turnis approximately
proportional
to u,3.At a givenu,, Fa
increasesas the size of the bombardingsand grains increases.On the basis of the hypothesisthat Fa is
proportional
to the kineticenergyflux of the saltatingsandgrains,we derivetheoreticallythe resultthat Fa
scaleswith the streamwise
saltating
sandgrainflux andthenceapproximately
with u,3, as observed
in this
experiment.
1.INTRODUCTION
Fd = aou.•(1 - u.,!u.)
Bagnold [1941] identified three particle transport modes
contributingto wind erosion: suspension,saltation, and creep.
Suspension,the natural transport mode for the smallest soil
particles(diameterlessthan about50 }am), leadsto transportof
fine soil constituents over large distances (kilometers to
thousandsof kilometers) from their point of origin. Because
these fine constituentscontain a disproportionateshare of soil
nutrient [Gupta et al., 1981; Zobeck and Fryrear, 1986], this
transport is a potential source of significant long-term land
degradation.
In principle, the movementof dust particlescan be initiated
either by aerodynamicforcesor by the impact of saltatingsand
grains, a processknown as bombardment.However, the part
played by aerodynamiclift on dust entrainmentis insignificant
under realistic wind conditions,becauseof the strong cohesive
forces associatedwith small particle size [Greeley and Iversen,
1985]. The interparticle bonds maintained by these cohesive
forces are not readily broken by the typical aerodynamicforces
actingon dustparticlesrestingon the surface;however,they are
easily disruptedby the impacts of saltating sand grains. Thus,
bombardmentis the most important mechanismresponsiblefor
eolian dust entrainment [Gillette, 1981].
The dependenceof bombardment-induceddust entrainment
upon wind velocity is rather indirect, as it involves the
relationship between wind and saltation as an intermediate
process.Despite this indirect connection,a simple expression
describingthe dependenceof dust entrainmentrate on wind
speed is a practical necessity,both for models of local wind
erosion and for estimatinglarge-scaledust movement. Gillette
and Passi [1988] suggested (on the basis of a personal
communicationfrom P. R. Owen) that the upward dust flux at
the surface,F,•, can be approximatedby
Copyright1993 by the AmericanGeophysicalUnion.
Papernumber93JD00396.
0148-0227/93/93JD-00396
$05.00
(u.t_<u
.)
(1)
where u. is the friction velocity, u., is the thresholdvelocity of
saltation,and ct0 is a dimensional
constant.
Owen'sunpublished
derivation of (1) (which was kindly communicatedto us by D.
A. Gillette) is based on aerodynamic considerations of the
vortex field generatedby a saltatingsand grain suddenlybrought
to rest by impaction on the surface. Gillette and Passi [1988]
presentedempirical evidence showing that (1) reasonably well
describesdust flux measurements,including those obtained by
Gillette [1977, 1981] for eroding fields, and the resultsof wind
tunnel experiments by Fairchild and Tillery [ 1982] and
Borrmann and Jaenicke [1987]. However, as discussedlater, the
scatterin this comparisonwas very large.
Our purpose here is to present, and explain theoretically,
results obtained in a wind tunnel investigationof dust emission
by saltation bombardment.The experimentaldata suggestthat
dust flux, F•, is approximately proportional to the vertically
integrated streamwise flux of saltating particles, Q,., and
thereforescalesapproximately
with u.3, the classicalresultfor
the dependenceof Q.,. on u. [Bagnold, 1941; Owen, 1964].
Therefore, (1) is not supportedby this study. In the following,
we first describe the experiment and next present the
observational results. We then outline a possible theoretical
explanation
for the observed
proportionality
of F• to u.3 and
finally discussour findings in the context of previous work,
especiallythe field observationsof Gillette [1977, 1981].
2. DESCRIPTION
OF EXPERIMENT
The experimentwas carried out in the portable wind tunnel
of the Department of Conservation and Land Management
(formerly the Soil ConservationService) of New South Wales.
The constructionand aerodynamicpropertiesof the tunnel are
described by Raupach and Leys [1990]. The maximum
operational
wind speedis 15 m s-• in a rectangular
working
section 1.15 m wide and 0.9 m high. Owen and Gillette [1985]
considered the constraints on the development of saltation
12,719
12,720
SHAO ET AL.: ENTRAINMENTOF DUST BY SALTATION
imposedby the wind tunnel dimensionsand concludedthat the
dustdepositionwas negligible.The sampler,identicalto the one
ß
tunnelFroudenumberU2/gH (whereU is windspeed,g is the usedby Leysand Raupach[1991], was a verticallyintegrating,
accelerationdue to gravity, and H is the height of tunnel),
should
be
less
than
20.
