Application Number:
Full Title:
The Origin of the Transverse Instability of Sand Ripples – 3D Approach Based on
Mathematical Models, Field and Wind Tunnel Experiments, and Grain Size Analysis
Principal Investigators: Itzhak Katra, Jasper Kok
Research Plan
1. Brief description of the subject and scientific and technological background
Aeolian ripples, which form regular patterns on sand beaches and desert floors, indicate the
fundamental instability of flat sand surfaces under the wind-induced transport of sand grains
(Yizhaq et al., 2012b). Ripples are also found on dunes as part of a hierarchy of bedforms. Two
different kinds of sand ripple—normal ripples and megaripples—are observed in nature (Bagnold
1941; Sharp 1963, Pye and Tsoar, 2009). The main features of these ripples are depicted in Fig.1.
Normal ripples and megaripples have also been observed on Mars (Sullivan et al., 2005; Sullivan et
al., 2008; Zimbelman et al., 2009, Zimbelman, 2010, Zimbelman et al., 2012), where aeolian
processes are also important for understanding the planet's geology (Rubin, 2006). Images from the
Mars Global Surveyor clearly portray dust storms, dust devil traces, dunes, and megaripples.
Various applications of sand ripple studies on Earth and Mars were reviewed by Rubin (2006).
The physical mechanism responsible for the formation of sand ripples is the action of the wind
on loose sand. When the wind strength exceeds some threshold, grains displaced by the direct
action of the wind are lifted into the air. However, sand grains are too heavy to be kept aloft even by
strong winds, and therefore, fall to the ground. During their flight, the grains reach a velocity
approximately equal to that of the wind, and upon their impact with the surface, impart energy and
momentum to the sand and eject other grains. Under sufficiently high wind velocities, this
bombardment by sand grains accelerated by the wind generates a cascade process, resulting in an
entire population of saltating grains “hopping” on the sand surface. When the saltating, high-energy
grains collide with the bed (see Fig. 2), they eject reptons, or grains of lower energy (Anderson,
1987, Yizhaq, 2004, Andreotti et al., 2004, Kok et al., 2012). The windward slopes of small bumps
on the sand surface are subjected to more impacts than the lee slopes. The flux of reptons is
therefore higher uphill than downhill, which causes the bumps to increase in size.
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Fig. 1 Different types of terrestrial ripples show different responses to transverse perturbations: whereas
normal ripples are relatively straight, megaripple crests have crescentic, barchanoid-like and irregular
planform geometry. (a) Megaripples at Grand Falls, Arizona (average wavelength ~1m). (b) Normal ripples
show almost straight lines at Nizzana dunes, Israel (wavelength ~7 cm) (c) Megaripples in the Sanshan
Desert, western Xinjiang, China. The average wavelength is about 1 m (the length of the measuring tape in
the lower right hand corner of the picture is 1 m. (d) Ripples (foreground) and megaripples (background) in
the Libyan Desert in Egypt, showing the difference in the planar pattern of the two bedforms. The normal
sand ripples (wavelength~4m) look almost straight whereas the megaripples (wavelength 7cm) in the
interdune area are more sinuous, comprising curved segments. Arrow indicates the prevailing wind direction.
