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Keywords:

  • LDA;
  • aeolian transport;
  • reynolds stress;
  • turbulent intensity;
  • wind tunnel

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Experimental Design
  5. 3. Variables Derivation
  6. 4. Results and Data Analysis
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[1] A great deal of effort has been expended in measuring turbulence phenomena in clean air flows. However, no previous measurements have been successfully made of the vertical distributions of turbulence intensity and Reynolds stress in a fully adjusted boundary-layer flow saturated with saltating particles. The present wind tunnel study addresses this knowledge gap using a custom designed laser-Doppler anemometer (LDA). The amount of turbulence is found to increase with the introduction of saltating particles to the airflow. Over the lowest 15% of boundary layer, vertical profiles of the streamwise wind speed provide friction velocities that lie well within the narrow range of those derived from direct measurement of the Reynolds stress. Relative to clean air, aeolian saltation is demonstrated to increase the magnitude but not the frequency of burst-sweep events that primarily contribute to the total fluid stress. Within several millimeters above the bed surface, all vertical profiles of wind speed converge upon a focal point, as the local fluid stress declines toward the mobile bed.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Experimental Design
  5. 3. Variables Derivation
  6. 4. Results and Data Analysis
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[2] It is standard practice in aeolian transport studies to derive the wind friction velocity (U*) from vertical profile measurements of the log-linear variation in the streamwise wind speed (Uz), and then to predict the mass transport rate (Q) as some function of U*3 [e.g., Bagnold, 1936; Kawamura, 1964; Lettau and Lettau, 1977]. When the boundary-layer flow becomes saturated with saltating particles, however, wind tunnel measurements demonstrate an upward convexity in profiles ofUz that is attributed to the loss of momentum from the fluid moving near the bed [e.g., McKenna Neuman and Nickling, 1994; Bauer et al., 2004]. In his early analytical model, Owen [1964] was first to partition the total shear stress (τ) within the saltation cloud between that borne by the particles (τp) and by the fluid (τa = ρU*2, ρ is fluid density). As the concentration of saltating particles increases rapidly toward the bed surface, the vertical flux of momentum established within the fluid declines. It therefore becomes a great challenge to derive and interpret U* when the profile of Uzis no longer log-linear as described by the law of the wall. Similarly, it is not known how estimates of the fluid stress within the saltation cloud (τa) relate to the turbulent Reynolds stress (τRe), as can be determined directly from instantaneous vertical (w) and streamwise (u) wind velocities sampled at high frequency within the airflow. Such measurements are further needed to characterize turbulent burst-sweep events [Leenders et al., 2005; Chapman et al., 2012] that are widely identified with particle entrainment from granular beds. At present, we do not know how these events are affected by the stress partitioning that occurs in sand-laden flows.

[3] The instantaneous wind field can be measured using fast-response instruments that are either intrusive or non-intrusive. Intrusive instruments include hotwire anemometers [Wiggs et al., 1996; Butterfield, 1999], X-wires [Raupach et al., 1980], hot film probes [Bauer et al., 1998; Zhang et al., 2007], and sonic/ultrasonic anemometers [van Boxel et al., 2004]. Non-intrusive instruments include particle imaging velocimetry (PIV) [Zhang et al., 2008; Yang et al., 2011] and laser-Doppler anemometry (LDA) [Taniere et al., 1997].

[4] Intrusive instruments can acquire instantaneous streamwise velocity measurements at a high sampling rate (in the order of kHz, except for sonic/ultrasonic anemometers, which have a sampling rate of 32 Hz or less). However, vertical instantaneous velocities are rarely measured because of their small magnitudes. Moreover, their intrusive deployment also disturbs the existing wind field, while their bulky size (for sonic/ultrasonic anemometers) or fragility (for hotwires, X-wires, and hot-films) prevents them from obtaining fine measurements within the saltation layer. Armored thermal probes were developed to address the fragility issue; however, their response rate is significantly reduced to 10 Hz or less, which limits their capability for turbulence measurement [Butterfield, 1999].