The
dimensions
of
the
tunnel
are
sufficiently large that this requirementis satisfiedfor normal
operationalwind speeds,so our results should be free of any
seriouseffects causedby tunnel constraints.In the first 2 m of
the working section, the development of a deep turbulent
boundarylayer is initiated by a tripping fence (40 mm high)
mounted on a roughened, nonerodible baseboard.The wind
tunnel length (excluding the initial 2-m flow development
section) can be extendedto 17 m, but for the purposeof this
experiment,a shorttunnel (6 m) was found to be sufficientand
easy to operate.The principal experimentalconfiguration,here
called the "bombardment"configuration,is illustratedin Figure
1. Two beds of material were placed in the tunnel: an upstream
bed of saltation material of streamwise length 1 m, which
produceda supplyof saltatinggrains,followed immediatelyby
a bed of dust of length 2 m, which was subjectedto saltation
bombardment.
The saltationmaterial was preparedfrom an eolian red sand
obtained from
a site near Balranald, New
South Wales,
Australia; the particle size distribution of the natural sand
(median diameter, 200 g m) is given by Shao and Raupach
[1993]. The sand was oven dried at 70øC and sieved into three
activetrap of height500 mm and slit width 5 mm. (This height
can be shownto be adequateto catchessentiallyall of the dust
plume,as follows.Supposethat dustparticlesdiffuseas rapidly
as fluid elements in the wind tunnel; then the characteristic
depthof the dustplume,77,can be estimatedby 7•=xu,/U,with
x beingthedistance
between
thedustsurface
andsampler.
Sinceu,/U
is around 1/25 and the maximum value of x is 5 m, 77 is
typically 200 mm, which is lessthan half the trap height.)The
trap was connectedto a pair of interchangeable
filter collectors
(only one of which was used at any one time), and air was
drawn through the trap and one collector by a high-volume
pump. Rapid sequential measurementsof particle fluxes,
integrated over short time periods, could be made by
interchanging
the collectorsto permit replacementof the filter in
the
off-line
collector.
Careful
calibration
showed
that
the
modified Bagnold sampler slightly oversampledthe vertically
integratedflux but that the oversamplingerror was less than
10% [Shao et al., in press].The sand and dust componentsof
the material caught in the filters were separatedby sieving
through a 75-•m sieve, with mechanicalagitation to eliminate
any aggregationof dustparticles.The sandand dustcomponents
were then weighed individually. Great care was taken to avoid
lossesduringthe sievingand weighingprocess.
Wind speedswere measuredwith three Pitot tubes at 30,
size classes, with sieve diameters 100 to 210, 210 to 530, and
530 to 1000 gm. The first 1 m of the tunnel floor in the
130, and 280 mm above the soil surface, at the same streamwise
working section (downstream of the 2-m flow development location as used for the modified Bagnold sampler.However,
section)was coveredwith sievedred sandto a depthof 20 mm. despite considerableefforts, the Pitot tubes at the two lower
Saltation from this sand bed occurred when the local u,
levels were often blocked by dust particles.The placementof
exceededa thresholdfriction velocity u,,, varying from about the measurement location 3 m downwind of the dust bed
0.2 m s-1for the 100 to 210-gm size classto 0.4 m s-• for the representedour attempt to overcomethe problem but was not
530 to 1000-lam size class [Greeley and Iversen, 1985]. Thus, entirely successful.The wind velocity profile measurements
are
the saltation material was produced by natural wind erosion not sufficientlyreliable to derive estimatesof friction velocity.
from a mobile sand surfacerather than by artificial injection as Therefore, throughoutthe paper, we use the measuredmean
in the experiments of Fairchild and Tillery [1982] and wind speedat height 280 mm, UR, as a reference.Where friction
Borrmann and Jaenicke [1987].
velocitiesare required, they are inferred from UR by using the
The dust bed, of length 2 m and immediately downwind of
surface
dragcoefficient,
C,•= U,2/UR
2 '" 0.0422,obtained
from
the sand bed, consisted of fine, loose kaolin clay. Kaolin measurementsover red sand surfaces in the same tunnel [Shao
particleshave a typical diameter of about 2 g m. Interparticle and Raupach, 1993].
Observations were made under four different wind conditions'
cohesiveforcescausetheseprimaryparticlesto form aggregates,
even in a non-compactedbed. However, for looseclay material, with nominal referencewind speeds,U•, of 8.0, 9.5, 11.0, and
the aggregatesare easily broken by external forces, including 12.5m s'•. Eachrunlasted9 min,starting
at timet -- 0 withthe
saltationbombardment,so that the dust particlesentering the wind speedbeing broughtfrom zero to a steadyvalue as rapidly
flow are likely to be almostcompletelydisaggregated.
as possible(less than 5 s). During the run, the two collectors
Vertically integratedstreamwisefluxes of both sand and dust connectedto the modified Bagnold sampler were interchanged
were measuredwith a modified Bagnold sampler,placed 6 m at times t -- 15 and 60 s and then at intervals of 60 s.
downstreamfrom the leadingedge of the sandsurface.The 3 rn
Besides the principal "bombardment"configuration(Figure
of surfacebetweenthe downwindedge of the dust bed and the 1), experimentswere done with two additional configurations:
samplerconsistedof smoothwood, upon which both sand and "pure dust" and "mixture."In the "pure dust" configuration,no
Dust
collectors
0.9m
•
( 0.5 rn high)
•
lm - ,_L
2m
,_1
6m
Fig. 1. Schematicillustrationof the principalexperimental("bombardment")configuration.
