The geomorphological significance of airflow patterns in transverse dune interdunes

The geomorphological significance of airflow patterns in transverse dune interdunes

Geomorphology 87 (2007) 322 – 336 The geomorphological significance of airf low patterns in transverse dune interdun...

913KB Sizes 0 Downloads 23 Views

Geomorphology 87 (2007) 322 – 336

The geomorphological significance of airf low patterns in transverse dune interdunes M.C. Baddock a , I. Livingstone a,⁎, G.F.S. Wiggs b b

a The University of Northampton, School of Applied Sciences, Park Campus, Northampton, NN2 7AL, UK Oxford University Centre for the Environment, University of Oxford, South Parks Road, Oxford, OX1 3QY, UK

Received 21 March 2006; received in revised form 20 September 2006; accepted 4 October 2006 Available online 21 November 2006

Abstract The interdunes between aeolian dunes have been relatively ignored when compared with the research attention on the morphodynamics of the dune bodies themselves. This neglect is in spite of the possible significance of interdune dynamics for the geomorphology of the sand dune system as a whole, especially with regard to dune spacing. This paper considers the mean airflow within four relatively simple transverse dune interdunes. The study locations were chosen in order to sample interdunes with different size and surface characteristics, the dynamics of which were investigated for when incident flow was normal to the upwind crest. The findings confirm existing models of flow reattachment length and recovery for aeolian dune lee-side flow, and show a consistent pattern of increasing near-surface velocity downwind of reattachment that supports a mechanism for interdunes as sand-free features. Flow dynamics are characterised for the different types of interdune observed, where two groups are recognised. The flow patterns in relatively short interdunes (where dunes are closely-spaced) with a sandy surface were accordant with those of the flow response model. In ‘extended’ interdunes, where bounding dunes were spaced with a length well over that for flow separation, evidence at the downwind edge of the interdunes suggested that flow reacted to the subsequent dune. For the case of these ‘extended’ interdunes, a new descriptive model is presented to characterise their dynamics. In this model, the variation in near-surface flow allowed process zones to be identified through the interdune. The geomorphological significance of the processes dominating each zone is discussed, and comparisons are made between the flow response case and the new interdune model from this study. In a discussion on the controls of spacing between dunes, where reattachment length exerts a fundamental control, the role of sediment availability is also highlighted as a significant factor. The presence of a sandy bed can, in some circumstances, determine whether dune development, and therefore spacing, is controlled primarily by elements of flow response. © 2006 Elsevier B.V. All rights reserved. Keywords: Sand dune; Interdune; Aeolian processes; Bedform spacing; Flow reattachment; Flow recovery

1. Introduction

⁎ Corresponding author. Fax: +44 1604 720636. E-mail addresses: [email protected] (M.C. Baddock), [email protected] (I. Livingstone), [email protected] (G.F.S. Wiggs). 0169-555X/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.geomorph.2006.10.006

In the work towards an improved understanding of aeolian sand dune dynamics, the interdune spaces within dune areas have been largely ignored. The spatial extent and form of interdunes can vary with dune type, with mean values of 60% and 10%, respectively, for the proportion of linear and transverse dune areas that are

M.C. Baddock et al. / Geomorphology 87 (2007) 322–336


Fig. 1. The generalised pattern of flow in the lee of dunes under perpendicular incident flow. Letters refer to identifiable flow layers. A) Interior B) Upper wake C) Lower wake D) Internal boundary layer (from Frank and Kocurek, 1996b).

made up by interdunes in parts of the Namib Sand Sea (Lancaster and Teller, 1988). Studies of the effect of dune bodies on flow have considerably increased our knowledge of aeolian dune morphodynamics, and have led to an appreciation of the interaction between flow and form as the primary control on variations in sand transport. These patterns of differential transport, in turn, control dune form and behaviour, and this understanding now exists for all the main types of dune. For transverse dunes, which make up around 40% of the global desert dune extent (Breed and Grow, 1979), the majority of work has been undertaken on the windward slope of dunes (Lancaster, 1985; Tsoar, 1985; Frank and Kocurek, 1996a; Lancaster et al., 1996; Wiggs et al., 1996; McKenna Neuman et al., 1997, 2000). Research attention into the lee-side flow over dunes saw early studies consider the controversial nature of the lee eddy (e.g. Cooper, 1958; Hoyt, 1966). More recently, focus has returned to the lee side of transverse dunes and there have been notable successes in obtaining a detailed insight into the secondary flow patterns (Sweet and Kocurek, 1990; Frank and Kocurek, 1996b; see also Walker and Nickling, 2002) and the associated sediment transport patterns (Walker, 1999). Particular difficulties exist where investigations are undertaken in the lee side of dunes. Here, complex wind patterns affected by the upwind dune result in non-log-linear vertical velocity profiles (Walker and Nickling, 2002, 2003). Such disruption of the log-linear nature of the velocity profile excludes the use of the commonly applied ‘law-of-thewall’ to determine local shear velocities and hence sediment transport (Wiggs, 2001). The majority of previous empirical dune studies have concentrated on the flow over isolated dunes. Most dunes however do not exist in isolation, but in a repeated form. Despite this, the enquiries that have reported any

data on the properties of flow in the entire space between successive dunes are relatively few (e.g. Livingstone, 1986; Lancaster, 1989; Sweet and Kocurek, 1990; Ha et al., 1999). Interdunes have often been considered simply as extensions of the lee side of the upwind dune and only recently has the interdune begun to be treated as a feature in its own right, especially in terms of monitoring its flow dynamics. For transverse dunes, the flow between closelyspaced reversing dunes has been measured through paired studies in the field (Walker, 1999) and wind tunnel (Walker and Nickling, 2003), the latter containing measurements of surface stress. In their key work on the structure of lee-side airflow, Frank and Kocurek (1996b) also examined the development of the wake through the interdunes downwind of transverse dunes (Fig. 1). The investigation by Frank and Kocurek (1996b) was the first to relate the structure of lee-side airflow for aeolian dunes to that already incorporated in a detailed model for the development of sub-aqueous bedforms (McLean and Smith, 1986). This ‘flow response’-based model accounted for the distribution of boundary shear stress in the lee of bedforms over which flow becomes separated. It proposed that downwind of reattachment, the shear stress exerted at the surface is controlled by the interaction between the wake and the internal boundary layer (IBL) growing beneath it (Fig. 1). Initially, the flow is dominated by an increase in velocity and surface shear stress as the IBL adjusts to momentum received from the turbulent wake above. With increasing distance downwind, the flow adjusts to the effect of the growing boundary layer thickness and a point is reached where surface stress no longer increases. Downwind of the point where maximum surface stress is established, the flow-response model suggests that deposition is possible, so allowing for the initiation