[5] Non-intrusive instruments employ seeding particles (∼1 to 10μm diameter) as tracers to measure the velocity of the fluid. They can acquire the instantaneous streamwise and vertical wind speed components with high spatial and temporal resolution. However, the complexity and high cost of these instruments primarily restricts them to use in the laboratory. Both PIV and LDA techniques require discrimination between the seed and sedimentary particles, which is very difficult to accomplish within the saltation layer, especially where high concentrations of particles are found near the bed. Compared to LDA, PIV requires complex image processing, while the algorithms designed to eliminate the sand particles are subjective. In order to attain suitable accuracy, PIV also requires a high concentration of seeding particles, which as compared to hydraulic flumes, is difficult to maintain in fast moving flows in wind tunnels [Zhang et al., 2008].

[6] To the authors' knowledge, only one LDA study [Taniere et al., 1997] and one PIV study [Zhang et al., 2008] have measured the turbulent wind field in the presence of saltating particles. However in both cases, the boundary-layer was under saturated with particles (i.e., a supply limited condition), as imposed by either a short bed length (<1 m) or the delivery of particles from a feed over an immobile bed. The purpose of the present study is to examine the turbulence characteristics of a boundary-layer that is saturated with saltating sand particles (i.e., a transport limited condition). We used a commercial LDA system to perform the experiment.

2. Experimental Design

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Experimental Design
  5. 3. Variables Derivation
  6. 4. Results and Data Analysis
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[7] The experiment was conducted in a straight-line wind tunnel located at Trent University. This facility is described in detail byMcKenna Neuman [2004]. Within the tunnel entrance, the air flow is straightened as it is sucked through a honeycomb filter within the intake bell. It then is compressed and passed over a trip and roughness plate built into the tunnel floor to create a shearing flow. The downwind tunnel test section is 13.8 m in length, 0.71 m in width and 0.76 m in height. Two metal rails installed on the inner and outer sides of the test floor contain the test material to a depth of 30 mm. Well-sorted coarse quartz sand (median diameter,D = 550 μm) formed the 13 m long test surface for each experiment described in this paper. The mass transport rate, Q, was monitored by collecting particles in a passive Guelph-Trent wedge trap equipped with an electronic scale, as described byNickling and McKenna Neuman [1997]. The effect of fetch length in the Trent wind tunnel is considered in a previous study by McKenna Neuman [2004]. For a full bed of mobile sand (dia 270 μm), the displacement height was found to vary at most between 10%–15% along the tunnel working section (5.6 m < × < 10.2 m) for freestream velocities below 8 m/s. At higher velocities, there was no fetch dependence.

[8] Wind velocity (u, w) was measured using a customized Dantec™ 2D LDA at a point 8 m downwind of the leading edge of the sand bed. The instrument generates two visible (wave length λ = 0.660 μm) and two invisible (λ = 0.785 μm) laser beams that intersect in a 0.04 mm3 sampling volume. When the ith particle passes through this volume, the fringe interference is measured to give ui and wi. The position of the sampling volume is controlled by a traverse, so that velocity measurements were obtained over a 50 second period at each of 21 logarithmically spaced heights between 3 mm and 270 mm above the sand surface, with each experiment therefore lasting about 20 min. The sampling rate is strongly dependent on the settings for the Burst Spectrum Analyzer (BSA) processor so that some fine tuning is required to optimize performance. In measuring uwith the visible lasers, the velocity span was set at 10.40 m/s, the sensitivity at 1000 V and the signal gain at 12 dB, as compared to 6.20 m/s, 1200 V and 18 dB to measure vertical velocity with the invisible lasers. The seeding particles required for airflow measurement were generated by a commercial haze machine (Antari™ HZ-300) with diameters in the order of 1 to 10μm.

[9] One of greatest challenges in the application of an LDA to aeolian transport studies is the need to discriminate between the saltating particles moving near the bed in ballistic trajectories, and the significantly smaller seed particles that follow the path of the airflow. The LDA anode current generated for each particle sampled is roughly proportional to its diameter. Since the diameters of the sand particles entrained from the test bed were approximately 50–500 times larger than those of the seed particles, it was possible to distinguish between these two populations using the BSA flow software. Sand particles that are finer than those used in the present study are more challenging to differentiate from the seed particles in the haze. However, the saltation cloud becomes highly concentrated with particles near granular mobile beds (z < 3 mm) at high wind speeds, so that relatively few seed particles can be detected within this region by the LDA. This is an important limitation for LDA technology in such applications.

