Application Number: 2012291
The Origin of the Transverse Instability of Sand Ripples –a 3D Approach Integrating
Numerical Simulations, Field and Wind Tunnel Experiments, and Grain Size Analyses
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, 2008;
Zimbelman et al., 2009, 2012; Zimbelman, 2010), 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~7cm) look almost straight whereas the megaripples (wavelength~4m) 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
3 gd where d is the grain diameter and g is the gravitational acceleration. Werner (1990) also studied
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extensively the collision process for shallow impact angles. He used sand grains and designed a 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 V z

V z

2 exp



V z
2
2

2


(1) where

2 
0.1
V gd i
and V is the impacting speed. Furthermore, laboratory and numerical i experiments indicate that the mean angle at which particles are splashed is ∼ 40 o –60 o 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.
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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 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).
However, 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 sand transport 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 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 experiment of the splash process in a boundary-layer wind tunnel 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
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state-of-the-art mathematical model of sand transport (Kok and Renno, 2009). We will then use this model to study in detail what the mechanisms that drive the transverse instability for megaripples
(Yizhaq et al., 2012b). (iii) Use field and wind tunnel experiments to study the correlation between the grain size segregation along the ripple crests and the ripples height and their pattern in plane.
Because the migration velocity is inversely related to the ripple height, lower portions associated with a thin coarse layer move faster than the higher portions where the coarse layer is thicker. This difference in celerity of adjacent sections along the ripple crest drives the transverse instability of megaripples.
The proposed study will improve our understanding of pattern formation and nonlinear dynamics in nature, which has implications also in other modern sciences (Cross and Greenside
2009; Rubin 2012). Especially it will deepen our understanding of one of the three possible mechanisms for straight bedforms in unidirectional flows (Rubin 2012): along-crest flow (nontransverse bedform orientation), gravitational transport along an inclined crest, or ballistic splash in air. We will mainly work on the ballistics splash of ejecting particles. 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 twodimensionality patterns arise in situations where along-crest coupling processes are strong enough to overcome the 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 formation is the splashing caused by the impacting saltating grains we propose that the ratio (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.
Our hypothesis is that small irregularities along the megaripples crest further develop to perturbations in megaripple height which are due to the smaller lateral reptation flux grow in time.
Thus, different portions of the megaripple migrate at different rates, which increase the crest sinuosity. Illustration of the evolution is presented in Fig. 3. The overall goal of understanding the mechanism behind the transverse instability of megaripples will be achieved by integrating theoretical, field and wind tunnel experiments, and numerical simulation into a 3D model as follow:
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I. Wind Tunnel Experiments
Wind tunnel experiments will be performed to quantify the distribution of ejected particles in the forward and the lateral directions for different sizes of bed particles using a high-speed imaging system. Despite the studies devoted to the ejection process (e.g., Rice et al., 1995; Beladjine et al.,
2007), 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 will study the development of ripples with polydisperse sand and measure changes of S in time – detailed experimental methodology and preliminary results are given in Section 3.1.
II. Mathematical Models
COMSALT (Kok and Renno, 2009) will be used 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

/ 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, 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 (1) correlation between ripples plain geometry, height and grain size segregation in megaripples, and (2) and document the development of ripple instability from an artificial flat bed in space and time. We
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will measure the ratio / in the field during wind storms and compare with the results of the wind tunnel experiments. Sand samples that will be collected during the field study will be analyzed in the laboratory to explore the grain size distributions involved in ripple formation/destruction processes.
Fig.3 A schematic diagram which represents one possible scenario for development of the transverse instability. Initial perturbations in the coarse grains distribution along the ripple crest lead to irregularities in ripple heights caus different migration rate of different points along the crest.
Small perturbations along the ripple crest (top panel) will grow 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 approach of this study is to integrate simulations and direct measurements into a 3D model.
The collaboration involves 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 size 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
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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 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 the 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 cross-wind 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 may 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 imaging system, including 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
8

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.
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 extract their velocity components ( , y
, z
) and their averages numbers. The splash distributions between the two cases of bed composition (fine and coarse) will be compared in order to test our hypothesis about the origin of the transverse instability.
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/s
2
, and particle density 3000 kg / m
3
) will give the ratio (
S ) for different grain sizes for Martian conditions and will help 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 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. The result that the ratio W/L is larger for megaripples than for normal ripples is a consequence of the high inertia of the megaripple coarse fraction.
This limits the acceleration of these particles in the along-wind direction during their hop, resulting in high values of W/L. These simulations thus predict that megaripples are more transverse 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
9 using the wind tunnel experiments determining the 3D splash process details (Objective I).

3.3 Field Experiments (objectives 3 & 2)
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 (see section 2 III).
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 test the theory scheme 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). In this study, we will 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.
The reptation flux will be measured in 12 directions (every 30 o
) 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:
W
 
2



0 cos(
 
) Q

2




0
Q

(2) where

is the bedform orientation and Q

represents the sand transport (reptation ) toward each direction from 0 to 2

(in intervals of 30 o ). 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
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magnitude of the sand-transport process that tends to create irregular planform geometries is given by:
L
 
2



0 sin(
 
) Q


2



0
Q

(3)
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:
S

2



2


0



0 cos(
 
) Q
 sin(
 
) Q

(4)
We will also analyze the grain size distribution of the sand collected by the traps as described in section 3.4.
3.3.2. Ripple evolution from a flat bed
Fig.6 Megaripple mapping in Nahal
Kasuy. A. The coarse fraction

) 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.
For the study of the transverse instability evolution, 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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3.4 Grain size analysis (Objectives 1 and 3)
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.
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 (from the laser diffractometer) 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,

and
1

, to describe the normalized grain size segregation and the
2 normalized frequency segregation, respectively. In addition, we defined

, the resultant segregation vector, and

, the direction of
 in the plane spanned by

and
2

, as follows:
1

1

D c

D f
D c
, 0
 
1

1;

2
 f c
 f f
, 1

1

1 f c
(5)
  
1
2  
2
2
, 0 2;
  arctan(
 
2
) 0 180
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
 
, the bimodal distribution is inverted since the maximum frequency is
2
0 associated with the fine mode, while for
 
, the bimodal distribution is typical of well-
2
0 developed 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 distributions (from the
ANALYSETTE 22 laser diffractometer) 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

and
1

values. This is the first time that such measurements along the
2 megaripples crest have been performed.
4. Risk analysis and alternative paths that will be followed if the suggested research plan fails
Overall we have done substantial preliminary work to demonstrate that our basic approach is feasible (see Figs. 4, 6 and 7). Possible pitfalls of this project manifest themselves as potential technical and environmental problems: 1) Loss of data from the field experiments due to electric
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failure of sensors. Damaged parts will be changed, and if necessary, the sensor will be 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 adapt the sand feeder configuration. 3) Creating highresolution images of the sand particle with high speed video cameras. To ensure the measurement, we will use first 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-year period of field measurements to ensure various situations 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 PC controlled 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), 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
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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 1 st
, 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.
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