Turbulent flow structures and aeolian sediment transport over a barchan sand dune



[1] The turbulent structure of airflow over a barchan sand dune is determined using quadrant analysis of wind velocity data derived from sonic anemometers. Results indicate an increased frequency of ejection and sweep events in the toe region of the dune, characteristic of the turbulent bursting process. In contrast, at the crest there was a significant increase in the occurrence of outward interactions. Combined with high frequency saltation data our analyses show that turbulent structures characterised by a positive streamwise fluctuating velocity (+u′; sweeps at the toe and outward interactions at the crest) have a dominant influence on sand transport on the dune, together accounting for up to 83% and 95% of transporting events at the toe and crest respectively.

1. Introduction

[2] Traditional models of dune dynamics rely on the application of sand transport equations driven by near-surface windflow over the dune form [e.g.,Weng et al., 1991]. As measurement and prediction of surface shear stress (τ0) is difficult, established practice is to consider the erosive power imparted to sand on the dune surface as being proportional to any one of a number of time-averaged flow parameters such as wind velocity (u), shear velocity (u*, as τ0 = ρu*2) and, more recently, Reynolds shear stress ( math formula). However, near rough surfaces these time-averaged flows have been shown to be highly heterogeneous [Nikora et al., 2007] and the response of sand flux to such windflow metrics has been queried in the literature [Wiggs et al., 1996; Bauer et al., 1998; Walker and Nickling, 2002, 2003; Baas and Sherman, 2005].

[3] There is now an increasing consideration that, in a similar manner to river flows [Bennett and Best, 1996; Kostaschuk and Villard, 1996; Venditti and Bauer, 2005], flow unsteadiness and turbulence of the order of ∼5.0–0.5 Hz in the boundary layer may also be a major driving force behind aeolian sediment entrainment and transport [Butterfield, 1991, 1993, 1999; Bauer et al., 1998; Sterk et al., 1998; Walker and Nickling, 2002; Schönfeldt and von Löwis, 2003; Baas, 2006, 2008; Livingstone et al., 2007; Baddock et al., 2011; Weaver and Wiggs, 2011]. However, our improving knowledge in this regard cannot be applied to enhance models of sand dune dynamics until data are gained concerning the nature of turbulent airflow over dune morphologies. Whilst more frequent application of sonic anemometry in the field is allowing the emergence of relevant knowledge [van Boxel et al., 2004; Walker, 2005; Baddock et al., 2011; Weaver and Wiggs, 2011], there is currently no quantification or understanding of the way in which the coherency or structured nature of turbulence reacts to the flow distortion caused by the intrusion of a dune into the atmospheric boundary layer. Such an understanding is required as comparable research in the fluvial domain has not only identified turbulence as the principal driving force behind sediment transport [Best, 2005], but also that such turbulence is highly organised with specific turbulent structures responsible for orders of magnitude variations in sediment transport rates [Shugar et al., 2010]. Specifically, coherent turbulent structures associated with the bursting process (sweeps and ejections) have been shown to be of critical significance to sediment transport over fluvial bedforms [Best and Kostaschuk, 2002; Yue et al., 2005] and emerging aeolian research has recognised the significance of these same turbulent structures to sediment entrainment on flat surfaces [Bauer et al., 1998; van Boxel et al., 2004; Leenders et al., 2005].

[4] In this letter we present the first measurements of the development of turbulent flow structures identified using quadrant analysis over the windward slope of a simple, barchan desert sand dune. Measurements of the response of sand transport on the dune surface to these evolving turbulent structures emphasise their potential significance for dune dynamics. We focus our analysis on two specific geomorphic zones, the upwind toe region and crest of the dune, because these demonstrate the operation of opposing flow dynamics. These are streamwise flow deceleration and streamline concavity in the toe region, and flow acceleration and convex streamline curvature at the crest [Weaver and Wiggs, 2011]. To date, no one single time-averaged flow parameter has adequately explained the measured sediment transport dynamics within both of these regions of a dune. Our data suggest that a quantification of turbulent windflow statistics is necessary for a complete understanding of dune dynamics, demonstrate the utility of quadrant analysis for assessing event-driven sediment transport, and provide a template for analysis of turbulent windflow data over other dune types.