M.C. Baddock et al. / Geomorphology 87 (2007) 322–336

of the next dune downwind. Furthermore, where successive dunes are already in place, the spacing of the existing dunes is controlled by this variation in stress that is established by the interplay between the wake and IBL (McLean and Smith, 1986; Nelson and Smith, 1989). The variation in shear stress proposed in the model also has several implications for the dynamics of the interdune. For example, in observing acceleration within the near-surface IBL downwind of reattachment, Frank and Kocurek (1996b) noted that this allowed potential for erosion of sediment throughout the interdune. Dynamics such as these could therefore explain the common occurrence of bare surfaces within interdunes where no sediment is deposited. The extent of the functional role of flow within aeolian interdunes remains an important research question. One of the most striking aspects of dunefield morphology is the repetition of form and arrangement that for aeolian contexts has been termed “replication” (Cooke et al., 1993). The McLean and Smith (1986) model accounts for a control on dune spacing, and holds that the flow pattern established within the interdune is

highly relevant to the mechanism governing the distance between dunes. The noted neglect of interdunes in aeolian research is therefore in spite of their possible importance for the spacing of dunes, one of the least understood aspects of the sand dune system. Progressing from the many informative studies of single dunes, the fact that most dunes do not exist in isolation means that there is a further requirement to investigate the dynamics of the relationship between replicated bedforms. This is reflected in current research trends that now include the modelling of dunes on a dunefield scale and the interactions between the bedforms (e.g. Schwämmle and Herrmann, 2004). Data on the airflow patterns between dunes are of further benefit to success in this direction. This study therefore aims to investigate the characteristics of airflow within interdunes, and the geomorphological role played by interdune dynamics within the transverse dune system, as part of a wider study of interdunes (Baddock, 2005). Particular attention is paid to the role of the flow response model in characterising airflow recovery across the interdunes.

Fig. 2. Location of the two study areas within Namibia.

M.C. Baddock et al. / Geomorphology 87 (2007) 322–336

2. Methods 2.1. Study areas Airflow patterns were measured in four different interdune settings between dunes of crescentic-ridge type according to the classification of McKee (1979), with practical considerations restricting the number of sample interdunes that could be studied in requisite detail. A series of criteria were established to define interdunes that were suitable for the study. The bounding dunes were of a manageable height (b7.0 m), simple form and aligned with the general wind conditions. Interdune length was not too extensive (b 40 m) in order to permit a high resolution of sampling, and interdunes with different surfaces (sandy and bare) were chosen to be investigated. Two study interdunes, each with a bare, flat gravel surface, were selected in the Skeleton Coast dunefield of Namibia. The second pair of interdunes had sandcovered surfaces, and were located near the delta of the Kuiseb River in the northern part of the Namib Sand Sea. Both field areas are shown in Fig. 2. The Skeleton Coast dunefield in north-western Namibia is a thin belt (up to 15 km wide) of transverse and barchanoid dunes that stretches parallel with the Atlantic coast for around 150 km. The geomorphology and climate of the hyperarid region were described in a detailed study by Lancaster (1982). A particular feature is the coastal setting with its strongly unimodal south to south-south westerley onshore wind regime which is responsible for the dominantly transverse bedforms. The two relatively simple interdune settings that were studied in the Skeleton Coast dune field lay between


transverse ridges that comprise the most common bedform in the interior of the dune field (Lancaster, 1982). The interdunes were located on the southern side of the dry Uniab River whose course travels through the dune field. The two bare transverse ridge interdune sites were identified as B1 and B2, where “B” refers to the bare surface (Table 1). Both of the upwind dune ridges had relatively straight brinklines in plan view, oriented at right angles to the wind at compass bearings approximately 320°–140°. The morphometries of all the studied interdunes are summarised in Table 1. A further two transverse interdune settings were selected for study within the delta region of the Kuiseb River, in the far north-western part of the Namib Sand Sea. The Kuiseb is an intermittently flowing channel, with periodic floods (around every nine years) that result in large depositions of sediment (Nagtegaal, 1971). The dunes in the immediate area of the Kuiseb river delta are dominated by transverse forms as a result of the dominant wind (Lancaster, 1989; Slattery, 1990; Barnes, 2001). The studied interdunes from this area were found between dunes on the north side of the Kuiseb river channel, where the transverse ridges are formed of sediment that has crossed from the sand sea to the south, and delivered to the area by the action of the river itself (Nagtegaal, 1971). Within this study area, the two interdunes were chosen based on the criteria of simple form and manageable size. These study interdunes were termed S1 and S2, designating the presence of a sandy interdune surface. 2.2. Instrumentation Wind speed was measured using Vector Instruments A-100R rotating cup anemometers. In order to measure

Table 1 A summary of the studied interdunes, with the morphometries of each case at the beginning of the study Name

Dune crest height (m)

Dune basal length (m)

Crest to crest spacing, λ (m) [λ / h]

Interdune length, I (m) [I / h]



Upwind dune 6.67

D/wind dune 4.99

Upwind dune 82.92

68.45 [10.70]

30.07 [4.71]

Bare interdune between transverse ridges





72.41 [15.20]

23.97 [5.03]

Bare interdune between transverse ridges





56.00 [13.06]

36.60 [8.54]

Sandy interdune between crescentic ridges





43.40 [13.44]

9.70 [3.12]

Sandy interdune between crescentic ridges

Interdune length is defined as base of the slip face to start of the downwind dune windward toe. Dune heights (h) are expressed as the relative elevation of the upwind brink above the lowest point of the interdune.


M.C. Baddock et al. / Geomorphology 87 (2007) 322–336

Fig. 3. Field experiment setup with transect of instrumentation through a study interdune.

the patterns of wind speed through interdune areas, straight-line transects of anemometers were set up from the slip face of the upwind dune to the windward slope of the subsequent downwind dune. These transects were orientated at right angles to the local crestline of the upwind dune and lay parallel to the dominant wind direction. Wind speed was sampled along the transects at two heights (z), 0.5 m and 1.9 m. The lower of these heights was determined by a compromise between measuring velocity as close to the surface as possible, and concern for potential damage to the instrumentation from sand transport. The distance between sampling points was chosen with regard to the transect length and a desire to sample frequently through the interdune. This resulted in sampling intervals ranging from between 4 and 7 m (Fig. 3). A reference tower was also established to record a vertical velocity profile of four heights at 0.5 m, 0.8 m, 1.3 m and 1.9 m, against which the transect wind speed data were normalised following an approach which has been successful in other dune studies (e.g. Walker, 1999). The reference tower was sited to sample airflow and boundary layer conditions that were as little disturbed as possible in the middle, or nearer the downwind edge, of the interdune area. Mean speed was calculated from samples of 10 s duration which were recorded using Campbell Instruments CR10x dataloggers. The total periods of data collection at the different study sites varied from one to several hours, at the end of which the dataloggers were accessed and data downloaded to a laptop PC.