_1
SHAO ET AL.: ENTR&INMENTOF DUST BY SALTATION
saltatingmaterial was usedand the dustbed extendedfor 3 m in
the streamwisedirection (encompassingthe section otherwise
occupied by the sand bed). The purpose of this test was to
determine the entrainment rate of dust by aerodynamic lift
alone, without saltation bombardment. The test was carried out
at the four standardwind speedsbut without replication.In the
"mixture" configuration,dried but unsieved sand was mixed
uniformly with dust in the ratio 1:2 (sand:dust)by volume; this
mixture was then spreadover the tunnel floor for a length of 3
m. The complete course of the experiment is summarized in,
Table
1.
12,721
3. RESULTS
3.1. Dust Entrainmentby SaltationBombardment
We first considerthe "pure dust" configuration(runs 1 to 4
in Table 1). Figure 2 shows that the streamwisedust flux, Q,t
(and thus the surfaceflux density,Fa, or dust entrainmentrate),
decays rapidly with time, becomingnegligible less than 200 s
after the onset of the wind. The initial dust fluxes (which are
small in comparison with the fluxes induced by saltation
bombardment,as shown later) are caused by the removal of
The streamwise flux measurementswere interpreted as
follows. The vertically integratedstreamwiseparticle massflux,
extremely loose dust particles from the newly prepared bed;
once these particles are removed, the dust bed stabilizesand is
Q, withdimension
g m'• s'•, is definedas
not subject to further erosion. This is a well-known
phenomenon,observedby Bagnold [1941] in experimentswith
cementparticles.Bagnold ascribedthe stability of the dust bed
to
the aerodynamicbehaviorof particlesat very small Reynolds
whereq is the streamwise
massflux density(dimension
g m'2
s'l) andz is the height.Conservation
of particlemassimplies numbers. However, a substantialbody of later work, reviewed
by Greeley and Iversen [1985, p. 80], has shown that the bed
that, in steady conditions,Q is related to the upward mass flux
stability is actually caused by the cohesive forces between
density at the surface,F, by
particles:the ratio of cohesiveto aerodynamicforcesactingon a
F -- dQIdx
(3) particle on the surface increases rapidly as particle size
decreases. In summary, aerodynamic lift alone induces
where x is the streamwise distance coordinate. If particle negligible eolian dust entrainment under normal wind
conditions.
entrainmentis occurringfrom a bed of streamwiselength L into
The "bombardment"configuration examined the effect of
a particle-freeincident airflow (so that Q = 0 at the upwind
saltation bombardmenton dust fluxes (runs 5 to 26 in Table 1).
edge of the bed), then the upward massflux densityof particles
Figure 3 shows the time evolution of the streamwisesand and
from the bed surface (averaged over the streamwiselength of
dust fluxes, Q.,. and Qa, in the presence of saltation
the bed) is F = Q/L, where Q is measured at the downwind
bombardment,for the 210 to 530-gm sandparticle size range at
edge of the bed. This argumentapplies to both the sand and
dust constituentsin the present experiment; hence, the bed- four wind speeds.The dust flux, Qa, is substantiallylarger than
even the maximum value producedby aerodynamicforcesalone
averagesurfaceupwardmassflux densitiesof sand(F,) and dust
at a correspondingwind speed and is sustainedfor far longer
(F•/) are given by
times, essentially for as long as there is a supply of both sand
and dust. In the two lower-wind-speedcases(Figures 3a and b),
both Q, and Q.,.remained constantwith time for the 9-min run
wherethe verticallyintegratedstreamwisesandand dust fluxes, duration,following a shortinitial period of lessthan 60 s during
Q,.and Q,•,are valuesat the downstream
edgesof the sandand which fluxes were abnormally high as very loose material was
dustbeds,respectively,and L., andL,•are the streamwiselengths blown off the newly preparedbed (as in Figure 2). The higherof the sand and dust beds.
wind-speedcases (Figures 3c and d) behaved similarly, except
Q--fl qdr,
(2)
TABLE 1. Runs in SaltationBombardmentExperiment
Run
U•, m s'•
SandSize,pm
Configuration
1,2,3,4
8.3, 9.8, 11.1, 12.9
5, 6, 7
8.4, 8.1, 8.1
210-530
bombardment
8, 9, 10
9.7, 9.7, 9.7
210-530
bombardment
11, 12, 13
10.9, 11.4, 11.2
210-530
bombardment
14, 15, 16
12.9, 12.3, 12.6
210-530
bombardment
17, 18, 19, 20
8.3, 9.7, 11.0, 12.4
530-1000
bombardment
21, 22, 23, 24
8.0, 9.5, 11.0, 12.5
100-210
bombardment
25, 26
8.2, 8.2
unsieved
mixture
27, 28
9.6, 9.6
unsieved
mixture
29
11.0
unsieved
mixture
30
12.5 (estimate)
unsieved
mixture
pure dust
12,722
SHAOET AL.: ENTRAINMENT
OFDUSTBY SALTATION
lO
UR(ms-1)
0
100
200
300
ß .........
