Characterization of three-dimensional (3D) airflow remains elusive within a variety of environments and is particularly challenging over complex dune topography. Previous work examining airflow over and in the lee of dunes has been restricted to two-dimensional studies and has concentrated on dune shapes containing angle of repose lee sides only. However, the presence of vegetation in coastal dunes creates topographic differences and irregular shapes that interfere with flow separation at the crest and significantly modify lee-side airflow patterns and potential transport. This paper presents the first 3D field characterization of airflow patterns at the lee side of a subaerial dune. Flow information was obtained using an array of 3D ultrasonic anemometers deployed over a beach surface during seven offshore wind events. Data were used to measure cross-shore and alongshore lee-side airflow patterns using the three dimensions of the wind vector. Distances to re-attachment were similar to previous studies, but the range of transverse incident wind directions resulting in flow separation (0+/−35°) was almost twice that previously reported (0+/−20°). Airflow reversal took place with winds as slow as 1 m s−1. Transverse offshore winds generated areas of opposing wind directions both within the reversed zone and beyond re-attachment, contrary to consistent deflection in only one direction found in transverse desert dunes. Patterns of flow convergence-divergence have been reported in fluvial studies. However, while convergence was associated with weak reversal in fluvial settings, it appeared to be related to strong flow reversal here and could be produced by pressure differentials at the dune crest.
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Table of symbols. The subscript i indicates instantaneous measurement, and its absence corresponds to 5 min average values. The subscripts C and L stand for dune “crest” and “lee side”, respectively. All values are expressed in International System Units with the exception of angles expressed in degrees.
Cartesian component of wind vector along x axis (m s−1); aligned perpendicular to the dune crest and positive offshore
Cartesian component of wind vector along y axis (m s−1); aligned perpendicular to u and positive alongshore to the West
Cartesian component of wind vector along z axis (m s−1); aligned perpendicular to the horizontal plane formed by u,v and positive upwards
horizontal flow vector angle (angle between u,v) (°)
vertical flow vector angle (angle between u,w) (°)
horizontal wind direction (dirh = 180 – α) (°)
“vertical” wind direction (directional data in the U-V plane) (dirv = 180 – β) (°)
wind speed (m s−1)
dune height (m)
dune height measured at the re-attachment point (m)
horizontal length from the dune crest to the dune toe, measured parallel to the wind direction (m)
Lee-slope dune angle (°)
distance to re-attachment from the dune crest (m)
dune aspect ratio (h/L)
 There has been significant progress in understanding lee-side flow dynamics of fluvial and aeolian bedforms. In rivers, the role of flow separation and reversal in bed morphology [McLean and Smith, 1986; Nelson and Smith, 1989; Nelson et al., 1993, 1995] and modes of sediment transport [McLean et al., 1994; Venditti and Bennett, 2000; Kostaschuk and Villard, 1996; Best and Kostaschuk, 2002] have been widely investigated. The differences between the fast flow at the dune crest and the slow flow in the recirculation cell generate eddy-like coherent structures that are “injected” in the flow downstream [Venditti and Bauer, 2005] and are related with macro turbulence and sediment suspension in the water column [Best et al., 2010]. In deserts, lee-side airflow patterns play a part in controlling spacing between migrating bedforms [Werner and Kocurek, 1999; Walker and Nickling, 2002; Kocurek et al., 2010], maintaining dune steepness and preventing dune erosion [Walker, 1999, 2000], regulating the dynamics of transverse dune interdunes [Baddock et al., 2007], and ejecting new barchans downwind [Hugenholtz and Barchyn, 2012]. Stratification on the lee side of aeolian dunes is often preserved in the rock record and hence important in geological studies [Frank and Kocurek, 1996a]. In coastlines with low, rounded foredune morphologies, lee-side airflows play a negligible role in sediment transport dynamics [Nordstrom et al., 1996; Walker et al., 2006] and lee-side wind speeds are often under the threshold of sand movement [Gares et al., 1993]. In coastlines with high, sharp-crested foredunes and relatively small grain sizes, offshore winds have the potential to deliver sediment from the beach into the foredune through the process of flow separation and reversal [Jackson et al., 2011], which can result in significant landward sediment transport and may account for a viable portion of the total sediment budget [Lynch et al., 2008, 2009, 2010]. Excellent reviews of flow patterns over dunes may be found in Walker and Nickling , Best [2005a], and Livingstone et al. .