The speed data throughout this study are presented in terms of the fractional speed-up ratio. This expression for wind speed involves the normalisation of data to a constant reference location and was first used for meteorological applications (Jackson and Hunt, 1975). It is now also the conventional manner of describing changes in flow speed for studies of dune dynamics (e.g. Mulligan, 1988; Wiggs, 1993). The extent of the wind speed change is described by the (fractional) speed-up ratio (δs); ds ¼ ðuz −Urz Þ=Urz where δs = fractional speed-up ratio, uz = wind speed at a height z on profile and Urz =wind speed at height z at a reference location (Jackson and Hunt, 1975). With all timeaveraged local speed data being referred to a common reference location, direct comparisons were permitted between the mean speed readings along a transect. The instruments used to obtain flow direction data were Vector Instruments W200P Potentiometer Wind Vanes. These devices respond to airflow guided by a fin which aligns with the wind and permits free-moving continuous rotation. The vanes sampled wind direction at z = 0.5 m, near to the surface and level with the lowest anemometer height. As there were insufficient vanes to instrument every post at which wind speed measurements were made, vanes were positioned along the transect to ensure a regular coverage of flow direction data throughout the interdune. Before each data run commenced, the vanes were aligned to magnetic north using compass measurements. Once

M.C. Baddock et al. / Geomorphology 87 (2007) 322–336


Fig. 4. Time-averaged wind speed (fractional speed-up ratio) in the closely-spaced interdune S2 for the two sampling heights (left axis scale) and normalised directional variability of flow (ω), measured at z = 0.5 m (right axis scale). Run i = 74°, duration 56 min. Ucr (mean crestal velocity) at z = 1.9 m, 7.33 m s− 1.

operating, the datalogger recorded the wind direction indicated at that instant for each vane at an interval of 10 s. The investigation of flow characteristics within interdunes was restricted to periods when flow was near to perpendicular to the upwind dune. Following Sweet and Kocurek (1990), transverse flow conditions were assumed when flow had an incident angle (i) to the upwind crestline of 90 ± 20°. For the presentation and analysis of flow directional variability, the spread of compass bearing data was used to create a normalised measure of flow unimodality. This was based on a trigonometric conversion of the direction data from bearing form, as produced in the field, to scalar co-ordinates. Each period of flow sampling had a resultant vector line with an angle and a length (ω). The angle was the mean direction, and the length represented the constancy of flow, indexed for the total number of readings for that run. In this case the vector length and value ω is the inverse of the flow directional variability, i.e. a longer line and higher ω value is a flow with a less variably directed flow. A potential ω value of unity represents a flow that is purely unimodal and unvarying in flow direction. 3. Results 3.1. Interdune with closely-spaced dunes The results shown in Fig. 4 (S2) are typical of those found in narrow interdunes with sandy surfaces that are

bounded closely by dunes. Maximum flow acceleration occurs at the crest of the upwind dune and is followed by an immediate deceleration within one equivalent dune height in the lee (x /h = 0.77). Here the near-surface flow speeds measured at 0.5 m and 1.9 m height are approximately 40% of their reference values (δs = −0.42 and −0.39, respectively). The consistent, reduced wind speeds and increased directional variability in the region downwind of the minimum speeds at x / h = 0.77 suggest the existence of a flow separation cell that extends at least to a downwind point of x /h = 3.89. At x /h = 4.98, the near-surface wind speed shows an increase which indicates that flow must have become reattached to the surface by this point. This distance for reattachment therefore corresponds well with the 4h mean separation length reported in other studies between bedforms (Engel, 1981; Nelson and Smith, 1989; Frank and Kocurek, 1996b). Downwind from the point of flow reattachment the speeds measured at heights of both 0.5 m and 1.9 m show acceleration because momentum from the upper wake above is transferred toward the surface. It is noticeable from Fig. 4 that the wind speed increase measured at 1.9 m indicates acceleration here is greater than at 0.5 m in the region between x / h = 2.67 and 4.98 because this flow is the first to benefit from the momentum transfer downward from the nearby upper wake. It is also further downwind of this region that the fractional speed-up ratios at both measured heights become positive (x / h = 6.56), indicating that flow is faster than at the reference site. This is due to a


M.C. Baddock et al. / Geomorphology 87 (2007) 322–336

Fig. 5. Time-averaged wind speed (fractional speed-up ratio) in the interdune B2 for the two sampling heights (left axis scale), and normalised directional variability of flow (ω) measured at z = 0.5 m (right axis scale). Run i = 92.6°, duration 15 min. Ucr at z = 1.9 m, 6.18 m s− 1. Reference tower not on transect.

combination of both continued momentum transfer from the upper wake, but also the initial impact of streamline compression as the wind flows across the toe region of the downwind dune. This cross-over from negative to positive speed-up ratios represents the reproduction of the upwind velocity profile and it occurs here at a downwind distance not dissimilar to the 8h reported by Frank and Kocurek (1996b). Downwind from x / h = 4.98, the speeds at 0.5 m height are accelerated to a greater extent than those measured at 1.9 m height. This increased acceleration at the lower measurement height agrees with the nearsurface ‘amplification layer’ detected in flow a few tens of centimetres above the windward slope (above the inner layer) by Burkinshaw et al. (1993) on transverse dunes of comparable size. 3.2. Interdune with ‘extended’ dune spacing The results shown in Fig. 5 (B2) typify those measured in interdunes that are ‘extended’ in character whereby the toe of the downwind dune does not emerge until some considerable distance from the separation cell and flow reattachment in the lee of the upwind dune. The interdune represented in Fig. 5 did not have a sandy substrate but was bare between the lee slope of the upwind dune and the toe of the downwind dune. The results shown in Fig. 5 are similar to those shown in Fig. 4 for the closely-spaced dunes. However, there are significant differences as described below.