Several experimental studies focusing on the collision process have been conducted. Willets and
Rice (1986) observed collision phenomena with sand grains in wind tunnel experiments by means
of high-speed video recordings. They found that the impacting grains hit the sand surface at small
angles between 10° and 16° and rebounded with an angle between 20° and 40°. In addition, they
established that the grains ejected from the granular bed have an average speed of one order of
magnitude less than the impact speed. Mitha et al. (1986) studied the collision between a steel bead
and a three-dimensional packing of steel beads. Beads of 4 mm diameter were used and the
impacting bead was launched at a speed of 20 m/s. They investigated essentially the influence of the
impact angle on the collision process. The mean normal restitution coefficient for the impacting
bead, defined as the ratio between the vertical rebound speed and the vertical incident speed, was
found to decrease with increasing impact angle from 0.7 at 17° to 0.3 at 31°. Furthermore, they
showed that the number of ejected beads does not vary significantly when the impact angle
increases from 17° to 31°, and that the average vertical speed of ejection is on the order of
3gd
where d is the grain diameter and g is the gravitational acceleration. Werner (1990) also studied
extensively the collision process for shallow impact angles. He used sand grains and designed a
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special apparatus to propel a sand grain with a given velocity. He found in particular that the normal
restitution coefficient for the impact grain is independent of the incident speed, and equaled 0.82 at
an impact angle of 15°. He observed in addition that the number of ejected grains increases with
increasing incident speed and that the distribution of the vertical ejection velocity is nearly
independent of the incoming velocity. More recently, Rioual et al. (2003) designed a two
dimensional setup to investigate the collision between a 6-mm-diameter incident bead and a twodimensional granular packing of identical beads confined between two parallel vertical glass walls.
This study confirmed Werner’s observations (1990): the normal restitution coefficient for the
impacting bead is independent of the impact speed, and the mean number of ejected grains varies
nearly linearly with the impact speed. However, Rioual et al. (2003) found that the mean vertical
ejection velocity Vz increases slightly with increasing incident speed, i.e., roughly as the square root
of the incident speed and proposed the Rayleigh probability distribution function of the vertical
ejection velocities (Rioual et al., 2009)
P(Vz ) 
 Vz2 
exp
  2 2 
2


Vz
where  2  0.1Vi gd
(1)
and Vi is the impacting speed. Furthermore, laboratory and numerical
experiments indicate that the mean angle at which particles are splashed is ∼40o–60o from
horizontal (Willetts and Rice 1985, 1986, 1989, Anderson and Haff 1988, 1991, Werner 1990,
McEwan and Willetts 1991, Rice et al. 1995, 1996, Gordon and McKenna Neuman 2011). Despite
these studies the splash function in the lateral direction is almost currently not known, either from
experiments or theory.
Fig. 2 Successive snapshots of the collision of 6 mm PVC beads and 0.2 g mass. The time step between
two successive images is 4 ms (adopted from Beladjine et al. 2007). The impact of a saltating particle on the
bed can produce a rebounding particle as well as one or more splashed lower energy particles. Analytical
and numerical treatments of saltation need to account for the creation of these particles. The interaction of
the impacting saltator with the bed is complex and stochastic and has been mostly studied in 2D.
Grain-size analyses from different parts of megaripples and normal ripples show that a bimodal
mixture of grain sizes are needed for megaripple formation and that the coarse particles are more
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abundant at the crest (Yizhaq et al., 2009, Isenberg et al., 2011). Megaripple growth starts with
small ripple coalescence. Coarse and fine particles began to segregate, and eventually, grain size
distributions on the ripple crest became bimodal, and an armored layer of coarse grains covers the
crest (Isenberg et al., 2011; Yizhaq et al., 2012a). The cover of coarse grains on the megaripple
crest allows the ripples to grow higher as strong winds needed to destroy the cover. In contrast,
normal ripples which composed only of fine grains cannot grow higher as weak wind may drive the
fine grains at the crest into the saltation cloud (Manukyan and Prigozhin, 2009), thus keeping its
height quite low. This is the main difference in the formation process between normal and
megaripples. The final wavelength is not simply correlated to the mean saltation length, but rather
evolves through interaction between ripples with different sizes. Normal ripples and megaripples
exhibit self- organization behavior where ordered spatio-temporal structures spontaneously emerged
(Hallet. 1990, Anderson, 1990, Yizhaq, 2008).
Observations of normal aeolian ripples in deserts or on sandy beaches indicate that ripple fields
are almost one-dimensional bedforms, and they display only small modulations in the direction
transverse to the wind, in contrast megaripples exhibit transverse instability (Yizhaq et al., 2012b
see Fig.1). The transverse instability increases megaripples sinuosity, which increases the merging
rate of incipient megaripples, thereby accelerating the growth of the ripple wavelength (coarsening).