 Despite this wealth of knowledge, the full characterization of three-dimensional (3D) lee-side flow and its effects on sediment transport remains elusive [Best, 2005b; Jackson et al., 2011]. Most work to date has been conducted over relatively simple two-dimensional (2D) transects, with straight dunes and smooth lee-side slopes that do not influence flow separation at the crest. Straight, regular-crested dunes are relatively easier to simulate both with water in the flume [e.g., Engel, 1981; Davies, 1982; Nelson et al., 1993; Bennett and Best, 1995; Best and Kostaschuk, 2002] and in the wind tunnel [e.g., Walker and Nickling, 2003; Dong et al., 2007, 2009]. The majority of lee-side flow numerical modeling has also been developed for 2D scenarios both over fluvial [e.g., McLean and Smith, 1986; Nelson and Smith, 1989] and aeolian dunes [e.g., Armalay et al., 1983; Le et al., 1997; Parsons et al., 2004a, 2004b; Schatz and Herrmann, 2006; Safarzadeh et al., 2009; Bechmann and Sørensen, 2010; Wakes et al., 2010]. Recent studies in natural rivers [Parsons et al., 2005] and flumes [Maddux et al., 2003; Venditti, 2007] suggest, however, that the spatial distribution of turbulence and the flow velocity field is strongly affected by 3D river bed morphologies. In aeolian settings, computational fluid dynamic (CFD) simulations [Beyers et al., 2010; Jackson et al., 2011; Smyth et al., 2011, 2012] suggest complex interactions between 3D dune morphologies and airflow, but there are currently no field data on lee-side airflow three dimensionality for transverse dunes.
 A principal issue in aeolian settings subjected to complex 3D lee-side airflow patterns is the need for multiple observations at relatively fine spatial resolutions compared to fluvial settings. In rivers, the focus of interest is likely more concerned with the role played by 3D bed morphologies in controlling dune shapes downstream or flow characteristics in the water column over the dune field [Parsons et al., 2005], as these are linked with considerable differences in overall flow resistance [Venditti, 2007] and turbulence [Maddux et al., 2003], and hence sediment entrainment and transport downstream. In many subaerial field settings, the interest lies within the separation zone and the strength of the reversed flow over the surface, rather than in the air column above the dune field. For example, during offshore wind events over coastal dunes with lee-side airflow separation and reversal [Jackson et al., 2011], the entire beach surface may be within the separating bubble. It is imperative to understand in detail those airflow processes that are within the area landward of the re-attachment point. It is the strength and spatio-temporal variability of the reversed flow and its transport potential over the surface inside the separation zone that has geomorphological implications [Lynch et al., 2008, 2009, 2010].
 Most studies on lee-side airflows have only defined the separation zone and the re-attachment point in two dimensions, and/or have inferred the extent of the wake and other lee-side airflow zones indirectly. The distance to re-attachment, for example, was identified based on overall shape of velocity profiles [Frank and Kocurek, 1996a], variations of shear stress [Walker, 2000; Walker and Nickling, 2003], and/or changes in wind direction [Sweet and Kocurek, 1990; Walker, 1999; Baddock et al., 2011; Jackson et al., 2011]. A spatially detailed (every 5 m) and direct, quantitative visualization of lee-side airflow zones average was conducted recently in coastal dunes by Delgado-Fernandez et al.  using a simple comparison of average downstream (u) and vertical (w) velocities (Figure 1b). However, and despite the current availability of 3D ultrasonic anemometers (UAs) [van Boxel et al., 2004; Walker, 2005], there is no field evidence of the effect of 3D dune morphologies on the spatial and temporal variability of the 3D wind vector over the lee-side surface. This is likely related to field limitations such as the need for large numbers of UAs over a wide area to ensure appropriate spatial coverage, which supports the development of alternative approaches such as CFD simulations [Beyers et al., 2010; Jackson et al., 2011; Smyth et al., 2011, 2012].