8.3
* ....
9.8
ß
11.1
[]
12.9
400
500
Time (s)
Fig.2. Decay
ofstreamwise
dustflux,Qa,withtimeforfourreference
windspeeds,
Un,inthe"pure
dust"
configuration.
I
2oIß
I
I--l__,
I
I'•' l
,--,.. ,
.._._ ==_=_+_==____$-----
dustentrainment,
while aerodynamic
forcesplay a negligible
a
role under normal wind conditions.
In the "mixture"configuration,
the bedconsisted
of a mixture
=---= $
UR=8.3ms'1
ß
40
ß
i•
i ,..--.-1---- ß•.
b
i__ ,1__,
of one third unsieved sand and two thirds dust. Somewhat
surprisingly,
the resultwas very similarto the "puredust"
configuration
(Figure2): aftera shortperiodof about100 s, the
streamwise
fluxesof both sandand dustwere negligible.An
explanation
is that as the sandparticlesare coatedby dust
particles,the cohesiveforces betweengrains are greatly
enhancedand the "coefficientof restitution"(crudely,the
20
rA/
&
$
•
-
•
elasticity)of the bed is greatlyreduced.Both effectscausethe
_
saltation
process
to be inefficient
[Anderson
andHaft, 1991,p.
9.8
28]. The sameexperimentwasdonewith a mixtureof half sand
and half dust and producedessentiallythe same result. It
appearsthat a muchhigherproportionof sandis requiredto
generatea significantamountof dust from intimate mixturesof
sandanddust,at leastwith the presentmaterials.
3.2. DustEmissionFlux is Proportionalto u.3
To examineexperimentally
the relationship
betweenthe
surfacedustflux, F,•, and the frictionvelocity,u., we usethe
directmeasurements
of thestreamwise
flux,Q,•,whichis relateo
to thebed-average
valueof F,•(overa streamwise
lengthL,•)by
loo
ß Total
80
=•
60
ß Sand
;•,
I/S/'
d
129
-
(4). As mentioned
earlier,themeasurements
of u. areunreliable;
hence,instead
of usingu., we studytherelationship
between
the
streamwise
fluxesandthereference
windspeed,Uk.
Figure4 showsthe verticallyintegrated
streamwise
fluxesof
sand,dust,andtotalmass(Q,= Q.,.+ Q,•)for the210to 530-1am
saltationsize fraction, plotted against Uk in logarithmic
coordinates.
The measurements
of Q.,.are in goodagreement
with thoseobtainedin anotherexperiment
[Shaoand Raupach,
ß
1993] using different traps in the same wind tunnel. The
t
logarithmic
plotsof eachof Q,.,Q,•,andQtagainst
U• arelinear,
with slopescloseto 3; least-square
fits showthat
0
200
400
60o
InQ,: 3.026In U• - 4.00
(5)
InQd= 2.832In % - 3.88
(6)
InQ, = 2.926In U• - 3.23
(7)
Time ( s )
Fig. 3. Timeevolution
of streamwise
fluxesof sand,Q,.,dust,Qe,and
total mass,Qt, for four referencewind speeds,in the "bombardment"
configuration.
Saltationsizeclassis 210 to 530 p m.
for rapid decreasesat the end of each run as a result of
exhaustion
of the supplyof sourcematerial(eithersandor dust);
Thus,thesaltation
flux, Q.,.,is proportional
to U•3 andthence
in otherwords,the processbecame"supply-limited"
ratherthan to u.3, consistent
withtheclassical
theoretical
predictions
of
"transport-limited."
Takentogether,Figures2 and3 confirmthat Bagnold
[1941]andOwen[1964].Greeley
andlversen
[1985,p.
bombardment
is the principalmechanism
responsible
for eolian 100] review numeroussubsequent
predictionsfor the
SHAOET AL.: ENTRAINMENTOF DUST BY SALTATION
12,723
UR ( rns-1)
8
10
12
I
I
I
15
ß Total
o
Sand
5O
" Dust
2O
10
2.O
2.2
2.4
2.6
In UR( rns-1)
Fig. 4. Streamwisefluxesof sand,Q.,.,dust,Qa, and total mass,Q,, for the 210 to 530-pm sakationsize class,plottedagainst
:eferencewind speed,Ur. in logarithmiccoordinates.
dependenceof Q.,.on u., which all tend to proportionalitywith
Tke close relationshipof Qa to Q.,.is verified in Figure 5c.
u.3 well abovesaltationthreshold.For the dust flux. however, which shows the ratio Qa/Q.,.,which can be regarded as a
Figure4 showsthatQais proportional
to Uk3 andthencethatFa measureof the efficiency of the bombardmentprocess.This
is proportional
to u.3. This resultis in contradiction
with the ratio is approximatelyconstant(independentof wind speed)for
only hypothesisaboutthe wind speeddependenceof Fa known a specifiedsaltationparticlesize class;the valuesof Q/Q.,. are
to us,equation
(1), whichsuggests
a u.4 dependence
well above about 0.25, 0.7, and 0.8 for the 100 to 210-, 210 to 530-, and
saltationthreshold.The implication of Figure 4 is that there is
no fundamentaldifferencebetweenthe wind speeddependencies
of Q.,. and Q,•; rather, the streamwise flux of dust, the
entrainment of which is caused almost entirely by saltation
bombardment,is proportional to the streamwise flux of the
bombardingmaterial.