The origin of the transverse instability of megaripples is still unknown and was little studied. Using
more quantitatively analysis of megaripples and ripples sinuosity in different sites will help to better
distinguish between these two types of ripples both on Earth and on Mars. For example, the
distinction between TARs (Transverse Aeolian Ridges, Balme et al., 2008, Zimbelman, 2010) and
megaripples and large normal ripples on Mars can be done on the basis of their plain sinuosity when
the underlying mechanism will be uncovered. Full understanding of this instability will become
possible only with a 3D megaripples mathematical model which presently does not exist.
2. Objectives and expected significance of the research
The objective of the proposed work is to understand what drives the transverse instability of
ripples and megaripples, and thereby solve the mystery of why megaripples are less transverse
stable than regular ripples. We will achieve this objective through the following tasks. (i) We will
perform a 3D study of the splash process with high speed cameras to quantify, for the first time, the
lateral reptation flux. The results will be used in the mathematical modeling of the next tasks. (ii)
Parameterize the measured lateral reptation flux, and implement it into COMSALT, a state-of-theart mathematical model of sand transport. We will then use this model to study in details what the
mechanisms are which drive the transverse instability for megaripples (Yizhaq et al., 2012b) and
why normal ripples are more transverse stable. (iii) Use field and wind tunnel experiments to study
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the correlation between the grain size segregation along the ripple crests and the ripples height and
their pattern in plane. Our hypothesis is that small irregularities along the megaripples crest further
develop to perturbations in megaripple height which due to the smaller lateral reptation flux grow in
time. Thus, different portions of the megaripple migrate in different rates which increase the crests
sinuosity.
The proposed study will improve our understanding of pattern formation and behaviors of
nonlinear dynamics in nature, which is very important in modern science (Cross and Greenside
2009; Rubin 2012). Especially it will deepen our standing of one of the three possible mechanisms
for straight bedforms in unidirectional flows (Rubin 2012): along-crest flow (non-transverse
bedform orientation), gravitational transport along an inclined crest, or ballistic splash in air. We
will mainly work on the ballistics splash of ejecting particles.
The main goal of the proposed research is to integrate theoretical, field and wind tunnel studies
with the aim of understanding the mechanism behind the transverse instability of megaripples. A
detailed understanding of what drives ripple transverse instability could allow ripple sinuosity to be
used to infer the wind regime and sediment properties that formed a given ripple. This provides an
additional tool for understanding the formation and geological history of planetary surfaces,
especially Earth and Mars (Jerolmack, et al., 2006, Bridges, et al., 2012). Following Rubin (2012)
our main assumption is that straight bedform crests or two-dimensionality patterns
arise in
situations where along-crest coupling processes are strong enough to overcome that tendency for
three-dimensionality. For a ripple or dune to have a straight continuous crest, some physical
mechanism must operate to couple the topography at different along-crest locations. Without such
coupling, different sites along a crest need not remain locked in phase and are free to form breaks,
bends, or junctions. Hypothetically, if flow and topography along every streamline were completely
decoupled from adjacent streamlines, “bedform” crests would be randomly phased from one
streamline to another, and coherent bedforms could not exist. As the main mechanism responsible
for ripples formations is the splashing caused by the impacting saltating grains we propose that the
ratio S (lateral reptation flux/along wind reptation flux) is smaller for megaripples than for normal
ripples, such that the along crest coupling in megaripples is small and thus will drive the transverse
instability. The overall goal of the proposal will be achieved by addressing the following specific
aims:
I. Wind Tunnel Experiments
Wind tunnel experiments will be performed to quantify the distribution of ejected particles in the
forward and the lateral direction for different sizes of bed particles using fast camera photography.
Despite the many studies devoted to the ejection process (e.g., Rice et al., 1995; Beladjine et al.,
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2007), very little is known about the lateral distribution of the ejected particles. The results will be
used by COMSALT in order to simulate the ratio between the lateral reptation flux and along-wind
flux, which determines the transverse stability (Yizhaq et al., 2012b). We also will study the
development of ripples with polydisperse sand and measure changes of S in time (see Fig.4 for
preliminary results). We discuss the detailed experimental methodology in Section 3.1.