[10] Both the clean air and sand-laden experiments were carried out at each of five time-averaged free stream velocities,U, corresponding to the Reynolds numbers (Re) reported in Table 1, where Re = inline image, δ is the boundary layer depth, ν is kinematic viscosity (∼1.5 × 10−6 m2/s), and δ= 0.15 m. The bed surface was level at the beginning of each run, but underwent deflation at various rates so that the measurement height relative to the bed surface varied slightly. For the clean air runs, the surface of the sand bed was moistened with water to prevent saltation. In the sand-laden runs, particles were trickled from a gravity-driven feed onto the leading edge of the test bed immediately downwind of the roughness plate in order to initiate formation of a saltation cloud and thereby minimize the fetch length required to attain equilibrium transport. Ballistic ripples formed during runs at free stream speeds exceeding 7 m/s. The height of these ripples varied between 1–3 mm, which is significantly smaller than the saltation cloud height (typically in the order of 10 cm). Therefore, the change in the turbulence characteristics measured in this study is mainly attributed to saltation rather than topographic roughness.

Table 1. Experimental Results
Run12345678910
U0 (m/s)6.246.747.107.638.126.266.767.187.718.18
Re (×105)5.96.36.77.27.65.96.36.77.27.7
Q (g/m/s)000001.084.447.7314.7123.01
z0 (mm)0.0160.0210.0210.0210.0270.0180.0280.0710.0820.117
U*/U00.0450.0470.0460.0470.0490.0450.0470.0530.0510.053
U*Re/U00.041–0.0470.042–0.0480.044–0.0480.043–0.0490.044–0.0490.044–0.0470.045–0.0490.049–0.0520.049–0.0550.047–0.058

3. Variables Derivation

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Experimental Design
  5. 3. Variables Derivation
  6. 4. Results and Data Analysis
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[11] After the sand particle data are filtered out, the time-averaged streamwise and vertical velocities,U and W, and the root-mean-square of turbulent velocity fluctuations,u′ and w′ and their cross-moment inline image can be calculated using the BSA flow software provided by Dantec Dynamics Inc. Here,

  • display math
  • display math
  • display math
  • display math
  • display math

where N is the number of velocity samples (typically in the order of 103 to 105 for each height), i refers to the ith sample, and ωi is a transit time weighing factor, which is recommended if the transit time (t) of the particle passing through the LDA measurement volume is not constant. Here, ωi is defined as

  • display math

The streamwise and vertical turbulence intensities, Tu and Tw, respectively, are defined below as:

  • display math
  • display math

Moreover, in order to incorporate the turbulence characteristics from both directions, a dimensionless Reynolds stress term Tuw is proposed here as:

  • display math

Tuwalso can be treated as either the cross-turbulence intensity or simply, a drag coefficient. The square root of the time-averaged turbulent shear stress inline image, obtained directly at each of eight elevations within 0.15δ, provides an independent sample of friction velocity (U*Re) values that can be compared with U* derived from a vertical profile of Uzusing the von Karman-Prandtl equation,

  • display math

where κ is the von Kármán constant with a value of about 0.4, and zo is the aerodynamic roughness length. In the context of the experiments reported in the present study, U* is both temporally and vertically averaged over 0.15δ as well.

[12] Finally, the saltation intensity I (counts/mm2/s) at each elevation above the bed surface was calculated from the number of sand particles passing through the LDA measurement volume, normalized by its cross-sectional area (0.24 mm2) and the run duration (50 s). The vertically integrated mass transport rate Q(g/m/s) was derived from the total weight of sediment (g) collected in a Guelph-Trent isokinetic trap, divided by the intake nozzle width (0.02 m) and the run duration (50 s).