 This paper presents comprehensive results from a 10 day field experiment conducted at the lee (beach) side of a coastal foredune using an extensive grid of UAs. The objectives of this paper are to (1) provide the first 3D quantitative flow visualization of mean lee-side airflow patterns in a field setting and compare findings with previous literature, (2) examine the geomorphologic implications of flow three dimensionality and discuss potential similarities/differences between airflow patterns observed at a coastal setting versus other environments, and (3) discuss methodological and theoretical limitations as a result of the findings presented here. Section 2 reviews models by Walker and Nickling  and Sweet and Kocurek  and previous findings on flow three dimensionality. Results include an analysis of 3D lee-side airflow patterns across a dune transect (section 5.1) and over a beach surface (section 5.2), and their relation with wind speed and direction and dune aspect ratio. Section 5.3 presents patterns of wind speed, and section 6.1 discusses their potential implications for sediment input to the dunes. The origin of three dimensionality and its implications in field experiments and data processing are discussed in sections 6.2 and 6.3
2.1 2D Description of Lee-Side Airflows
 As the airflow approaches a high, sharp-crested dune, it propels over the crest (overshoots) as a result of airflow compression and acceleration up the stoss slope [Figure 1A; Walker and Nickling, 2002]. This results in airflow separation from the underlying surface and the formation of a “wake” region within which the airflow is reversed. Downstream from the dune crest the airflow rejoins the surface (re-attachment point) at a distance (r) that varies slightly with the environment, with r ≈ 4–8 times the dune height (h) for desert dunes [Frank and Kocurek, 1996b], r ≈ 5–10h for broad hills [Cooke et al., 1993] and dunes simulated in wind tunnels [Walker, 2000], or r ≈ 4h from computer simulations [Beyers et al., 2010; Jackson et al., 2011] and coastal dunes [Delgado-Fernandez et al., 2011]. The re-attachment point is in practice a re-attachment zone with an estimated width of ≈ 0.5h [Walker, 2000; Walker and Nickling, 2003]. An inner boundary layer (IBL) develops beyond re-attachment [Walker and Nickling, 2002], with implications for velocity profiles [Frank and Kocurek, 1996a].
 In an extensive study involving different dune morphologies at three desert dune fields, Sweet and Kocurek  observed that the nature of lee-side airflows was controlled by (1) the incident wind angle at the dune crest (αC), (2) dune shape, characterized by the lee-slope angle (λ) and the aspect ratio (AR = h/L, where L is the horizontal distance from the dune crest to the dune toe), and (3) atmospheric stability. Trade-offs between the three controls resulted in three broad types of lee-side airflow: (1) separated, (2) attached and deflected, and (3) attached and not deflected. Figure 1C shows a modified version by Walker and Nickling  of the original diagram of Sweet and Kocurek . In general terms, airflow separation was related to αC normal to the dune crest, increases in AR, and strong reductions in lee-side airflow speed (SL less than 30% of incident wind speed, SC). Sweet and Kocurek  suggested that separated airflows switched toward “attached and deflected” at αC > 20°. This is a lower threshold compared to that proposed by Allen , who attributed “roller” vortices to αC < 45° and “helical” vortices to αC > 45° (Figure 1D).
2.2 Three Dimensionality
Walker and Nickling  suggested that Allen's  rollers and helical vortices are the 3D lateral extensions of the lee-side back-eddies shown in Figure 1A, which generate consistent patterns of airflow deflection and sediment transport within interdune corridors of transverse ridges [Walker, 1999, 2000]. Recent CFD and fluvial studies suggested, however, that the interaction between flow and crest irregularities or 3D morphologies produces recirculation zones that are strongly non-2D, with lateral flows and secondary recirculation zones [Maddux et al., 2003; Best, 2005b; Jackson et al., 2011].