II. Mathematical Models
In the proposed research we will use COMSALT (Kok and Renno, 2009) to calculate the
ratio between the cross wind reptation flux ( W ) to the along wind reptation flux ( L ) for different
grain sizes and different wind velocities. S  W / L is a dimensionless measure of the importance of
straightening processes (Rubin 2012). COMSALT includes many of the advances of previous
numerical saltation models (e.g., Werner, 1990), and in addition, it includes (1) a physically based
parameterization of the splashing of surface particles that is in good agreement with experimental
and numerical studies, (2) a generalization of this splashing process to beds of mixed particle sizes,
and (3) a detailed treatment of the influence of turbulence on particle trajectories, which agrees with
laboratory measurements. Partially because of these advances, COMSALT can reproduce a much
wider range of measurements than any previous numerical saltation model (Kok and Renno, 2009).
COMSALT has also recently been used to show that saltation can be maintained on Mars by wind
speeds an order of magnitude less than that required to initiate it (Kok, 2010a, 2010b). The results
of the above wind tunnel studies will be used for a numerical study of the ratio ( S ) for different
grain sizes and wind velocities. The experiments will help to better simulate the physics of the
splashing mechanism in the lateral direction. The dependence of S on the bed grain size will be
used to predict the degree of sinuosity of ripples and megaripples which differ by size of the coarse
particles on the crest.
III. Sand ripple analysis
Detailed field work will be conducted in the Southern Negev of Israel (Nahal Kasuy), where
the megaripple wavelength is a maximum of 1 m (Yizhaq et al., 2012b). We will study the
correlation between ripples plain geometry, height and grain size segregation in developed
ripples (see Fig. 6) and will document the evolution of their spatial pattern in time and the
development of the instability from an artificial flat bed. The field study will enable us to
elucidate the development of the transverse instability and correlation with ripple height and
grain size segregation along the crest. We will measure the ratio W / L in the field during
wind storms and compare between with the results of wind tunnel experiments. Sand samples
that will be collected during the field experiments will be analyzed in the laboratory to explore
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the grain size distributions involved in ripple formation/destruction processes. Our main
hypothesis for the transverse instability is illustrated and explained in Fig.3.
Fig.3 A schematic diagram which
represents one possible scenario of the
development of the transverse
instability. Initial perturbations in the
coarse grains distribution along the
ripple crest lead to irregularities in
ripple heights which cause to different
migration rate of different points
along the crest. Small perturbations
along the ripple crest (top panel) will
grow if in accordance with their
heights. Points B and D are higher
points along the ripple crest where the
coarse layer is thick (denoted in the
figure by black thick line), thus their
migration rate is smaller than points A
and C which are lower and with thin
coarse layer.
3. Comprehensive description of the methodology and plan of operation
The proposed project is collaboration between geomorphologist and physicists each of which will
lead the area of his specialization. Itzhak Katra (geomorphologist) and Hezi Yizhaq (physicist) will
focus on: 1. laboratory experiments with the boundary-layer wind tunnel of the Aeolian Simulation
Laboratory at Ben Gurion University; 2. measurements of ripples in the field (Nahal Kasuy) 2; 3.
Grain analyses in the Soil Laboratory at Ben Gurion University. The results will serve as the basis
for the calibration of the mathematical modeling of the origin of the transverse instability of
megaripples. Jasper Kok (physicist) has developed the COMSALT model, which is a leading
numerical model for aeolian sand transport. Kok will use COMSALT to simulate the transverse and
longitudinal reptation flux on Earth and Mars.
3.1 Wind tunnel experiments (Objective 1)
3.1.1 2D flux measurements
Experiments of the process of megaripples evolution from a flat bed will be conducted in the
stationary boundary-layer tunnel of the Aeolian Simulation Laboratory at Ben Gurion University.