4. Results and Data Analysis

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Experimental Design
  5. 3. Variables Derivation
  6. 4. Results and Data Analysis
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[13] Table 1 summarizes the main experimental results. For the sand transport experiments, Q clearly increases with U, although the exact relationship was not examined because of the small sample size. Re varies from 5.9 × 105 to 7.7 × 105, confirming that the flow was always turbulent. On average zo is ∼0.02 mm with little variation in clean air, while it increases linearly with Q (r2 = 0.92) from 0.018 mm to 0.117 mm when a mobile sand bed is present. The drag coefficient U*/U generally falls within the range of U*Re/U for all runs except for Run 8, whose U*/U value (0.053) slightly exceeds the upper limit (0.052) of U*Re/U. The drag coefficient for the clean air runs over a fixed bed (0.045–0.049) demonstrates a very small, positive Reynolds number dependence (r2 = 0.73). Although this variation in U*/U falls within the acceptable range (10%) of measurement error for determining U* in aeolian transport research, correlation with Re suggests that the boundary layer flow may not quite have been fully adjusted at the position of measurement (x = 8 m). This could be verified in future work by obtaining vertical velocity profiles at various positions along the full working section of the tunnel; however, with only a single LDA instrument this cannot be accomplished synchronously over the exact same surface.

[14] Vertical profiles of the time-averaged streamwise velocity (Uz), turbulence intensity (Tu and Tw ), and the normalized Reynolds stress (Tuw) are depicted in Figures 1a–1h. Height is given in dimensionless form as z/δ. Since the elevation of the test bed surface was reduced by 1 mm to 8 mm with sand transport, a correction was applied to the profiles in Figure 1 to account for this.

image

Figure 1. Profiles of (a, b) streamwise velocity, (c–f) turbulent intensities, (g, h) dimensionless Reynolds stress, (i) total and quadrant-based shear stresses for Run 5 (clean air) and Run 10 (sand-laden), and (j) saltation intensity.

Download figure to PowerPoint

[15] In the absence of mass transport, vertical profiles of the streamwise wind velocity appear log-linear (Figure 1a). For airflows over a mobile sand bed at low wind speeds (e.g., U = 6.26 m/s and 6.76 m/s), the velocity profiles remain indistinguishable from those in clean air. However with increased saltation under stronger winds, Uz decreases more rapidly toward the bed than in clean air, indicating a significant transfer of momentum from the airflow to the particles moving within the saltation cloud. These results are in good agreement with previous experiments addressing this phenomenon [e.g., McKenna Neuman and Nickling, 1994; Bauer et al., 2004]. Regardless of the magnitude of the free stream flow in the core of the tunnel working section, all velocity profiles obtained during fully developed sediment transport (Figure 1b) converge upon a focal point just above the bed surface (z ∼ 4 mm, Uz ∼ 3.5 m/s for D = 550 μm), confirming similar observations (z ∼ 3 mm, Uz ∼ 2.5 m/s for D = 250 μm) in the early work of Bagnold [1941].

[16] In regard to the clean air flows, the vertical profiles of Tu and Tw are almost identical to one another in every plot (cf. Figures 1c and 1e), as are the normalized Reynolds stress profiles (Tuw, Figure 1g). The turbulence intensity is greatest near the bed surface, then decreases slowly toward z ∼ 0.15δ. Above this elevation, a rapid decrease occurs until the top of the boundary layer is reached. Within the free stream flow, the turbulence intensities are low and constant. These results are consistent with the findings of many previous wind tunnel studies involving flows over smooth surfaces in clean air [e.g., Löfdahl et al., 1995; Krogstadt and Antonia, 1999].

[17] In comparison, the presence of sand particles appears to enhance both the turbulence level and Reynolds stress in a given airflow. As shown in Figures 1d, 1f, and 1h, Tu, Tw and Tuw generally increase with increasing U, with their vertical profiles demonstrating a convex shape. In comparison, just two previous wind tunnel studies have measured the turbulence intensity of airflows carrying saltating particles, one using LDA [Taniere et al., 1997] and the other using PIV [Zhang et al., 2008]. No convexity in the turbulence intensity profiles was found in either experiment, likely because of under-saturation of the boundary layer with sand particles. The sand bed in the PIV experiment was only 1 m long, while in the LDA experiment, particles were simply fed into the air flow at a low rate and then saltated over a fixed floor in the wind tunnel.