Similar to the results shown in Fig. 4, the region of low and consistent near-surface speeds in the immediate lee of the upwind dune in Fig. 5, coupled with the directional variability data, suggest that separated flow reattaches to the surface within the area between x / h = 4.21 and 5.04. Downwind of this point of reattachment, measured speeds at both 0.5 m and 1.9 m height show strong acceleration all the way to the toe of the downwind dune at x / h = 6.71. Through this region between upwind flow reattachment and the toe of the downwind dune the wind speed data measured at 0.5 m height indicate approximately 18% flow acceleration for every 0.75h in distance downwind. However, at the toe of the downwind dune this acceleration is seen to nearly halve in value to approximately 10% between x / h = 6.71 and 7.54. This observed reduction in flow acceleration is likely to be a manifestation of the positive pressure field induced by the downwind bedform. Where such pressure fields have been measured upwind of isolated dunes (e.g. Wiggs et al., 1996) they have resulted in flow deceleration and stagnation. Whilst the effect evident in Fig. 5 is not so dramatic, the observed reduction in deceleration may have a similar genesis. Indeed, the reduction in acceleration is similar to the region of diminished velocity increase observed by McKenna Neuman et al. (1997) on the lower windward slopes of a reversing dune. They attributed this result to the effects of flow stagnation. The reduction in acceleration is even more apparent for data measured at 1.9 m height where only a

M.C. Baddock et al. / Geomorphology 87 (2007) 322–336 Table 2 Flow characteristics within different interdune settings Interdune character S2 (Fig. 4)

Sandy, closely-spaced

B2 (Fig. 5)

Bare, extended


Bare, extended


Sandy, extended

Flow acceleration (%) (m) 0.5 1.9 0.5 1.9 0.5 1.9 0.5 1.9

Region A 24 19 18 13 9 9 13 11

Region B 21 16 10 5 3 9 10 8

Region A = between upwind flow reattachment and downwind dune toe. Region B = between downwind dune toe and downwind dune mid-slope.

5% acceleration in flow is evident between x / h = 6.71 and 7.54. These results are in stark contrast to those shown in Fig. 4 for the closely-spaced dunes. Table 2 summarises the development of nearsurface flow acceleration for all the interdunes measured in this study. The table distinguishes between flow acceleration in the region from the point of flow reattachment to the downwind dune toe, and that in the region between the downwind dune toe and downwind dune mid-slope. In contrast to the closely-spaced interdune, the extended interdunes are characterised by a greater reduction in acceleration as flow approaches the downwind dune toe. 4. Discussion


slope of the downwind dune, where the toe of the slope effectively starts at x / h = 3.89 and where reattachment is detected just downwind of this. In the flow response model developed for subaqueous bedforms by McLean and Smith (1986) the IBL that is established at reattachment also forms over the following dune's stoss slope. This situation exists in aeolian dunes where the windward slope of the downwind dune begins close to the point of reattachment after the upwind dune, and is seen to be the case for S2. Further evidence for the notion that it is flow response elements that explain the dynamics in S2 is provided by the change from erosional to depositional stages that is central to the McLean and Smith model. This change is reflected in the form of the downwind windward slope in S2. The evolution from erosion to deposition predicted by the flow response model occurs due to the contrasting wake (positive) and IBL growth (negative) effects balancing out by a certain distance downwind of the upwind dune. When another dune is present downwind, the response of the flow to initial separation and then reattachment occurs over the downwind dune's stoss slope (McLean and Smith, 1986; Nelson and Smith, 1989). The resultant erosion pattern on this slope tends to create a windward form characterised by a gently convex profile starting from around mid-slope (Cooke et al., 1993). The concavity in the form of the S2 slope exists until around x / h = 10 (Fig. 4) where the onset of convexity suggests that the stress and transport are distributed through the interdune in the way prescribed by the flow response model.

4.1. Characterising the different interdune settings 4.1.1. Interdunes with closely-spaced dunes Fig. 4 represents the typical flow pattern within S2, the sandy-floored interdune with the shortest interdune length. The observations show consistent evidence of flow separation at the brink, and then subsequent reattachment of flow to the surface, with a mean distance between 3.89 and 4.98h. Following reattachment, the flow near the surface accelerates immediately. This speed-up can be attributed to the increased momentum reaching nearer the surface with the end of the separation cell allowing the influence of the faster overlying wake flow to expand downward to the bed (Fig. 1). Close to the reattachment zone anemometers at z = 0.5 m are above the newly formed IBL. Other studies (e.g. Nelson and Smith, 1989; Nelson et al., 1993) have established that underneath the wake an IBL begins to develop from the point where the separated flow reattaches. For S2, the development of the IBL therefore occurs in conjunction with the presence of the windward

4.1.2. Interdunes with ‘extended’ dune spacing While the flow in the closely-spaced interdune, S2, suggests the occurrence of flow response (McLean and Smith, 1986), the dynamics of the other studied interdunes appear to be less well characterised by this particular model. This is the case for both the study interdunes with bare, eroded surfaces, as well as for S1, the sandy example that had the longest interdune length of the sample of interdunes (Table 1). Frank and Kocurek (1996b) highlighted the fact that aeolian settings commonly have “flat interdune areas that extend well beyond the point of reattachment” (p. 456), so the term ‘extended’ interdunes is used for such interdunes here. Importantly, Frank and Kocurek also added the observation that the sub-aqueous flow response model did not yield such flat interdunes. In ‘extended’ interdunes, the IBL that develops where flow reattaches is not associated immediately with the windward slope of the subsequent bedform. In other words, the surface shear stress variation that the IBL


M.C. Baddock et al. / Geomorphology 87 (2007) 322–336

Table 3 A descriptive model for near-surface flow dynamics in the ‘extended interdunes’ of transverse dunes under conditions of perpendicular incident flow

Interdune zones progress downwind.

establishes does not instigate the next bedform near to reattachment as the flow response model would suggest. The example in Fig. 5 shows that mean reattachment in the ‘extended’ interdunes occurred some way upwind of the downwind dune. Furthermore, the near-surface wind speed data where the interdune is relatively extensive also demonstrate the way flow can react to the downwind dune in ‘extended’ interdunes (Table 2, Region B). This is identifiable as a result of the adverse pressure gradient, or stacking effect, at the toe of the obstacle (Hunt and Simpson, 1982). Actual reductions in velocity caused by the pressure at the upwind toe were not observed here; rather, decreased accelerations are more often seen for the toe region (also McKenna Neuman et al., 1997). The absence of an overall retardation at the toe is attributed partly to the sampling height (z = 0.5 m) because the drop in flow speed may occur below this height. In their study (with lowest anemometers at z = 0.1 m) Frank and Kocurek (1996b) reported an identifiable drop in wind speed upwind of the next dune wherever an interdune flat was present. The most pertinent aspect for interdune dynamics of this change in acceleration is that it signifies flow at the downwind edge of ‘extended’ interdunes undergoing a reaction to the presence of the next dune. Such a change in speed is not incorporated in the flow response model, nor seen in Fig. 4, since the flow acceleration from reattachment negates any adverse pressure build-up from the almost adjacent downwind stoss slope. It is suggested here that where flow demonstrates a reaction of slowed acceleration (or actual deceleration) to the presence of the downwind dune in