2. Study Area and Data Collection

[5] Our study dune was a 9.67 m high and 92 m long crest-brink separated barchan located in the Skeleton Coast, Namibia (20°07′08″ S, 13°12′15″ E). The computed inner layer boundary thickness was 1.52 m [Jackson and Hunt, 1975] with aerodynamic roughness (z0) of 0.0005 m (as determined from a ‘law-of-the-wall’ calculation using cup anemometers on a 6.0 m tower located on the surface upwind of the dune) and a half length (L) of 38.01 m as measured by field survey. The dune and surrounding surfaces were dry and devoid of vegetation. The dune sand had an average particle size of 228 μm and the surrounding surface consisted of a matrix of poorly sorted pebbles and gravel of average particle size 611 μm. Relative to the upwind dune toe (x = 0 m), six measurement sites were established along a 109 m transect upwind of (x < 0 m) and along (x> 0 m) the centre-line of the dune. Practically defining what constituted the precise location of the dune toe was difficult and whilst there was clear sand deposition and some positive topography atx = 0 m, significant dune morphology was only apparent downwind from x = 18 m. The following analysis therefore defines the ‘toe region’ consisting of data collected at x = 18 m which is where the initial topographic forcing of the airflow might be expected to be present.

[6] 3-D sonic anemometers (Campbell C-SAT3) were deployed at 1.5 m and 0.3 m height (within the inner layer of flow over the dune) successively at each measurement site along the dune centre-line to collect wind velocity data (u, streamwise; v, spanwise; w, vertical) at a sampling frequency of 10 Hz. The C-SAT3 sonic anemometer has a wind speed range of up to 30 ms−1 with measurement resolutions of 0.001 ms−1 and 0.005 ms−1 (RMS) in the u + v and wplanes respectively. The measurement path length of the anemometer is 0.100 m in the vertical and 0.058 m in the horizontal. Some data loss was evident in the wind data collected at 0.3 m height due to saltating particle trajectories interrupting the sonic path signal. This was particularly the case at higher wind velocities associated with sediment transport. In contrast, whilst data capture at 1.5 m height was near 100% the anemometer was positioned close to the top of the inner-layer and, according to the top-down model of turbulence [Baas and Sherman, 2005] may therefore not have recorded all the changes in turbulence structure that might be expected below this height as eddies were squeezed against the dune surface. Such difficulties are inherent in measuring windflow on dynamic dune surfaces and a balance has to be found between them to allow reasonable interpretation of data. At each site on the transect measurement runs were conducted for 10 minutes, sufficient at our measurement heights to capture the lower frequency turbulent structures in the boundary layer [van Boxel et al., 2004]. The sonic anemometers were aligned parallel with the prevailing wind direction ( math formula = 0) and level in the horizontal plane. The vertical frame of reference of each anemometer was rotated to the local streamline angle in the data analysis stage using yaw and pitch rotation following the conventions of Walker [2005], Roy et al. [1999] and Baddock et al. [2011]. All data were normalised using data measured simultaneously by a third C-SAT3 sonic anemometer situated at a height of 1.5 m at a reference station established 50 m offset and upwind of the dune.

[7] Concurrent 10 Hz measurements of sediment transport intensities were provided by the deployment of Saltation Flux Impact Responders (Safires) at both the reference station and sonic measurement sites on the dune. These circular (0.02 m diameter) (piezoelectric instruments provide a sensor frontal area of 0.0004 m2 and are capable of recording the impact of saltating sand grains at frequencies of up to 12.5 kHz with a time required for signal analysis of 80 ms [Baas, 2004]. In our experiment the Safires were located with their sensing ring flush to the sand surface at each site and they were used to determine the presence or absence of saltation during each 10 Hz measurement period. For a full discussion of the Safire specifications see Baas [2004].