The wind tunnel is an open-circuit tunnel configured for the air-suction mode, allowing maximum
wind speed of 25 m/s. The cross sectional area is of the order of 0.7 × 0.7 m and the working
lengths is 12 m (7 m of test section). The tunnel has a sand feeder to control sand supply and thus
the occurrence of saltation in the test section. We propose to explore the mechanism of the
megaripple evolution based on promise results obtained during a preliminary experiment. We used
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sand collected from the megaripple field of Nahal Kausy to develop megaripple in the wind tunnel.
Small megaripples were developed (Fig. 4) from the initial state of a flat surface of mixed sand
under wind speed of 7 m/s (measured at 15 cm above the wind tunnel surface). We documented the
response of these megaripples by photographing and through grain size analysis of sand collected in
a trap (cross sectional area of 0.01 × 0.02 m) oriented in the along-wind direction.
Fig.4 Time evolution of
incipient megaripples in the
wind tunnel (wind speed 7
m/s) with natural sand
collected from Nahal kasuy
(time measured in minutes).
The bottom graph shows the
mass of reptating sand
collected in both directions
(parallel and transverse to
wind direction). The mass in
the trap along the wind
direction is at least four times
larger than that in the crosswind direction. The inset
shows the ripple height (in
mm) during the experiment.
3.1.2 Experiment of the collision process
According to our preliminary studies the origin of the transverse instability of megaripples is related
to the ratio of the reptation flux in the lateral direction to the flux in the flow direction. To simulate
these fluxes using COMSALT, we need information of the splash function in 3D and its
dependence on the bed composition. The collision process will be studied in the wind tunnel by
using two high speed video cameras (fps > 3000) that will be installed in perpendicular to the
incident plane and above the ripples in the test section. We will use fine impactors (200  m ) to
examine the ejected grains for two bed compositions sieved from natural sand collected from Nahal
Kasuy. One bed with fine sand (200  m ) and the other with coarse fraction (700  m ). The
experimental set-up will resemble the one that used by Rice et al. (1995) with sand bed (a tray 20
cm long, 2 cm wide and 1 cm deep) on the floor of a side corridor in the wind tunnel. The impact
grains will be fed into the tunnel 1 m upstream. They will be dropped through a tube that extends
from the roof of the tunnel to 6 cm.
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The consecutive images of the collision will be processed to extract the kinematic properties of
the incident particle and the ejected ones. By means of image analysis software, the positions of the
splashed particles will be determined on each image, then the trajectories of all ejected particles will
be reconstructed. We will analyze the trajectories of the splashed particles in the in 3D and will
extract their velocity components (Vx ,Vy ,Vz ) and their averages numbers. We will compare the
splash distributions between the two cases of bed composition (fine and coarse) in order to check
whether our hypothesis about the origin of the transverse instability of megaripples is correct.
3.2 COMSALT (Objective 2)
COMSALT is the most comprehensive and advanced physically based numerical model of saltation
to date (see sec. 2 II for more details). COMSALT will be used for computing the ratio S for
different grain sizes under Earth and Martian conditions. Fig 5 shows the results of a preliminary
simulation of the transverse (W) to longitudinal (L) flux of reptators for a monodisperse ripple.
Running COMSALT (Kok 2010a) for Martian conditions (air pressure 700 Pa, air temperature
220 K, gravitational acceleration 3.72 m/s2, and particle density 3000 kg / m3 ) will give the ratio (
S ) for different grain sizes for Martian conditions and will help up to understand the conditions
for the transverse instability on Mars. The dependence of on the bed grain size will be used to
predict the degree of sinuosity of ripples and megaripples which differ by size of the coarse
particles on the crest. We will investigate whether the substantial differences in the mechanics of
Martian sand transport, and in particular the much lower wind shear stress at which sand transport
can be sustained on Mars (Kok 2010a, b), affects the transverse stability of (mega) ripples.