‘extended’ interdunes, it is apparent that the flow response model in its pure form is not applicable. 4.2. A conceptual model for ‘extended’ interdunes While the mechanism of flow response (McLean and Smith, 1986) explains the flow pattern and dynamics in the closely-spaced interdune, S2, ‘extended’ interdunes require some other explanation. The new conceptual model outlined here serves to explain the characteristics of ‘extended’ flow, and their geomorphological significance. It is not possible to recognise a finite length for the ‘extended’ interdune at which point the dynamics behave differently from pure flow response. The examples here are B1, B2 and S1, where the interdunes are largely flat and not closely-spaced. Walker (1999) and Walker and Nickling (2003) studied dunes with what they termed a “close spacing”, where the interdune length was 0.5h. Table 1 confirms the smallest interdune length studied (excluding S2, 3.1h) was B1 where the interdune length was 4.7h. Based on the nature of the variation in the patterns of near-surface flow, sand transport potential can be estimated and a series of zones can be identified across the ‘extended’ interdune (Table 3 and Fig. 6). 4.2.1. Zone of separation In the area upwind of the mean point of flow reattachment, mean velocities are reduced greatly in the immediate lee as a result of streamline expansion beyond the dune brink and the separation of flow from the surface. After the severe initial drop, cup anemometers

M.C. Baddock et al. / Geomorphology 87 (2007) 322–336


Fig. 6. A conceptual model for dynamics in ‘extended’ interdunes between transverse dunes. Erosional potential is based on near-surface mean speed under a perpendicular wind. Dotted line in Zone B indicates intermittent erosivity. Dashed line in Zone D represents possible velocity retardation at downwind dune toe. Not to scale.

indicate an area of reduced velocity for the near-surface flow that is relatively constant within the cell forming the zone of separation. This is reinforced by the wind direction, which regularly shows the occurrence of reversed flow with a sufficient constancy to indicate it is the dominant component. The low mean speeds indicate that this area is one of low transport potential. Furthermore, under certain flow conditions, there may be a sediment input due to grain fallout from the separated flow (Nickling et al., 2002). Walker (1999) measured appreciable sediment movement back toward the slip face in the separation cell and stressed the importance of this reversed sediment transport to the maintenance of dune form although uncertainty remains about this component. The geomorphological significance of reversed flow of sediment is necessarily largely restricted to the upwind dune. 4.2.2. Zone of reattachment Estimates for separation length and position of the zone of reattachment within the ‘extended’ interdunes average around 4.8h for the bare interdunes, B1 and B2, which is slightly longer than (but in general agreement with) estimates of other aeolian and sub-aqueous studies (e.g. Engel, 1981; Nelson and Smith, 1989; Frank and Kocurek, 1996b). The distance for flow reattachment in the ‘extended’ interdunes is greater than for the closelyspaced interdune (S2, 4.4h), but is also considerably less than the length of 7.5h measured on an individual barchan. For data from cup anemometers, as a result of timeaveraging, the point of flow reattachment is best marked by the onset of acceleration that ends the area of constant flow representing the separation cell. The migration of the point of reattachment by a distance of around 0.5h (Walker and Nickling, 2002) is also supported in the data presented here. The inconsistency of the point of flow reattachment over this small distance means flow

direction variability is greatest within the zone of reattachment. The high variability means that mean direction is actually unrepresentative of any real preferred flow direction in this zone (Sweet and Kocurek, 1990). With a low mean velocity, the mean sediment transport potential is accordingly limited in the zone of reattachment but there is evidence that it is intermittently enhanced at turbulent time scales (Nelson et al., 1993; McLean et al., 1994) (Fig. 6). However, these enhancements are remarkably efficient in terms of transport since, over time, the zone of reattachment is not an area for deposition, and the erosive ability there is sufficient to maintain the reattachment area as sand free in the bare interdunes. Wind tunnel findings have shown peak surface shear stress variability at reattachment too (Walker and Nickling, 2003). 4.2.3. Zone of recovering flow With the onset of recovery beginning with flow reattachment and the development of an IBL at the surface, the zone of recovering flow is the region within the interdune where the return of the flow to primary conditions is seen to take place. One of the most apparent and important characteristics of the dynamics here is the ongoing increase in near-surface velocity throughout the zone. Reattachment is indicated by the onset of acceleration in the time-averaged data. In the zone of recovering flow, this acceleration continues for the whole zone due to the wake dissipation and downward momentum extraction. Driven by the accelerating flow, directional variability undergoes a continued decrease with distance in this zone, and ω will reach upwind values before velocity does (Fig. 5). The geomorphological significance for this region is one of erosive potential. The increasing velocity means that when wind speed exceeds the threshold, wind in the zone of recovering flow will be capable of eroding throughout the whole of the zone. Wind speed-up


M.C. Baddock et al. / Geomorphology 87 (2007) 322–336

increases transport capacity so that sediment entrained upwind as well as sediment downwind can be moved through the interdune. This pattern accounts for the existence of bare interdunes, as first suggested in terms of the interdune sediment budget by Frank and Kocurek (1996b). Crucially, laboratory-based studies (using flumes and wind tunnels) sampling within the developing IBL show that shear stress increases at the surface, making the zone of recovering flow a region of potential erosion (McLean and Smith, 1986; Nelson et al., 1993; Walker and Nickling, 2003). The form of lee-side dune aprons provides further evidence of the dominant geomorphological processes of this interdune region. These aprons are sand piles that are found attached to many dune slip faces (Cooke et al., 1993). It is seen in this study that the downwind extent of aprons is co-incident with the instigation of flow recovery and therefore potential erosivity in sandy interdunes (S1). This relationship between apron extent and flow reattachment length was also evident in the data presented by Sweet and Kocurek (1990) but was not commented on. 4.2.4. Zone of recovered flow The zone of recovered flow is shaded in Table 3 to indicate that it is not always present within an ‘extended’ interdune, and may only appear in certain large interdunes or under non-transverse incident flow conditions where flow angle effectively elongates the interdune length. In cases where this hypothetical zone is identifiable (no examples in this study), the flow velocity will be steady throughout the zone, having recovered to upwind speeds and direction. The zone of recovered flow only ends when the flow shows signs of reacting to a downwind dune. Where the downwind dune impacts on the flow before it is fully recovered, as is the case for all interdune situations reported here, the zone is nonexistent for an ‘extended’ interdune. Distances of 10h for a return to unperturbed velocity (Lancaster, 1989) and 16–18h for an isolated barchan provide a possible minimum length scale before the recovered flow zone is seen. Whilst near-surface velocity is constant at a recovered level in this zone, it is unlikely that the flow will be recovered in terms of turbulence. Turbulent elements have been seen to remain higher than the unperturbed boundary layer conditions for downwind distances up to 50h from a modelled step or bedform perturbation (e.g. Bradshaw and Wong, 1972; McLean et al., 1996; Walker and Nickling, 2003). The geomorphological significance of this zone is debatable given its rarity. In actual fact, given the long distance necessary for the zone of recovered flow to