3. Data Analysis

[8] 86 separate 10 minute wind periods were analysed representing a range of wind and saltation conditions (Figure 1a). Mean wind velocities at the reference tower during the measurement periods ranged from 5.59 ms−1 to 13.2 ms−1at a cup measurement height of 2.2 m and included intermittent sand transport activity through to continuous saltation along the length of the dune centre-line. During the experimental period wind direction varied by a maximum of 4.5° either side of the centre-line. For each 10 minute period we used Reynolds decomposition of the sonic anemometer data to determine fluctuating streamwise (u′) and vertical (w′) velocities from math formula and math formula [Stull, 1988], where the overbar indicates the time-average. From these we established the incidence of turbulent structures in the flow using the conditional-sampling technique of quadrant analysis [Lu and Willmarth, 1973]. This analytical technique partitions the flow into four discrete categories of momentum exchange on the basis of the relative signs of u′ and w′ (Figure 1b). Given that Reynolds stress ( math formula) is given by the negative co-variance ofu′ and w′, quadrant analysis can be used to segregate the stress budget between different structures [Nelson et al., 1995; Keylock, 2008]. Specifically, such segregation can identify those structures that provide a positive contribution to Reynolds stress (ejections [Q2] and sweeps [Q4]) and those that provide a negative contribution (outward [Q1] and inward [Q3] interactions). In order to identify events during which a significant proportion of the turbulent stresses were exerted, stress events of low magnitude, which indicate an absence of coherency in the flow, were removed from the analysis using a threshold (H) equivalent to one standard deviation (σ) of the kinematic stress ( math formula) such that positive classification of a flow structure occurred where math formula. There is no agreed convention for the setting of an appropriate threshold (H) for quadrant analysis [Keylock, 2008] however, the value of one standard deviation of the kinematic stress chosen here is becoming the custom and is equivalent to those employed by Bennett and Best [1995], Sterk et al. [1998], Leenders et al. [2005] and Bauer et al. [1998] (Figure 1b).

Figure 1.

(a) An example of a 10 minute sample of wind velocity (upper line) and saltation count (lower line) upwind of the dune toe. (b) The data in Figure 1a plotted as quadrant events defined by the relative values of fluctuating velocity components in the horizontal (u′) and vertical (w′) plane [after Lu and Willmarth, 1973]. Q1 = outward interaction, Q2 = ejection, Q3 = inward interaction, Q4 = sweep. Kinematic stresses ( math formula) below a threshold (H) were disregarded in the analysis of coherency and these data are shown in light grey.

[9] For each 10 minute wind period the frequency of occurrence of each quadrant event was calculated at the respective measurement position on the dune transect. Each frequency calculation was then normalised by the frequency of that event occurring simultaneously at the upwind reference station. Quadrant data are presented as fractional perturbations (−1.0 to +1.0) in frequency from the equivalent frequency data measured at the reference station.

[10] Cross-correlation analysis was undertaken of the wind and sand transport time series data to determine the lag between changes in velocity and subsequent changes in sand transport. The best correspondence between the data series was found to occur with sand transport lagged by 0.2 s for the wind data recorded at 0.3 m height and 1.0 s for wind data recorded at 1.5 m height. Response times of this order have also been documented byAnderson and Haff [1988], Butterfield [1991, 1993], McEwan and Willetts [1991], Spies et al. [2000], Arnold [2002] and Baas [2006]. The lagged sand transport data were then used to define the presence or absence of saltation and were attributed to the respective individual quadrant events that occurred simultaneously in the airflow.

4. Turbulent Flow Structures

[11] The spatial evolution in the frequencies of turbulent flow structures over the dune centre-line are presented inFigure 2. Data at both measurement heights of 1.5 m (Figure 2b) and 0.3 m (Figure 2c) clearly demonstrate topographic forcing of the flow field with the structure of the turbulent wind altering dramatically as it flows over the dune surface. In the toe region of the dune (x = 18 m) the fractional perturbation in quadrant frequency diverges into two distinct groupings: ejections and sweeps become more frequent in occurrence in comparison to upwind values (+ve perturbations) whilst inward and outward interactions decline to negative perturbations.