Fig. 5 Results of a preliminary simulation of the
ratio of the transverse (W) to longitudinal (L)
flux of reptators for a monodisperse ripple
(magenta line) and a megaripple (blue line),
plotted as a function of the mean size of soil
particles. This is a consequence of the high
inertia of the megaripple coarse fraction, which
limits the acceleration of these particles in the
along-wind direction during their hop, thus
resulting in a relatively high ratio of W/L. That
is, these simulations predict that megaripples are
more tranverse stable than normal ripples, which
is in stark contrast to observations (see Fig. 1).
Clearly, an essential process determining the
transverse stability of (mega) ripples is missing
from these simulations. One of the objectives of
this proposal is to identify this missing process
using the wind tunnel experiments determining
the 3D splash process details (Objective I).
3.3 Field Experiments (objective 3 & 2)
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The experimental study will be conducted in the Southern Negev (Nahal Kasuy) where we have
already done a three years field study (Yizhaq et al., 2009; Isenberg et al., 2011; Yizhaq et al.,
2012a; Yizhaq et al., 2012b). See Isenberg et al. (2011) for more details on the research site. This
task is to focus on the 3D characteristics of natural megaripples and their evolution from initially
flat bed to study the development of the size segregation and height irregularities during the
megaripple development. We will measures the reptation flux along and transverse to prevailing
wind direction and compare the results with the wind tunnel experiments to study how close they
are to natural conditions. We will also study how the average sinuosity of the ripples changes in
time.
3.3.1 3D mapping of megaripples
We will conduct a 3D mapping of 10 megaripples, including their plain geometry, height and grainanalysis of samples along the crest (every 15 cm with depth of 1 cm) as shown in Fig. 6. We will
measure the thickness of the coarse layer at minimum and maximum points along the crest and the
ripple sinuosity (the ratio between the length along the crest and the length along a straight line). All
this data will be used to correlate between the ripple plain geometry to the ripple morphometry and
to check the theory presented in Fig.3. The dynamics of this ripple in time (once in a month along
the two first years) will be studied by using photogrammetric method which has been successfully
implemented (Yizhaq et al., 2009). We plan to use digital timelapse camera (Lorenz and Valdez,
2011; Lorenz, 2011) for continuous documentation throughout the process of megaripples
development. This new technique can be a powerful supplement to the more conventional
documentation during successive visits.
We will measure the reptation flux in 12 directions (every 30o) using creep traps. Since in contrast
to the controlled wind tunnel experiments in the field the situation is much more complex and the
wind can come from different directions, we will use the analysis suggested by Rubin (2012). The
transport that smoothes and straightens the ripples W is given by:
2
W
 cos(   )Q
 0
2
 Q
(2)
 0
where  is the bedform orientation and Q represents the sand transport (reptation ) toward each
direction from 0 to 2 (in intervals of 30o). The absolute values are used because along crest
transport couples adjacent locations when the transport is toward either of the two along-crest
directions, along-crest transport is summed regardless of sign of direction of transport. The
magnitude of the sand-transport process that tends to create irregular planform geometries is given
by:
10
2
L
 sin(   )Q

0
2
 Q
(3)
 0
Thus the ratio of W to L (which denoted by S ) is the dimensionless measure of the importance of
the straightening processes for a specified sequence of sand transport events is given by:
2
S
 cos(   )Q
 0
2
 sin(   )Q
(4)
 0
We will also analyze the grain size distribution of the sand collected by the traps as described in
section 3.4.
Fig.6 Megaripple mapping in Nahal
Kasuy. A. The coarse fraction (above 500
 m ) along a megaripple crest
(megaripple sinuosity is 1.12). Note that
there is a correlation between the ripple
height and the abundance of coarse
particles.
B. 3D mapping of the
megaripples showed in panel C. Note that
the height is mm. D. A cross section in
the highest point along the megaripple.
The white line indicates the coarse layer
armoring (width 10 mm). E. A cross
section in the lowest part along the crest
line. The width of the coarse layer is only
6 mm.