exist, it may be that wake dissipation and IBL growth lead to the distribution of shear stress at the surface which is prescribed in the flow response model. The imposition of a surface shear stress maximum and a change to deposition as wake and IBL interact behind a dune in that model is the mechanism for the initiation of a new dune (McLean and Smith, 1986). 4.2.5. Zone of interaction This zone is found at the downwind edge of the ‘extended’ interdune and is marked by flow influenced by the next dune downwind. Where a zone of recovered flow is not present in an ‘extended’ interdune, the zone of interaction is immediately downwind of the zone of recovery. For the case of a flat interdune, the interaction of flow with the downwind dune is two-part; this effectively splits the zone of interaction into an upwind (I) and downwind (II) part. Zone of interaction I is within the interdune proper and is where a negative effect on near-surface velocity is seen. This negative change is manifested either as a reduction in the rate of flow acceleration or as an actual retardation of flow, and is due to the adverse pressure created by the downwind dune (the ‘stacking’ effect). The extent of the stacking effect on velocity is variable though, and a physical decrease in speed-up is not always apparent. With a zone of recovered flow present in an interdune, or the nearer that flow gets to a recovered state, the more the observation of actual retardation at the windward toe is likely. This is because in the zone of interaction I, there is a balance between three important influences on flow. These are the growth of the IBL from reattachment, the dissipation of the wake (both of which occur through the zone of recovery) and finally the influence of the downwind dune. The type of negative velocity change observed at the toe will reflect this interaction. In terms of geomorphological significance, a fall in velocity in the zone of interaction I suggests a reduction in sediment transport competence. From wind tunnel work, Wiggs et al. (1996) found an increase in turbulent shear stress that they suggested compensated for the drop in mean velocity at the toe (also Castro and Wiggs, 1994). They attributed this to positive streamline curvature at the toe that destabilised flow, introducing greater turbulence that prevented a reduction in sand flux. This positive role of turbulence for transport at the upwind toe of dunes has been supported by Walker and Nickling (2003) and in the field by Baddock (2005). The zone of interaction II is characterised by acceleration caused by streamline compression on the downwind dune, and is therefore effectively outside of

M.C. Baddock et al. / Geomorphology 87 (2007) 322–336

the interdune in terms of topography if not process. The zone is discussed here because, depending on interdune length, it can feature flow that is still accelerating due to recovery in the interdune merged with the speed-up caused by the windward slope. Recovering flow will impinge on the downwind dune slope to a greater extent when interdune spacing is smaller. A key idea concerning the dynamics of ‘extended’ interdunes put forward by Frank and Kocurek (1996a,b) is that a second IBL in effect forms at the base of the downwind dune stoss slope in the zone of interaction II. While the first IBL forms at reattachment and develops over the interdune, the shear stress increase under the second IBL on the downwind dune drives the sediment transport necessary for windward slope morphodynamics (Tsoar, 1985; Lancaster, 1985). This useful idea accounts for the dynamics of extensive, bare interdunes as well as for the downwind bounding dune, but could not be verified here due to the difficulties with sampling the IBL in the field (Frank and Kocurek, 1996a; Lancaster et al., 1996). 4.3. Geomorphological significance of the different interdune types By recognising the occurrence of distinctive flow response behaviour within S2, and then by introducing a new model for the different flow dynamics that were common to the sampled ‘extended’ interdunes, the observed interdune dynamics have been divided into two. To examine the most important differences between the ‘extended’ interdune model and the original model of flow response for closely-spaced dunes, Table 4 explores the geomorphological significance for the interdune spaces in the two different interdune types. Here the zones identified for the ‘extended’ interdunes are imposed onto the flow response model to provide a framework for the comparison. Table 4 re-states the geomorphological significance for the ‘extended’ interdune zones offered in Table 3 and alongside this, the


geomorphological significance for the flow response model is inferred in the same terms (based on McLean and Smith, 1986). There is essentially no difference between both models in terms of the geomorphological significance of separation and reattachment. Given both models are related to bedform spacing, the distance for flow reattachment effectively establishes a minimum distance for spacing, acting as a control that is common to both types of interdune. This minimum spacing point is fixed geomorphologically due to the limited erosion within the separation cell, and the high intermittent transport at the mean point where flow re-couples. It follows, and is seen, that for flow response situations, the minimum spacing governed by mean reattachment length will also be relatively close to the overall bedform spacing that is actually exhibited (Engel, 1981; Nelson and Smith, 1989). The fundamental difference between the models is located in the recovering flow zone. In this zone on ‘extended’ interdunes there is recovery in the wake airflow following dune-generated flow separation plus IBL development near the surface after reattachment, with both occurring within the interdune for some distance. For the flow response model however, the recovery of flow and the establishment of the IBL takes place in conjunction with the windward slope of the downwind dune. The effects of flow recovery and topographic forcing of flow are therefore combined in closely-spaced settings. In such dune pairings, where the IBL growth occurs over the windward slope, it also means that actual erosion on the slope can occur (with sufficiently strong winds) since a sediment supply is guaranteed. The geomorphological difference between the models in this respect is that the onset of windward slope flow–form interaction in the dynamics of the ‘extended’ interdune model is not exhibited until further downwind, and in the zone of interaction (Table 4). Furthermore, when flow-form interaction with the downwind dune does occur in ‘extended’ interdunes, the

Table 4 Comparison of geomorphological significance for the interdunes described by the ‘extended’ interdune and flow response models Model

Interdune zone Separation

‘Extended’ interdune model

Zero to low erosive potential Related to upwind dune? Flow response model Zero to low erosive potential


Recovering flow

Highly intermittent Increasing erosive erosive potential potential/transport prevents deposition competence

Recovered flow Interaction I Steady transport competence

Highly intermittent Onset of flow–form No equivalent erosive potential interaction, and actual prevents deposition erosion