Figure 2.

Fractional perturbations (normalised by upwind reference data) in (a) calculated kinematic stress ( math formula); (b) quadrant frequency measured at 1.5 m height; (c) quadrant frequency measured at 0.3 m height. Note that the quadrant frequency data at 0.3 m height (Figure 2c) were normalised by reference data measured at 1.5 m height. This results in perturbations for all quadrant events ≠ 0 upwind of the dune and, because of their predominance close to the surface [Best and Kostaschuk, 2002], consistently positive perturbations in sweep events (Q4) across the whole windward slope. Standard error bars (1σ) are shown to demonstrate statistical uncertainty. Wind from left to right.

[12] Downwind from this position the pattern generally inverses with a progressive decline towards the crest (x = 72 m) in the frequency of ejection and sweep events (towards −ve perturbations) and a contrasting rise (to +ve perturbations) in the frequency of outward interactions.

[13] The most substantial changes in frequency of occurrence of turbulent structures between the dune toe and crest are apparent for sweep (Q4) and outward interactions (Q1), which display dramatically opposing patterns of spatial development along the dune centre-line. It seems likely that this response is associated with the previously reported topographic forcing in turbulence intensity, streamline curvature and flow de/acceleration from toe to crest. The toe region of the dune is known to be characterised by high turbulence intensities, concave (upward flexing) streamline curvature and mean flow velocity deceleration caused by the blockage to the airflow provided by the dune mass [Weaver and Wiggs, 2011]. Such deceleration allows an increase in the strength and coherence of turbulence and concave streamline curvature tends to encourage the downward conveyance of elevated high velocity eddy structures towards the surface [Wiggs et al., 1996]. In contrast, the crest region is characterised by low turbulence intensities, convex (downward flexing) streamline curvature and an accelerated mean flow velocity [Weaver and Wiggs, 2011]. Such acceleration evident along the windward slope and culminating in maximum velocities at the crest may stretch vortices and dampen turbulent structures [Nelson et al., 1993]. Further, the streamline convexity evident at the crest may encourage the advection of eddies away from the surface. Whilst the specific relationships between these flow parameters requires further attention it seems clear that topographic forcing of the flow field has a distinct impact on the structure and character of the turbulent flow with opposing trends in the toe and crest regions of the dune.

[14] Significantly, our data support and provide some explanation for published Reynolds stress ( math formula) data over dune topographies that demonstrate an increase in math formula in the upwind toe region, and a decrease towards the crest [Wiggs et al., 1996; Baddock et al, 2011; Weaver and Wiggs, 2011] as shown in Figure 2a for the data in this study. The increased frequency of ejection and sweep events evident in the region of the dune toe is indicative of the presence of the turbulent bursting process [Lu and Willmarth, 1973; Jackson, 1976; Robinson, 1991] which makes a positive contribution to math formula. In contrast, the increased frequency of outward interactions towards the dune crest and brink contributes negatively to math formula.

5. Sand Transport

[15] The percentage of sand transport events assigned to each specific turbulent flow structure at the toe (x = 18 m) and crest (x = 72 m) regions of the dune are shown in Table 1. It is noticeable that the trend in data at both measurement heights is broadly similar. In the toe region it is apparent that whilst ejections were one of the most frequently occurring turbulent structures in the airflow, they were responsible for only a minor percentage of sand transporting events. The increased frequency of ejection events in this region (Figure 2) is therefore not greatly significant in a sediment transport context. Similarly, our data reveal that inward interactions are also of very low significance accounting for between only 5–8% of sand transport events depending on measurement height. In contrast, sweep events have a dominating role in sediment transport being associated with around half of all sand transport events, despite displaying a frequency of occurrence of only around 25–31%. Furthermore, nearly one third of sediment transport events are associated with the occurrence of outward interactions, despite their overall negative contribution to Reynolds stress ( math formula).