3.3. BombardmentEfficiency
Figure 5 shows the time evolution of the sand and dust
streamwisefluxes,Q.,.and Q,/, togetherwith their ratio, Q,/Q.,.,at
the four referencewind speedsfor all three saltationparticle
size ranges.Both Q.,.(Figure 5a) and Qa (Figure 5b) show the
expectedincreasewith wind speed, apart from some supply
limitation at the later stagesof runs at the two higher wind
speeds,which causedthe fluxes to decay toward zero. The trend
with saltationparticle size class is for Q.,.to decreasewith
increasingparticlesize (at a given wind speed),mainly because
of the increasein thresholdfriction velocity with increasing
particle size above 100 I.tm [Greeley and Iversen, 1985]. For the
largest size class (530 to 1000 I.tm), Q.,.is negligible at the
lowestwind speed(Uk = 8 m s-•, u. = 0.34 m s'l) because
the
wind speedis below (or just at) the entrainmentthreshold.
We have arguedthat the dust flux, Q,/, is closely linked to
the sand flux, Q.,.,by the bombardmentmechanism,so similar
patternsof evolution are expectedin both fluxes; this is what is
observed(Figures 5a and b). In particular, the dust flux is
negligible for the largest saltation particle size class at the
lowest wind speed, which was below saltation threshold.Also,
limitation of sand supply at the two higher wind speeds
producednot only declinesin Q.,.but also declines in Qa at
correspondingtimes.
530 to 1000-pm size classes, respectively. These constant
values are observedthroughout,apart from short initial periods
during which extremely loose material is blown off the freshly
prepared beds. as in Figure 1, and periods of acute supply
limitation late in the higher wind speed runs, when the ratio
becomes undefined.
In summary,Figure 5 showsthat the efficiency ratio, Q,/Q,., is
independentof wind speed for a given saltation particle size
class and increaseswith saltationparticle size at a given wind
speed.
4. THEORY FOR THE DUST EMISSION FLUX
The following theory for dust emission by saltation
bombardmentis formed from two components:a theory for the
dependenceof saltation on friction velocity (following wellestablishedlines), and a hypothesisabout the energeticsof dust
emission.
Saltation: In general terms, the theory of saltation is well
established,following Bagnold [1941] and the detailed analysis
of Owen [1964]. The purposeof this sectionis to draw a few
resultsfrom this theory by outlining a simplified summary.We
considerthe saltationof identicalparticles(saltators)of massm,.The vertically integratedstreamwisesaltationflux, Q,., is given
by
O,: %nX,
(8)
where n is the ejection rate or dislodgmentrate (the flux density
of saltatorsat the surface, either up or down, in particles per
unit area per second)and X,-is the mean saltationjump lengthin
the streamwise (x) direction. The total momentum flux to the
groundsurface,
('c = pu.2, wherep is air density),
canbe
12,724
SHAOET AL.' ENTRAINMENTOF DUST BY SALTATION
writtenas the sum'ct,+ 'c, of contributions
fromthe saltator
motion('ct,)andturbulent
andviscous
transfer
through
theair
('c,).
The
particle contribution at
the
-
-
surface is
'ct,- nm.,.(Ux-Uo),
whereU0 andU] arethestreamwise
velocity where c is a dimensionlessO(1) constant.This is the saltation
componentsof the saltatorat ejection from the surfaceand on
impact, respectively.The air contributioncan be taken to be
'c,- pu•, whereu,t is the threshold
friction
velocity
for
saltation,as statedby Owen [1964]. It followsthat n is givenby
2
n
=
2
pu,(1- u,t/u,
2)
(9)
[see Raupach, 1991, equations(3) and (11)]. A form for
follows by noting that the jump length, X,-, in equation(8) is
U,vt., where U,,,,is the averageparticle velocity during a jump
and t.,.is the averagesaltationjump time. Approximatingt.,.with
the ballistic time, 2Wo/g, where W0 is the initial (ejection)
vertical velocity of the saltatingparticle, (8) and (9) give
equationof Owen [1964, equation(41c)], thoughOwen's form
includesa small additionalu, dependence
in c.