Best [2005a] highlighted the three dimensionality in river dune shapes and its effect on turbulence as one of the five areas where future research should focus. When present, three dimensionality generates both flow parallel and spanwise vorticity and complex areas of flow convergence and divergence [Allen, 1968]. Flume experiments by Maddux et al.  showed that 3D dune morphologies were associated with larger friction coefficients but less turbulence compared to 2D dune morphologies. Parsons et al.  also suggested that river beds with 3D dunes had smaller levels of large-scale turbulence, which could lead to less suspension of bed sediment and a reduction of overall sediment transport. A detailed flume study by Venditti  revealed that dunes with convex (lobes) versus concave (saddles) plan forms introduced opposite effects in downstream turbulence. Lobes caused lateral and vertical divergence of momentum and energy which resulted in lower mean velocities but stronger wake regions with higher turbulent intensities. Saddles caused a convergence of flow in the hollow which resulted in less energy extraction from the mean flow, higher velocities, and decreases in turbulence, with small or absent wakes and separation zones. Venditti  suggested that these patterns were complicated even further by the existence of regular versus irregular dune plan form shape patterns, with irregularly arranged lobes and saddle plan forms having similar effects on flow patterns. Beyers et al.  and Jackson et al.  used CFD techniques to simulate airflow over detailed 3D coastal dune topography and found alongshore heterogeneous patterns of airflow reversal and deflection at the beach surface. Even under directly offshore (transverse) winds, the airflow responded to dune heterogeneities in ways that would not be immediately obvious during 2D experiments concentrated along a dune cross section. Interestingly, plan form patterns of flow deflection observed by Jackson et al.  in a coastal setting seemed opposite to those described by Venditti  in the flume. While stronger wake regions were still associated with lower mean velocities, these areas showed flow convergence, not divergence as in the flume case.
 The data presented in this paper allow detailed exploration of the role of incident wind directions (αC) and speeds (SC) in generating lee-side separation flow and turbulence at a coastal dune site with 3D dune forms. The study area corresponds to a section of the coast with relatively small changes in h (from 10–12 m compared to desert dunes of 2–60 m studied by Sweet and Kocurek  and thus allows only partial discussion of the role played by the AR. Atmospheric stability conditions can usually be considered neutral in mid-latitude coastal environments, as thermal buoyancy effects are negligible relative to the strong mechanical turbulence of the boundary layer flow.
3 Study Site
 Data were collected during a short-term field experiment at Magilligan Strand, Northern Ireland (Figure 2). The strand is oriented NW-SE and is approximately 6 km long. The beach is up to 100 m wide during low tide and displays a dissipative, planar topography due to the effect of high energy Atlantic swell waves [Jackson et al., 2005]. The coast is microtidal with a tidal range of approximately 1.6 m. Beach sediment consists predominantly of very well sorted quartz sand with a mean grain diameter of 0.17 mm. The foredune ranges in height from 6 to 12 m, and it is densely vegetated by Ammophila arenaria of approximately 0.4 m in height. A well-formed embryo dune approximately 1 m high by 3 m wide was present at the site during the experiment. Prevailing winds are from the SW (offshore) and are thought to dominate the aeolian system [Jackson et al., 2011]. Lynch et al.  reported significant secondary airflow effects at sections along Magilligan Strand where the foredune was of sufficient height (> 10 m) and the sharpness of the dune crest introduced abrupt changes in topography. Hence, the experimental site for this study was located at a section of the beach-dune system where the foredune crest reaches its highest (10–12 m) and where previous high-frequency wind measurements and CFD modelling have reported airflow separation under offshore winds [Beyers et al., 2010; Jackson et al., 2011; Delgado-Fernandez et al., 2011].