3.3.2. Ripple evolution from a flat bed
For the evolution of the transverse instability of ripples from a flat bed, the initial state will be a flat
surface with mixed (local) ripple sand. We will study the development of sand segregation as we
did in Yizhaq et al. (2012a), but along the megaripple crest. This experiment will allow us to better
compare the results with the wind tunnel experiments as they both concentrate in the initial stage of
ripples formation, The analyses of ripple morphometery, sinuosity and grain size distribution will
help us to understand how the instability starts and to relate it with the plain geometry of the ripple
(see Fig. 7).
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Fig.7 The four suggested basic dynamics of curved
section of the ripple (top view). H is for higher points
and L for low points. In cases (a) and (b) the initial
perturbation will grow as the lower parts will move
downwind faster than the higher points. In contrast in
(c) and (d), initial perturbations will diminish. We
will try to indentify which of these cases are more
common. Note that the difference in heights is
probably reflected in the thickness of the coarse layer.
3.4 Grain size analysis (Objectives 1 and 3)
This task is to explore the sand size distribution of meagaripples in space and time depending on the
specific field or wind-tunnel experiment. The sand samples will be analyzed in the laboratory for
high-resolution size distribution with a laser diffractometer (ANALYSETTE 22 MicroTec Plus).
The instrument measures particle sizes over the range of 0.08 to 2000 μm. The sand sample will be
transferred to the fluid module of the instrument (containing deionized water). The data will be
processed using the Fraunhofer diffraction model. By using MasControl software, we will be able to
determine statistically the parameters that are relevant for the research purposes: mean size, median,
modes in multiple modal distributions, sorting values, size fraction weights, and more. The size
resolution for analyses will be 1 micrometer.
Since the usual grain size analysis technique by moments (sorting, skewness and kurtosis) is less
applicable for a bimodal distribution (Blott and Pye, 2001), we suggest here a new way of analyzing
the degree of segregation of samples that have clear bimodal distributions as expected in
megaripple sand (e.g., Yizhak et al., 2011). Two main features are used to characterize bimodal
distribution: grain size segregation, which is the difference between coarse and fine grain diameters,
and frequency segregation, which can be described by the difference in the frequencies between the
two modes. To better describe these two elements, we defined two indices, 1 and  2 , to describe
the normalized grain size segregation and the normalized frequency segregation, respectively. In
addition, we defined  , the resultant segregation vector, and  , the direction of  in the plane
spanned by  2 and 1 , as follows:
1 
Dc  D f
Dc
, 0  1  1;  2 
fc  f f
fc
,  1  1  1
(5)
     , 0    2;   arctan( 1 /  2 ) 0    180
2
1
2
2
0
where the 'c' and 'f' subscripts stand for coarse and fine grains, respectively. Thus, each bimodal
distribution can be represented by a point in the plane spanned by the coordinates (  2 , 1 ) as shown
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in Fig. 8. Note that for  2  0 , the bimodal distribution is inverted since the maximum frequency is
associated with the fine mode, while for  2  0 , the bimodal distribution is typical of welldeveloped megaripples (see Yizhaq et al. 2012a). Each distribution can be represented in polar
coordinates (Eq. 5), where  defines the distance from the origin and  is the angle relative to the
positive horizontal axis (  2 ). The larger the value of  , the greater the segregation.
Fig. 8 Preliminary results of field experiment in Nahal kasuy. Panel (a) show the pictures of four
megaripples which were mapped. Panel B shows the grain size analysis of samples taken from
maximum and minimum points along the crests and subplot E shows the  analysis of these
samples. For ripples A and C there is a clear differences in 1 and  2 values. This is the first time
that such measurements along the megaripples crest have been performed.