Dust
emission:
The
emission
of
dust
under
saltation
bombardment
is causedby the rupturingof interparticlebonds
betweendustgrainsby the impactof a saltator.Let • be the
typicalbindingpotentialenergyof a dustparticleon the surface,
equal to the energy requiredto dislodgethe particlefrom the
"potentialwell" inducedby the binding forces. The energy
suppliedto the surfaceby a saltationimpactis E] - E2, whereE•
is the kineticenergyof an impactingsaltatorandE2 is the total
kineticenergyof the saltatorsejectedby the impact,whichmay
cause both ricochet of the original saltator and ejection of
others.(The subscripts
0, 1, and 2 denotean ejection,impact,
and subsequent
ejection sequence.)Letting N be the typical
number of dust particlesejected by a saltationimpact, we
supposethat N satisfies
./•ql -- ½3/(•'1
- •'2)
If we take U,,/(Ux-Uo) and Wo/u, as constantsof order 1
[Andersonand Hallet, 1986], then (10) becomes
60
i
ß
40
21o
•, 21o-
530
ß 530
20
I
lOO-
I
where C•vis a constantof proportionality,which must be less
than 1, to satisfythe energeticrequirement
thatE• - E2 exceeds
I
a
pm
UR= 8.3 ms'•
/
20 •--
ß lOO- 21o pm
•, 210 - 530
a /
UR= 8.3 ms-1--I
[
ß530- 1000
•A•A•A
0 kt'•.• eL : A•A
: ;
- lOOO
--
•
0
•
(12)
•
•
]
ßII
A•A•A
.; ..
•
Go
b
40
9.8 _
o
_
/,,,.&•
60
40
c_
c
_
11.1<2• 6•6••ø•ø••ø••••g•
1
11.1
'
20
ß
dJ
60
.
.
d
40
20
•
0
100
•
•*
200
300
400
Time (s)
0 /
500
0
I
I
100
200
300
400
Time (s)
Fig. 5. Timeevolution
of (a) streamwise
sandflux,Q.,.,(b) streamwise
dustflux,Q½,and(c) theratioQ2Q,for t•ee saltation
sizeclassesat four referencewind speeds,U•.
500
SHAOET AL.: ENTRAINMENTOF DUST BY SALTATION
!
•
1.5
i
i
I
* 100- 210 lam
--
a
-•• •210
-530 UR
=8.3
ms
-1ß 530
1.0
- 1000
12,725
•1 I,•,3(1 -
2 2
u,,iu,)
(14b)
whereo•, is a dimensional
parameter
whichdetermines
the
efficiencyof the bombardmentprocess.
Equation(14a) showsthat the basicquantitiesgoverningthe
dust emission flux are embodied in the proportionality
F,/- m,/gQ.,./u/(apart
fromthe dimensionless
factorc•/2c and
0.5
'••A•A•A•A•
ß•A •
ß
andthenceproportional
to u.3 (well abovesaltation
threshold).
b
This is the observedbehaviorin Figure 5. Also, for a given
the dustflux decreasesas the binding energy, •, increases'that
is, the bombardment efficiency decreases.Equation (14b)
1.5
e•
1.0
the dimensionlesswind parameter (U0 + U,)/u., which is
typically of order 10; see Owen [1964]). In particular,F,• is
predictedto be proportional
to the streamwise
saltationflux, Q,.,
e•e•e
-
expresses
our result in a form comparableto (1), where the
dimensionalparameter0[l = (map/•)(%/2) (U, + Uo)/U., or
ot•- cNmap/•.Hence,o•l depends
on qvproportionally
andon
0.5
A-
-- ß
• inversely, qv reflecting the proportion of the incoming
bombardmentenergy available for breaking bonds; and
reflecting the resistanceof the surface to breakdownby this
A•A
available energy.
1.5
11.1
ß
10 •.
•
8••
A--A•
•/'l
However,the experimentallyobservedchangein Q,/Q, with d is
large only for the transitionfrom the smallestto the middle d
class (100-210 to 210-530 pm) and is quite small for the
transition from the middle to the largest d class (210-530 to
530-1000 pm). It is thereforepossiblethat (12) (with a constant
qv) is reasonablefor saltatorsabove a certain thresholdsize,
perhapsof order 200-500 pm, given the dust materialusedin
1.5
d
12.9
1.o
•A•A•
0
this experiment.
A__A•A
100
200
oversimplification
and that the constantof proportionality,
relatingN to (E• - E2)/Ill is dependent
on saltatordiameter,d.
A•/A
o
0.5
One aspectof the experimentalresultsnot predictedby (14a
and b) is the observed increase in the efficiency of the
bombardmentprocess,as measuredby the ratio Qa/Q,.,with
saltation particle size. This indicates that (12) is an
5. DISCUSSION
400
300
500
It is important to compare our findings with field data.
Gillette [1977] presentedfield measurementsof F,• and Q, as
functionsof u. for nine soils; Q,. was obtainedfrom a modified
Fig. 5. (continued)
Bagnoldtrap, and F,/ from measurements
of dustconcentrations
•
and wind speedsat heights 1.5 and 6.0 m, assumingsimilarity
the sum of the binding energiesof all dislodgeddust particles.