4 Material and Methods
4.1 Instrumentation and Data Collection
 The experiment was carried out between 25 April and 5 May 5, 2010. A total of seven offshore wind events were monitored, resulting in approximately 111 h of different incident wind speeds and directions. Twenty four UAs (3D Gill HS-50 model) were deployed in a grid extending 90 m alongshore by 60 m cross-shore (Figure 3). This particular field deployment was based on preliminary CFD simulations and field data indicating the extent of the reversed and re-attached zones [Jackson et al., 2011]. Nineteen UAs were placed at 0.5 m elevations over the beach surface (Figure 4A). The height of the UAs over the surface was similar to that adopted by Lynch et al.  and was deemed adequate for avoiding sediment transport abrasion during strong winds while providing measurements of wind airflow close to the surface. Instruments were spaced every 10 m along profiles A, C, and D, and every 5 m along profile B. The alongshore distance between profiles was 30 m. Four UAs at elevations of 0.5, 1, 2, and 4 m over the beach surface were also deployed in a vertical array at position B2, at an approximate horizontal distance of 35 m from the dune crest (Figure 4B). This location coincided with the location of mast 6 in Jackson et al.  where previous data suggested the presence of a well-developed area of flow reversal in the vertical. Only one vertical mast was deployed during this study to maximize the alongshore and cross-shore deployment of UAs over the beach surface. While thislimited the understanding of the vertical structure of the airflow to one location, it allowed the collection of synchronized airflow data over an extensive grid, especially near the surface where it is important for sediment transport. The most landward UA was mounted on a 6 m high mast on top of the dune crest, providing a total mean elevation of 18 m over the beach surface. Previous analysis by Jackson et al.  suggested that wind recorded at 6 m over the dune crest was a reliable reference for free stream wind speed and direction. Some UAs located closer to the shoreline (rows 3 and 4 in Figure 3) needed to be removed during high spring tides and wave run-up which resulted in some measuring periods containing fewer UAs (Table 1). All instruments were connected through a series of terminals to a computer interface located in a trailer at the back beach at a distance far enough to avoid interference with wind measurements. Instruments measured at 25 Hz with data streamed real-time back to the central PC which allowed precise synchronization of the output files with the PC's time. A Trimble 4800 Differential Global Positioning System (DGPS) was used to map instrument positions and obtain a detailed topographic survey of the entire study site (Figure 3).
Table 1. Summary of Data Collected During the Experiment in April–May 2010a
Date - Duration
N. of UAs
N. 5 min records
The total duration of all events was ≈ 111 h (1292 5 min records); UA: 3D ultrasonic anemometer; αC: incident horizontal wind angle (°), positive when the airflow is deflected anticlockwise (in a top-down view) from crest-normal (αC = 0°); SC: wind speed (m s−1) at the dune crest.
25 April – 3.2h
−32 to −15
25 April – 20.7h
−173 to 176
27 April – 23.3h
−32 to 22
29 April – 16.2h
−105 to 145
3 May – 21h
−145 to −37
4 May – 4.2h
−91 to −57
4 May – 18.2h
−167 to 154
4.2 UA Data Handling
 UAs allow the collection of rich data sets of the three orthogonal components of the wind vector, u, v, w at very high frequencies. These may be used to derive turbulent parameters such as Reynolds shear stress [Baddock et al., 2011; Weaver and Wiggs, 2011; Chapman et al., 2012] and/or to “visualize” the wind vector. While the first necessitates the rotation of the frame of reference onto the streamlines [van Boxel et al., 2004; Walker, 2005] the second is straightforward and consists of determining the angles of the (instantaneous) wind vector relative to a “fixed” (un-rotated) coordinate system. During the experiment, UAs were oriented in the same direction at the beach and levelled with respect to the horizontal gravity plane. A right-handed Cartesian coordinate system was defined for all UAs such that u was aligned perpendicular to the dune crest and positive offshore, v was perpendicular to u and positive alongshore to the West, and w was perpendicular to the horizontal plane formed by u, v, and positive upwards. Calculation of the horizontal flow vector angle (α) (equation (1)) and the vertical flow vector angle (β) (equation (2)) were conducted over the original 25 Hz data (i.e., using instantaneous values, denoted by i). Both angles should be calculated using the atan2 function which allows resolving angles from 0 to ±180°:
 The instantaneous wind speed (Si) was calculated using the three coordinates of the wind vector:
 UAs were sampled at 25 Hz, and thus the resulting time series may be used to explore high-frequency variability of any of the wind variables (ui, vi, wi, Si, αi, βi). For the purpose of unravelling mean streamline behavior, the original three Cartesian components of the wind vector (ui, vi, wi) were averaged into 5 min records, which were subsequently used to recalculate flow angles and wind speed. Table 1 lists the number of 5 min records for each event, adding to a total of 1292 records over the seven monitored offshore wind events. The minimum wind speed at the dune crest, SC, was 0.8 m s−1, and the maximum was 15.5 m s−1. Wind direction at the dune crest was variable with 80% of the winds approaching the dune at an incident angle of αC ≈ 6 to −90°. Similar to the procedure adopted by Jackson et al. , it was possible to bin 5 min records depending on αC and isolate corresponding synchronized records at each of the sensor locations, which permits exploration of lee-side airflow patterns under different wind scenarios. These were graphed using directional data in the horizontal (dirh) and vertical (dirv) planes which were obtained from the opposites of the horizontal (dirh = 180 - αα) and vertical (dirv = 180 – β) wind angles, respectively. Note that while the resultant 5 min average uvw wind vector could be plotted alone at measurement locations, the large amount of 5 min records conveyed in the resulting figures would have made the graphs illegible. Alternatively, a mean uvw wind vector could have been plotted for each of the wind scenarios presented in section 5, but this would have hampered rich information on the variability of wind directionality at each of the sensors locations. Hence, and in line with a number of studies [e.g., Sweet and Kocurek, 1990; Lynch et al., 2009, 2010; Jackson et al., 2011], conventional wind roses were used to present the full degree of wind vertical and horizontal variability at each of the sensors locations (Figures 6-9). Supporting information for this article contains three tables with the values of flow vectors at each of the sensors locations.