Table 1. Frequencies (%) of Turbulent Flow Structures Evident in the Airflow and Related to Sand Transport Events at the Dune Toe (x = 18 m) and Crest (x = 72 m)
PositionParameterOutward interaction (Q1)Ejection (Q2)Inward interaction (Q3)Sweep (Q4)
Toe 1.5 m     
sand transport29.8115.777.9246.50
Toe 0.3 m     
sand transport30.8012.215.1551.84
Crest 1.5 m     
sand transport44.582.941.9850.50
Crest 0.3 m     
sand transport36.989.753.5349.74

[16] Data collected at the crest of the dune (x = 72 m, Table 1) show a similar trend to the toe region in the association of sand transport events with specific turbulent structures. However, here, a greater proportion of sand transport events are associated with outward interactions and fewer with ejections or inward interactions.

[17] Both in the toe region and at the crest it is clear that turbulent flow structures displaying a positive streamwise velocity component (+u′; sweeps and outward interactions) dominate sand transport. Depending on measurement height, at the toe these structures are associated with around 76–83% of the sand transport events, whilst at the crest they are associated with 86–95%. This dominance is clearly shown in Table 2 in which the percentage of quadrant events associated with sand transport have been normalised by the percent occurrence of each event in the airflow (percentage frequency ratio). This eliminates the impact of the differing frequencies of occurrence of each flow structure in the analysis [Nelson et al., 1995].

Table 2. Percentage Frequency Ratioa Showing the Relative Importance of Each Turbulent Flow Structure to Sand Transport at the Dune Toe (x = 18 m) and Crest (x = 72 m)
PositionOutward Interaction (Q1)Ejection (Q2)Inward Interaction (Q3)Sweep (Q4)
  • a

    Percentage of quadrant events associated with sand transport normalised by percent occurrence of each event in the airflow.

Toe 1.5 m1.620.440.411.79
Toe 0.3 m1.410.430.291.65
Crest 1.5 m1.820.100.091.99
Crest 0.3 m1.630.340.191.67

[18] These data demonstrate the pre-eminent competence of sweeps and outward interactions in driving sand transport with values of percentage frequency ratio far greater than parity at both the dune toe and crest.Table 2 also reveals the negligible impact of ejections and inward interactions on sand transport.

6. Conclusions

[19] Our findings have shown that topographic forcing has a dramatic influence on the spatial development of turbulent flow structures on the windward slope of a barchan sand dune. Quadrant analysis has provided evidence of the increased frequency of sweeps and ejections in the toe region of the dune and the greater occurrence of outward interactions towards the dune crest. The spatial development of these structures has a significant influence on the streamwise progression of Reynolds stress ( math formula) along the dune centre-line and also on the competence of the airflow to drive sand transport. In contrast to research in the fluvial domain where both turbulent structures associated with the bursting process (ejections and sweeps) have been shown to be of critical importance to sediment transport [Best and Kostaschuk, 2002], our data suggest that it is only the structures characterised by a positive streamwise fluctuating velocity (+u′; sweeps and outward interactions) that have any significant influence on sand transport over an aeolian dune. This is likely due to the greater disparity evident in the density ratios between the particles and transporting medium for the aeolian case in comparison to the fluvial case. So, despite contributing positively to Reynolds stress, low speed ejections of fluid in the aeolian system have only a minor bearing on sediment transport.

[20] It has been previously hypothesised that increased turbulence intensity may maintain sand flux through the region of decelerated mean wind velocity evident at the toe of aeolian dunes [Wiggs et al., 1996; Parsons et al., 2004; Livingstone et al., 2007]. However, our data suggest that it is the sweep component of the turbulent bursting process which drives the sediment transport system here. As the frequency of these sweep events diminishes towards the crest of the dune, a greater proportion of the sand transport is driven by outward interactions, generated by flow acceleration up the windward slope. Quadrant analysis of turbulent winds may therefore offer an explanation of the complete development of sand flux across dune windward slopes.


[21] This research was funded by a Natural Environment Research Council studentship (NER/S/A/2004/12431). We are grateful for the help of the Ministry of Environment and Tourism, Namibia (permit 928/2005) and Dave Matthews at Rössing Mine.