Interaction II

Maintenance of Increase in actual transport erosion on downwind competence dune No equivalent

Continued actual erosion on downwind dune


M.C. Baddock et al. / Geomorphology 87 (2007) 322–336

nature of the interaction is initially different to that for the case of the pure flow response model. This is reflected by the extended interdune showing a two-part zone of interaction, where flow at first has an element of slow-down at the downwind edge. For closely-spaced dunes, this stacking effect is not evident in the flow (e.g. Nelson et al., 1993; Bennett and Best, 1995; Walker, 1999). The flow acceleration on the downwind stoss slope (zone of interaction II) has been suggested to involve the formation of a second IBL on the windward slope (Frank and Kocurek, 1996a,b). 4.4. Transverse interdune dynamics and dune spacing The significance of the different behaviour of IBLs between the models for flow response and ‘extended’ interdunes has interesting implications for the controls on transverse dune spacing. The flow response model, developed for sub-aqueous bedforms, assumes the existence of an erodible bed. The IBL at reattachment can therefore lead to the development of a bed in direct response to the variation in surface shear stress established by flow recovery following the dune perturbation. Within ‘extended’ interdunes, the same pattern of shear stress will be produced at the surface, yet spacing of the dunes for the same height may be different to where sediment-uninhibited flow response operates, i.e. where the bed is wholly erodible. This introduces the control of sand availability on bedform spacing, with statistics of spacing arrangements acting as an expression of this (Lancaster, 1988). In bare ‘extended’ interdunes, where interdune dynamics are characterised by a speed-up of flow throughout the interdune, the increasing erosive potential of the interdune flow has a geomorphological role in that it can account for the presence of sand-free stretches between dunes (Frank and Kocurek, 1996b). However, where dune development is considered for an area of limited sand availability, it seems that due to the sediment control, the dynamics of the interdune flow may be much more ‘dynamically neutral’ in terms of controlling spacing. This is especially so when compared with the role that interdune dynamics have in fixing spacing when sediment is readily available, and the flow response model holds. An important control on the spacing between a given pair of dunes would therefore seem to be whether the flow response model can operate for the pair. In turn, an important determinant of this is the presence or not of an erodible bed, since such a substrate is inherent to the working of the flow response model. Given that dune development can begin near to reattachment when

erodibility is not a limiting factor, interdune length will be relatively small where sand covers the entire space between the dunes, and flow response is in operation. The distance for flow reattachment exists as the primary control on dune spacing. 5. Conclusion The data for airflow over the interdunes reported here suggest that certain aspects of wind speed and directional variability are replicated in all types of interdune. It is possible, for instance, to detect separation and reversal of flow, and to quantify the mean reattachment length. Separation lengths in interdunes range from 4.4h to 5.0h, thereby revealing the extent to which separated flow occupied the different interdunes. Patterns of flow in interdunes can be characterised in two groups. The first group covers sandy interdunes with closely-spaced dunes where the near-surface velocity pattern, interdune topography and the close relationship between these two variables supports a flow response model (McLean and Smith, 1986). The second group covers interdunes that are identifiably long and flat (‘extended’ interdunes) where the interdune is considerably longer than the separation length. These interdunes show an overall wind speed distribution within them that is different to velocity patterns established by flow response. Diagnostic of this is the reaction of flow to the downwind dune, a feature not present in the flow response model, indicating this model does not completely account for the spacing of dunes of this type (Frank and Kocurek, 1996b). Whilst recognising that the research presented here is based on a relatively small dataset, it follows an approach that has been successful for many aeolian investigations where the findings from single dunes have informed wider inferences (e.g. Wiggs et al., 1996). The observed dynamics of ‘extended’ interdunes can therefore be characterised by a new descriptive model. This model identifies zones based on interdune processes with the fundamental difference between the interdune types being the nature of the flow–form interaction. For controls on dune spacing, the separation length of flow within interdunes fixes a minimum distance to establish a minimum spacing between dunes. An important control on spacing is also exerted by the model of interdune dynamics that fits for each setting. Flow response will tend to produce relatively closelyspaced dunes, where dunes develop a little distance after reattachment (McLean and Smith, 1986; Nelson and

M.C. Baddock et al. / Geomorphology 87 (2007) 322–336

Smith, 1989). Such interdune spacings will be less than those that exist for ‘extended’ interdunes. In turn, the primary determinant of whether flow response will control dune development will be sediment availability, since flow response requires an erodible, sandy bed. Given the relative advancement of fluvial bedform studies, and the recent increasing concentration on this topic for the case of aeolian settings, this current research offers a contribution to the overall geomorphological interest in bedforms. It is anticipated that with the growing attention on bedform dynamics, progress will continue toward more rigorous models that are better developed for both environments. For this better understanding of aeolian dunes, the dynamics of the interdune area will certainly need to be incorporated. Acknowledgements Permission for the fieldwork in the Skeleton Coast and Namib-Naukluft National Park was granted by the Ministry of Environment and Tourism permit number 463/2001. Equipment for surveying was loaned by the Polytechnic of Namibia and the Desert Ecological Research Unit of Namibia (DERUN). Finally, the research was supported in part by a studentship from The University of Northampton (MB) and some expenses were covered by a Leslie Church Research Award. References Baddock, M.C., 2005. Airflow dynamics in transverse dune interdunes. Unpublished PhD thesis, University of Leicester, UK. Barnes, J., 2001. Barchan dunes on the Kuiseb River Delta, Namibia. South African Geographical Journal 83, 283–292. Bennett, S.J., Best, J.L., 1995. Mean flow and turbulence structure over fixed, two-dimensional dunes: implications for sediment transport and bedform stability. Sedimentology 42, 491–513. Bradshaw, P., Wong, F.Y.F., 1972. The reattachment and relaxation of a turbulent boundary layer. Journal of Fluid Mechanics 52, 113–135. Breed, C.S., Grow, T., 1979. Morphology and distribution of dunes in sand seas observed by remote sensing. In: McKee, E.D. (Ed.), A Study of Global Sand Seas. United States Geological Survey Professional Paper, vol. 1052, pp. 253–303. Burkinshaw, J.R., Illenberger, W., Rust, I.C., 1993. Wind-speed profiles over a reversing transverse dune. In: Pye, K. (Ed.), The Dynamics and Environmental Context of Aeolian Sedimentary Systems. Geological Society Special Publication, vol. 72. Geological Society, London, pp. 25–36. Castro, I.P., Wiggs, G.F.S., 1994. Pulsed-wire anemometry on rough surfaces, with application to desert sand dunes. Journal of Wind Engineering and Industrial Aerodynamics 52, 53–71. Cooke, R.U., Warren, A., Goudie, A.S., 1993. Desert Geomorphology. UCL Press, London. Cooper, W.S., 1958. Coastal sand dunes of Oregon and Washington. Geological Society of America, Memoir 72 167 pp.