4.3 Morphological Parameters
 Dune morphological attributes were measured after Sweet and Kocurek . Figure 5 displays profiles A–D and the definition of dune height (h), length (L), and lee-side slope angle (λ) adapted for this study. An accurate quantification of these three parameters may be difficult in coastal foredunes as it involves oversimplifications and the use of relatively undefined boundaries. The majority of desert dunes monitored by Sweet and Kocurek  presented a lee-side face with considerably long distances and gentle slopes (< 10°) between the dune crest and the dune brink, and steep slopes from the brink to the dune toe. Thus, those authors measured λ as the angle between the brink-to-toe face and the horizontal plane. Many desert and asymmetrical fluvial dunes are characterized by angle of repose lee-side slopes of 20–35° that generate well-developed separation zones of permanent, recirculating flow [Bagnold, 1941; Sweet and Kocurek, 1990; Roden, 1998; Kostaschuk, 2000, Best and Kostaschuk, 2002]. However, seaward faces of foredunes are often quite complex with morphologies that reflect the combined effect of processes other than wind and aeolian transport. These include wave scarping or vegetation growth, which can produce dune sections with considerably larger seaward angles. Profile B in Figure 5, for example, reflects a history of recent foredune erosion by waves, followed by the growth of an embryo dune at approximately 10 m and the subsequent growth of a newer embryo dune at approximately 25 m from the foredune crest taking place over 2 years. The location of the dune toe is also somewhat difficult to define as the dune-beach intersection may lack a sharp change in slope, especially when a dune ramp or embryo dune is present. Also, the beach itself is not usually flat, which affects the relation between the dune crest height and the distance to re-attachment (r). Due to beach slope, the dune crest elevation measured at the re-attachment point (hr) may be considerably higher than that measured at the dune toe (h). This changes the relation r = Xh (see section 2.1), X being the “number of dune heights” needed to reach the re-attachment point. As it is not possible to measure hr prior to knowing r itself, and AR is a morphological descriptor, h was used in calculations of morphological parameters, and hr was used in comparisons with observed r. Finally, L (and hence λ) depends on αC, and so it was measured parallel to the incident wind direction. Dune steepness and the presence of vegetation preclude differences in the distance to re-attachment due to grain size differences [Engel, 1981]. Table 2 summarizes measured and calculated morphological values considered in this study.
Table 2. Numerical Values for the Morphological Variables Used in This Studya
See Figure 5 for definitions; h: dune height (m); L: dune length (m); λ: lee-side (seaward) slope (°); AR: aspect ratio; r: distance to re-attachment (m); hr: dune height at the re-attachment point (m); Pr: profile number. Subscripts 0, −25, and −50 indicate corresponding incident horizontal wind angles at the dune crest (αC). No clear flow reversal was observed in profiles B–D for αC = −50 (NA stands for “not applicable”).