of turbulent transfer of dust and momentum. The Q.,. data
On the right hand side of (12) we have excludedthe initial
generally conform to (11). The F,/ data show a strong increase
kinetic energy of dust particles obtained from the impact by with u. but are so scattered that for most of the nine soils it is
assumingthat this energy is either much smaller than or
impossibleto distinguishbetween a third- and a fourth-power
proportionalto •. The emissiondustflux acrossthe surfaceis
dependenceon u.. However, the ratio F,/Q.,. (which Gillette
F,t = re,inN,wherem,/is the massof a dustparticleandn is the
plotted separatelyagainstu.) does not dependsystematicallyon
number of saltationimpactsper unit area per second.We use
u., in agreement with the experimental and theoretical
(9) and (12) for n and N, respectively, and write
conclusionof this paper. The only clear exceptionis Gillette's
E, - E2 -- (m.,./2)(U•
2 - U02)
to relatethe kineticenergysoil 3, "a loamy soil with very little surface coherence,"for
difference,El - E2, to the ejectionand impactvelocities,U0 and
which Fd increasedvery rapidly with u., apparentlyto a power
Time (s)
U, respectively,
of a typicalsaltator(which is an approximation
becauseof the possibilityof multiple ejectionsfrom a single
impact).It follows that
pu,(1 - u,iu,2)
-- ,ha
-
- u0)
(13)
2,
' u,
In this context, we must allow for two major differences
betweenour idealized bombardmentexperimentand natural dust
emissionin the field. First, the fetch was extremely short in our
experiment,so that depositionof dust (as opposedto emission)
is greatly underestimated.
This is unlikely to affect our basic
finding about dust emission, which is externally driven by
saltationbombardmentand is thereforelargely independentof
dust concentration.In contrast,depositionis stronglydependent
whichsimplifiesthroughthe use of (11) to
,
around 7 or more.
(14a)
on dust concentration [Chamberlain, 1983], which in turn is
controlledby the upwind emissionflux and fetch.
12,726
The
SHAO ET AL.: ENTRAINMENTOF DUST BY SALTATION
second
main
difference
is that both the sand and dust
particle characteristicswere carefully controlled (idealized) in
our experiment: both particle size distributionswere sharply
peaked, and the dust bed was loose, implying that the binding
energies between dust particles were low and not broadly
scattered.It is likely that this group of soil-dependentfactors
accounts
for
much
of the difference
between
our results
and
those of Gillette [1977] and also for much of the large
variability between field soils observedby Gillette. If there is a
broad distributionof the binding energy, • (say over several
ordersof magnitude),then a progressivelygreaterfractionof the
bombarded
surface
will
become
amenable
to dust emission
as
thewindspeed
(andsaltator
kinetic
energy)
increases,
leading
toF,•o•u.'•
with n > 3. In this view, both the F,•(u.) relationshipand its
..variability in the field are controlledby a combinationof
saltation energeticsand soil mechanics.This can be contrasted
with the view that dust emissionis dominatedby aerodynamic
processes,which underlies(1).
Finally, the present work on saltationbombardmentcan be
comparedwith investigationsof eolian abrasionas a weathering
process [Anderson, 1986]. Dietrich [1977] concludedthat the
fundamental parameterswhich control eolian abrasion are the
kinetic energyof the impactinggrain and the bond strengthof
the abraded material. This was confirmed by Greeley et al.
[1982], who investigated the susceptibility of surfaces to
abrasion,S,, defined as mass of material eroded per particle
impact.They found that for a given size of impactparticle,S, is
proportional
to the squareof the impacting-particle
velocity,v2,
whilefor a givenimpactvelocity,S,,is proportional
to d3,where
d is the impacting-particle diameter. Hence, the combined
relationshipis that S,,is proportionalto the kinetic energyof the
impactingparticle:
S• •, d•v2 •, rove12
(15)
statisticsof the binding potential energy, W, which must be
exceededto dislodgedust grainsfrom the surface.
Acknowledgments.
J. F. Leys, Departmentof Conservationand Land
Management,New South Wales, made the wind tunnel available for this
investigation.
K. S. Venugobanprovidedvaluableassistance
in carrying
out the experiment.
The experimental
partof this work wasdoneduring
an extendedvisit by P. A. Findlater to the Centre for Environmental
Mechanics,supportedby the NationalSoil Conservation
Program.We
thankD. A. Gillette for extensivediscussions
and for makingavailable
the unpublished
manuscript
by P. R. Owen derivingequation(1).
REFERENCES
Anderson,R. S., Erosion profiles due to particlesentrainedby wind:
Application of an eolian sediment-transport
model, Geol. Soc. Am.
Bull., 97, 1270-1278, 1986.
Anderson,R. S., and P. K. Haft, Wind modificationand bed response
during saltationof sandin air, Acta Mech. Suppl. 1, 21-51, 1991.
Anderson,R. S., and B. Hallet, Sedimenttransportby wind: Toward a
general model, Geol. Soc. Am. Bull., 97, 523-535, 1986.
Bagnold,R. A., The Physicsof Blown Sand and Desert Dunes, Methuen,
New York, 1941.
Borrmann, S., and R. Jaenicke, Wind tunnel experimentson the
resuspension
of sub-micrometerparticlesfrom a sandsurface,Atmos.
Environ., 21, 1891-1898, 1987.
Chamberlain,A. C., Deposition and resuspension,in Precipitation
Scavenging,Dry Depositionand Resuspension,
vol. 2, edited by H.