Engel, P., 1981. Length of flow separation over dunes. Proceedings of the American Society of Civil Engineers 107, 1133–1143. Frank, A., Kocurek, G., 1996a. Airflow up the stoss slope of sand dunes: limitations of current understanding. Geomorphology 17, 47–54. Frank, A., Kocurek, G., 1996b. Toward a model for airflow on the lee side of aeolian dunes. Sedimentology 43, 451–458. Ha, S., Dong, G., Wang, G., 1999. Morphodynamic study of reticulate dunes at southeastern fringe of the Tengger Desert. Science in China (Series D) 42, 207–215. Hoyt, J., 1966. Air and sand movements to the lee of dunes. Sedimentology 7, 137–143. Hunt, J.C.R., Simpson, J.E., 1982. Atmospheric boundary layers over non-homogenous terrain. In: Plate, E.J. (Ed.), Engineering Meteorology. Elsevier, Amsterdam, pp. 1–32. Jackson, P.S., Hunt, J.C.R., 1975. Turbulent wind flow over a low hill. Quarterly Journal of the Royal Meteorological Society 101, 929–955. Lancaster, N., 1982. Dunes on the Skeleton Coast, SWA/Namibia: geomorphology and grain size relationships. Earth Surface Processes and Landforms 7, 575–587. Lancaster, N., 1985. Variations in wind velocity and sand transport on the windward flanks of desert sand dunes. Sedimentology 32, 581–593. Lancaster, N., 1988. Controls of eolian dune size and spacing. Geology 16, 972–975. Lancaster, N., 1989. The Namib Sand Sea: Dune Forms, Processes and Sediments. A.A. Balkema, Rotterdam. Lancaster, N., Teller, J.T., 1988. Interdune deposits of the Namib Sand Sea. Sedimentary Geology 55, 91–107. Lancaster, N., Nickling, W.G., McKenna Neuman, C.K., Wyatt, V.E., 1996. Sediment flux and airflow on the stoss slope of a barchan dune. Geomorphology 17, 55–62. Livingstone, I., 1986. Geomorphological significance of wind flow patterns over a Namib linear dune. In: Nickling, W.G. (Ed.), Aeolian Geomorphology. Allen and Unwin, Boston, pp. 97–112. McKee, E.D., 1979. Introduction to a study of global sand seas. In: McKee, E.D. (Ed.), A Study of Global Sand Seas. United States Geological Survey Professional Paper, vol. 1052, pp. 3–19. McKenna Neuman, C., Lancaster, N., Nickling, W.G., 1997. Relations between dune morphology, air flow and sediment flux on reversing dunes, Silver Peak, Nevada. Sedimentology 44, 1103–1113. McKenna Neuman, C., Lancaster, N., Nickling, W.G., 2000. The effect of unsteady winds on sediment transport on the stoss slope of a transverse dune, Silver Peak, Nevada, USA. Sedimentology 47, 211–226. McLean, S.R., Smith, J.D., 1986. A model for flow over two-dimensional bed forms. Journal of Hydraulic Engineering 112, 300–317. McLean, S.R., Nelson, J.M., Wolfe, S.R., 1994. Turbulence structure over two-dimensional bed forms: implications for sediment transport. Journal of Geophysical Research 99 (C6), 12729–12747. McLean, S.R., Nelson, J.M., Shreve, R.L., 1996. Flow–sediment interactions in separating flows over bedforms. In: Ashworth, P.J., Bennett, S.J., Best, J.L., McLelland, S.J. (Eds.), Coherent Flow Structures in Open Channels. John Wiley and Sons, Chichester, pp. 203–226. Mulligan, K.R., 1988. Velocity profiles measured on the windward slope of a transverse dune. Earth Surface Processes and Landforms 13, 573–582. Nagtegaal, P.J.C., 1971. Adhesion-ripple and barchan-dune sands of the recent Namib (SW Africa) and Permian Rotliegend (NW Europe) Deserts. Madoqua Series II 2, 5–19. Nelson, J.M., Smith, J.D., 1989. Mechanics of flow over ripples and dunes. Journal of Geophysical Research 94 (C6), 8146–8162.


M.C. Baddock et al. / Geomorphology 87 (2007) 322–336

Nelson, J.M., McLean, S.R., Wolfe, S.R., 1993. Mean flow and turbulence fields over two-dimensional bed forms. Water Resources Research 29, 3935–3953. Nickling, W.G., McKenna Neuman, C., Lancaster, N., 2002. Grainfall processes in the lee of transverse dunes, Silver Peak, Nevada. Sedimentology 49, 191–209. Schwämmle, V., Herrmann, H., 2004. Modelling transverse dunes. Earth Surface Processes and Landforms 29, 769–784. Slattery, M.C., 1990. Barchan migration on Kuiseb River Delta, Namibia. South African Geographical Journal 72, 5–10. Sweet, M.L., Kocurek, G., 1990. An empirical model of aeolian dune lee-face airflow. Sedimentology 37, 1023–1038. Tsoar, H., 1985. Profiles analysis of sand dunes and their steady state signification. Geografiska Annaler 67A, 47–59. Walker, I.J., 1999. Secondary airflow and sediment transport in the lee of a reversing dune. Earth Surface Processes and Landforms 24, 437–448.

Walker, I.J., Nickling, W.G., 2002. Dynamics of secondary airflow and sediment transport over and in the lee of transverse dunes. Progress in Physical Geography 26, 47–75. Walker, I.J., Nickling, W.G., 2003. Simulation and measurement of surface shear stress over isolated and closely spaced transverse dunes in a wind tunnel. Earth Surface Processes and Landforms 28, 1111–1124. Wiggs, G.F.S., 1993. Desert dunes dynamics and the evaluation of shear velocity. In: Pye, K. (Ed.), The Dynamics and Environmental Context of Aeolian Sedimentary Systems. Geological Society Special Publication, vol. 72. Geological Society, London, pp. 37–48. Wiggs, G.F.S., 2001. Desert dune processes and dynamics. Progress in Physical Geography 25, 55–81. Wiggs, G.F.S., Livingstone, I., Warren, A., 1996. The role of streamline curvature in sand dune dynamics: evidence from field and wind tunnel measurements. Geomorphology 17, 29–46.