[18] Quadrant analysis of the instantaneous product − inline imagewas carried out for both the clean air and sand-laden flow conditions. The total Reynolds stress and the Reynolds stress contribution from each quadrant are plotted and compared inFigure 1i for Runs 5 (clean) and 10 (saltation), both at U= 8.1 m/s. The results suggest that burst-sweep (Q2 and Q4) events are the main contributors to the air-borne stress. Stresses from Q1 and Q3 remain at a consistently low level (−0.05 ∼ 0 m2/s2) and contribute negatively to the air-borne stress regardless of either the presence or absence of sand particles in the flow. These findings are consistent with recent field measurements reported byChapman et al. [2012]. In clean air flows, the total Reynolds stress and stress contributions from Q2 and Q4 events reported in Figure 1igenerally decrease with increasing height. In the case of the sand-laden flows the vertical profiles of − inline image for Q2 and Q4 events are strongly convex. However, a separate analysis on event frequency for Runs 5 and 10 shows that regardless of the presence or absence of sand transport, both Q2 and Q4 events represent 30% to 35% of all events while both Q1 and Q3 events occur 15% to 20% of the time at z < 0.15δ.As a general rule, burst-sweep events in the clear airflows are smaller in magnitude, but near identical in frequency, to those observed for sand-laden flows.

[19] The calculated saltation intensity I is plotted in Figure 1j. As expected, I decreases dramatically with increasing height, with higher wind speeds generating greater amounts of saltation. The majority of saltators are concentrated immediately above the bed.

5. Discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Experimental Design
  5. 3. Variables Derivation
  6. 4. Results and Data Analysis
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[20] Wind tunnel experiments carried out in clean air only [e.g., Raupach et al., 1980; Krogstadt and Antonia, 1999; Brzek et al., 2007] suggest that the aerodynamic roughness strongly governs vertical variation in the turbulence intensity and dimensionless Reynolds stress. When a given surface is aerodynamically rough, the dimensionless Reynolds stress is well recognized to first increase and then decrease with height [cf. Krogstadt and Antonia, 1999, Figure 4c], which is entirely consistent with the results of the present study in which saltation, rather than perturbations in the surface micro-topography, extracts momentum from the flow. This association lends support to Owen's original suggestion [Owen, 1964; Raupach, 1991] that aeolian saltation can be treated as an apparent increase of roughness height.

[21] For sand-laden flows,Owen [1964]further argued that neither the grain-borne, nor (by default) the air-borne stress, is strictly a constant within the saltation layer. As compared to our measurements in clean air that support the concept of a constant shear layer immediately above the bed surface, those obtained within the saltation cloud confirm the hypothesis of several numerical and analytical models [e.g.,Owen, 1964; Raupach, 1991; Shao and Li, 1999] in demonstrating a continual decrease in the turbulent Reynolds stress toward the surface of the mobile bed, especially when the flow is saturated with large amounts of sand.

[22] From Figure 1j, it would appear that sand particles are detected above 15% of the relatively thin boundary layer flow in wind tunnels. As a result, the constant air-borne stress layer is not observed above the saltation layer, as it is in most field situations where a large fetch exists and the boundary-layer height extends to heights in the order of meters or more. Indeed, the stress perturbation caused by grain-borne momentum extraction would appear to extend well into the outer layer of flow where large scale mixing processes are constrained primarily by inertia rather than viscosity.Bauer et al. [2004] highlight this problem in showing that during aeolian saltation, friction velocities derived from vertical profiles of Uz do not match when calculated over varied ranges in height above the bed surface. In a very large wind tunnel facility, the boundary layer depth could well be increased relative to that of the saltation cloud by a factor of ten or more, thereby resolving these scaling issues to some degree. However in practice, the time and costs associated with handling the extraordinarily large amounts of sediment required for bed preparation become prohibitive.

[23] Therefore, with regard to existing wind tunnel research facilities and programs, a great deal of confusion persists in regard to a suitable protocol that should be followed when measuring and analyzing airflow data in experiments intended to simulate aeolian transport in the atmospheric boundary-layer. In view of the general agreement betweenU* and U*Re demonstrated in the present study, estimates of U*derived from approximately log-linearUzprofiles below 10%–15% of the boundary layer depth would seem to be acceptable for use in wind tunnel studies of aeolian transport, provided that profiles of the Reynolds stress cannot be obtained directly. Above this level, perturbation of the flow adjustment to the saltation cloud is superimposed upon large-scale mixing processes (similar to flow in a wake) that are constrained primarily by inertia rather than viscosity, so that the velocity profile is poorly approximated by a log-linear relation (e.g.,equation (10)). Earlier studies have demonstrated that in order to model the full extent of boundary layer flow in such situations, particularly in the case of high concentrations of saltators, Coles' [1956] wake function (Π/κ)w(z/δ) must be added to that provided in equation (10) for the inner flow [Janin and Cermak, 1988; Spies et al., 1995; McKenna Neuman and Maljaars, 1997]. However, calibration of this model is strongly governed by wind tunnel artifact (i.e., the pressure gradient along the working section dP/dx), so that no agreement as yet exists on suitable values for Coles' wake parameter Π.