R. Pruppacher,R. G. Semonin,and W. G. N. Slinn, pp. 731-751,
Elsevier, New York, 1983.
Dietrich, R. V., Impact abrasionof harderby softermaterials,J. Geol.,
85, 242-246, 1977.
Fairchild, C. I., and M. I. Tillery, Wind tunnel measurementsof the
resuspension
of ideal particles,Atmos.Environ., 16, 229-238, 1982.
Gillette, D. A., Fine particulateemissionsdue to wind erosion, Trans.
ASAE, 20, 890-897, 1977.
Gillette, D. A., Productionof dust that may be carried great distances,
Spec. Pap. Geol. Soc. Am., 186, 11-26, 1981.
Gillette, D. A., and R. Passi, Modeling dust emissioncausedby wind
erosion,J. Geophys.Res., 93, 14,233-14,242, 1988.
Greeley, R., and J. D. Iversen, Wind as a GeologicalProcesson Earth,
Mars, Venus and Titan, Cambridge University Press, Cambridge,
1985.
where rn is the impacting-particlemass.These findingsare fully
Greeley,
R., R. N. Leach, S. H. Williams, B. R. White, J. B. Pollack, D.
consistentwith the basic assumptionof our analysis,equation
(•2).
6. CONCLUSIONS
H. Kfinsley, and J. R. Marshall, Rate of wind abrasionon Mars, J.
Geophys.Res., 87, 10,009-10,024, 1982.
Gupta, J.P., R. K. Aggarwal, and N. P. Raikhy, Soil erosionby wind
from bare sandyplains in westernRajasthan,India, J. Arid Environ.,
(1) The experiments confirm that under normal wind,
conditions, saltation bombardment (as opposed to direct
aerodynamiclift) is the dominant mechanismmaintainingdust
Leys, J. F., and M. R. Raupach,Soil flux measurements
with a portable
emission
Owen, P. R., Saltationof uniform grainsin air, J. Fluid Mech., 20, 225-
fluxes from the surface.
4, 15-20, 1981.
wind erosion tunnel, Aust. J. Soil Res., 29, 533-552, 1991.
242, 1964.
(2) The streamwisedust flux, Qa, which is relatedlinearly to
Owen, P. R., and D. A. Gillette, Wind tunnel constraint on saltation, in
the surface dust emission flux, F,•, in our experiment, is
Proceedingsof the International Worlcvhop
on the Physicsof Blown
observedto be proportionalto the streamwisesaltationflux, Q.•.;
Sand, editedby O. E. Bamdorff-Nielsen,pp. 253-269, Universityof
Aarhus, Aarhus, Denmark, 1985.
both streamwisefluxes are proportionalto the cube of the wind
speed(U••) or of frictionvelocity(u.•) in the velocityrangeof
this experiment.
(3) To derive an expressionfor the wind speeddependence
of the dust flux inducedby saltationbombardment,we assumed
that the numberof dust particlesdislodgedfrom the surfaceper
saltationimpact is proportionalto the ratio of the kinetic energy
loss during a saltafionimpact to the typical binding potential
energy holding a dust particle to the surface, •. This
assumptionleads to the prediction that dust flux, F,•, is
proportional
to rnagQ•./•andin particular
thatF,•is proportional
to Q.,.,as observedin this experiment.
(4) The efficiency of bombardment(the ratio Qa/Q.•)was
observed to increase with the size of saltation particles: the
efficiency was about 0.2 for 100 to 210-gm saltators,0.7 for
210 to 530-gm saltators,and 0.8 for 530 to 1000-•m saltators.
(5) The scatterof field measurements
of Fa(u.) is very large,
but mostdataare consistent
with a u.3 dependence
of F,•.The
large field variability is likely to be related to differencesin the
Raupach,M. R., Saltation layers, vegetationcanopiesand roughness
lengths,Acta Mech. Suppl. 1, 135-144, 1991.
Raupach,M. R., and J. F. Leys, Aerodynamicsof a portable wind
erosiontunnel for measuringsoil erodibility by wind, Aust. J. Soil
Res., 28, 177-191, 1990.
Shao, Y., and M. R. Raupach, The overshootand equilibrationof
saltation,J. Geophys.Res., 97, 20,559-20,564, 1993.
Shao,Y., G.H. McTainsh, J.F. Leys, and M.R. Raupach,Efficienciesof
sedimentsamplersfor wind erosionmeasurement,
Aust. J. Soil Res.,
in press.
Zobeck,T. M., and D. W. Fryrear,Chemicaland physicalcharacteristics
of windblown sediment, II, Chemical characteristics and total soil
and nutrientdischarge,Trans.ASAE, 29, 1037-1041, 1986.
P.A. Findlater,WesternAustralianDepartment
of Agriculture,P.O.
Box 110, Geraldton, WA 6530, Australia.
M.R. Raupach and Y. Shao, CSIRO Centre for Environmental
Mechanics,G.P.O. Box 821, Canberra,ACT 2601, Australia.
(ReceivedAugust27, 1992;
revisedFebruary10, 1993;
acceptedFebruary11, 1993.)