4. Risk analysis and alternative paths that will be followed if the suggested research plan fails
Overall we have already done substantial preliminary work to demonstrate that our basic approach
is feasible (see Figs. 4, 6 and 7). However, possible pitfalls of this project manifest themselves as
potential technical and environmental problems: 1) Loss of data from the field experiments due to
electric failure of sensors. Damaged parts will be changed, and if necessary, the sensor will be
13
replaced by another. 2) Operation of the stationary wind-tunnel on low/high saltation flux that may
contain interference for the megaripple development. The sediment flux will be controlled and
measured for each experiment and if necessary we will change the sand feeder configuration. 3)
Creating high-resolution images of the sand particle with high speed video cameras. In this case we
will use different sized of PVC beads (6 and 3 mm) and use the same procedure used by Beladjine
et al. (2007). The larger beads will allow us to track the ejected particles by the video cameras. We
will need to use an air gun to propel a single bead onto the packing. (4) The wind regime in the field
– we suggest a two-years period of field measurements to ensure the study of megaripple evolution
under various wind speeds. (5) A failure of COMSALT to provide realistic simulations of the
transverse and lateral flux, in agreement with the wind tunnel experiments. In this case, we will
improve the parameterization of the splash process following, for instance, recent theoretical
models for viscoelastic particles (Brilliantov et al., 1996; Ramirez et al., 1999; Muller and Poschel,
2001).
5. Detailed account of available U.S. and Israeli resources
5.1. Israel (Ben-Gurion University)
Dr. Itzhak Katra established two laboratories at BGU that will support the proposed study:
Aeolian Simulation Laboratory (ASL) – this lab will support the megaripple experiments. The
laboratory is equipped with 2 boundary-layer wind tunnels. The stationary wind tunnel is an opencircuit tunnel configured for the air-suction mode, allowing maximum wind speed of 25 m/s. The
cross sectional area is of the order of 0.7 × 0.7 m and the working lengths is 12 m (7 m of test
section). The tunnel has a sand feeder to control sand supply and thus the occurrence of saltation in
the test section. The second wind tunnel is a portable one developed at BGU for field experiments
tunnel and built from light-weight materials. The cross sectional area is in the order of 0.5 × 0.5 m
and the working lengths is up to 10 m. The maximum wind speed of at air-suck configuration is 18
m/s. Various instruments installed in the test sections of the wind tunnels to measure wind and
particle variables. Instruments and data collections are controlled by a computer during the
experiments.
Soil and Dust Laboratory – this lab will support the analyses of the sand grains. The lab is equipped
with a laser diffraction instrument (ANALYSETTE 22 MicroTec Plus) for particle size analysis.
Additional useful instruments for sand studies are mechanical sieve shaker (Retsch) with sieves,
binocular stereomicroscopes (Nikon SMZ800) with digital camera attached, and analytical balances
Dr. Hezi Yizhaq of the Department of Solar Energy and Environmental Physics, Institute for
Desert Research (BIDR), BGU, will work in this project as Senior Scientist. Dr. Yizhaq, who holds
14
a position as a part time researcher at BDIR, has developed mathematical models of wind ripples
and is the leading scientist in Israel working on mathematical modeling of aeolian ripples. The
Physics Laboratory of BIDR is equipped with ERDAS-Imagine image processing and LPS tool
softwares for analyzing the aerial photographs and complementary digital data. The group also has
considerable experience in change detection analysis and simulations based the MATLAB and
Fortran softwares. These packages are installed on several powerful PCs and a Unix workstation.
5. 2. USA (University of California – Los Angeles, CA)
Dr. Jasper Kok will start a position as Assistant Professor at the University of California – Los
Angeles on July 1st, 2013. Dr. Kok developed the numerical saltation model COMSALT as part of
his Ph.D. in Applied Physics from the University of Michigan in Ann Arbor. COMSALT is capable
of simulating saltation of sand with different grain size distributions, including the bimodal
distribution of megaripples, and can thus be used to simulate and understand many aeolian
bedforms on Earth and Mars. The main task of PI Kok is thus the application of COMSALT to
study the transverse instability of (mega)ripples, using the results of the wind tunnel and field
experiments as input. The necessary software (Matlab) and hardware (a desktop computer) will be
provided as part of the academic start-up package of Kok. UCLA offers access to other necessary
facilities, such as printers.
15
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