[24] In clean air flows as shown in Figure 1g, there exists a region within the lowest 15% of the boundary layer that is characterized by an approximately constant flux of momentum, so that the bed shear stress (τo) is well approximated by the air-borne stress (τa). Considering the extremely low sand transport rate at U = 6.26 m s−1 and using Table 1, we estimate the impact threshold velocity (U*t) to be 0.28 m/s or − inline image ∼ 0.078 m2/s2, represented as the dashed line in Figure 1i. In comparison, the air-borne stress for Run 5 (U= 8.12 m/s) well exceeds the impact threshold, although saltation should occur upon drying of the surface. For the equivalent sand-laden run (Run 10,U= 8.18 m/s), the air-borne stress is generally higher than the impact threshold for all elevations below 0.4δ. As the surface is approached, however, it drops rapidly toward but does not quite reach the impact threshold at the lowest elevation sampled. This general trend is present for the remaining experiments as well, but is less obvious with a low mass transport rate. Our results therefore are entirely consistent with Owen's [1964]suggestion that during large mass transport events, the constant air-borne stress associated with the inner region of flow in clean air is replaced by a continuous decline toward the bed surface as the concentration of particles increases.Owen's further suggestion that the fluid stress on the bed surface drops to the impact threshold remains unconfirmed in this study, because measurements below 3 mm are unattainable with current LDA technology and extrapolation of τa to determine τo introduces an unacceptable level of uncertainty.

6. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Experimental Design
  5. 3. Variables Derivation
  6. 4. Results and Data Analysis
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[25] Profiles of the streamwise and vertical turbulence intensity were measured in a wind tunnel experiment using a customized LDA, both in clean air and in flows where the concentration of saltating particles approached saturation. Good agreement is obtained with previous work carried out over smooth surfaces in the absence of particles. In contrast, patterns in the turbulence intensity obtained within sand-laden airflows appear to strongly resemble those obtained in clean air over aerodynamically rough surfaces. In the near bed region,z ≤ 0.15δ, turbulence intensities and dimensionless Reynolds stress increase with the mass transport rate, while friction velocities derived from the standard wind profile method and Reynolds stress measurements overlap. Quadrant analysis shows that contributions to the total Reynolds stress primarily arise from burst and sweep events, regardless of whether the airflow is clean or bearing sand. The magnitude but not the frequency of these events increases when the inner region of flow is saturated with particles. Although the vertical distribution of the air-borne stress demonstrates a tendency to drop toward the impact threshold as the surface is approached, this hypothesis remains unconfirmed since the LDA laser configuration prevents measurement below 3 mm.

[26] While previous analytical and numerical models have speculated on such relations, direct measurements at the high level of precision reported in this study have not been previously reported for a large test bed intended to approximate equilibrium between the boundary layer flow and saltation cloud. It is hoped that such measurements will inform future refinements of numerical saltation models, and aid in their validation.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Experimental Design
  5. 3. Variables Derivation
  6. 4. Results and Data Analysis
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[27] This research was supported by grants to C. McKenna Neuman from the Natural Sciences and Engineering Research Council of Canada and the Canadian Foundation for Innovation. The authors wish to particularly thank R. Steve Sanderson for his technical assistance. The comments from Jack Gillies and an anonymous reviewer have greatly improved the quality of this paper.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Experimental Design
  5. 3. Variables Derivation
  6. 4. Results and Data Analysis
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Experimental Design
  5. 3. Variables Derivation
  6. 4. Results and Data Analysis
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information
FilenameFormatSizeDescription
grl29338-sup-0001-t01.txtplain text document0KTab-delimited Table 1.

Please note: Wiley Blackwell is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.