5.1 Quantitative 3D Airflow Visualization Across a 2D Transect
 Figure 6 displays results for αC = 0+/−5° along profile B, where the location of UAs every 5 m allowed detailed monitoring of lee-side airflow zones. In line with previous studies [Walker and Nickling, 2002; Delgado-Fernandez et al., 2011], dirv (cross-section view) followed a series of complex patterns that resulted in overshoot (positive β) at the dune crest and airflow re-attachment (negative β) at a distance of approximately 45 m from the dune crest (r ≈ 4.3hr). This fits well with observations by Frank and Kocurek  and Walker  in aeolian dunes, McLean and Smith  and Nelson and Smith  in fluvial dunes, and CFD simulations by Jackson et al. , with re-attached zones of 4–8h. The transition from reversed airflow (40 m) to re-attached airflow (45 m) was clear both from the increase in dirh variability (plan view) and opposite dirv (cross section view). Vertical directions, however, showed a sharper zonation and suggested that the transition zone might be more defined and slightly narrower (≈ 0.4h) than that observed in previous studies [e.g., Walker and Nickling, 2002]. The IBL zone was characterized by a series of downward and upward streamline movements (see section 6.2) and a gradual change of dirh toward almost directly offshore at 60–65 m from the dune crest. Despite the constant αC, airflow across this transect was consistently steered to the west (plan view). The vertical array of UAs suggests that the area of airflow reversal was at least 2 m high at 35 m from the dune crest.
5.1.1 Changes With Incident Wind Speed
 Wind speed at the dune crest (SC) for αC = 0+/−5° varied from 1 to almost 13 m s−1. To explore the effects of increasing SC, wind speeds were binned into three scenarios: “slow” (SC < 4 m s−1), “medium” (4 ≤ SC < 8 m s−1), and “fast” (SC ≥ 8 m s−1). Figure 7 shows wind angles along profile B for the three cases and ranges of wind speed at the dune lee side (SL) at 30 (reversed), 45 (re-attached), and 65 m (IBL) distances from dune crest. There was no relation between increasing SC and the location of the main lee-side airflow zones in general. UAs positioned at 30, 35, and 40 m were consistently within the reversed zone, and UAs beyond 50 m were within the re-attached zone, regardless of wind speed at the dune crest. The only sensor that reflected changes was the UA at 45 m, which recorded dirh and dirv characteristic of a transition zone during low SC, but shifted to re-attachment during medium and high SC. At low SC, the transition zone was ≈ 10 m and contained wind speeds of SL = 0.5−1.3 m s−1. At SC > 4 m s−1, the transition zone narrowed to less than 5 m and a clearer re-attachment point with faster wind speeds appeared at 45 m. The degree of dirh steering at 40 m also varied. The wind was onshore in the three cases but more oblique at high SC. Interestingly, SL was very similar along the profile under the three different scenarios. Further research with wind speeds faster than the ones recorded here is needed, but the results suggest that lee-side airflow zones existed at approximately the same distance downwind from the dune crest under winds of SC < 4 m s−1 and winds of SC up to 13 m s−1. Therefore, the extent of the reversed flow area under offshore events will likely be the same for fast and slow winds.
5.1.2 Changes With Wind Direction
 Figures 8A and 8B display dirh and dirv for oblique offshore winds from the SW, corresponding to αC = −25° and αC = −50° (+/−5°), respectively. The dataset did not contain enough wind data of αC = 25° or αC = 50° (from the South East), and thus these were not analyzed. The distribution of lee-side airflow zones during αC = −25° (Figure 8A) did not change substantially with respect to αC = 0°. Airflow re-attachment still occurred at 45 m but the UA at 40 m showed highly variable dirv characteristic of a transition zone. In contrast, the dirh at this location was quite constant and was consistently deflected alongshore. Changes in the distribution of lee-side airflow zones were more clear for αC = −50° (Figure 8B). The reversed zone disappeared almost completely from profile B, both cross-shore and vertically, with the only exception of a narrower and less clear zone of airflow reversal at 30 m. At this location, the airflow was directed downward and slightly onshore but mostly steered parallel to the dune toe. The extremely low variability of dirh cross-shore contrasts with a significant variability of the dirv, with a clear sequence of upward and downward movements beyond re-attachment (see section 6.2). In general, patterns in dirh agree well with Beyers et al.  and Jackson et al. , who measured similar changes in lee-side airflows at the same location for winds of αC = 0° (direction respect to the geographical north of ≈ 217°) and αC = −50° (≈ 270°).
5.2 Quantitative 3D Airflow Visualization Over a 3D Surface
 Figures 6 and 7 indicate that transitions from one zone to another may occur within less than 5 m and thus larger spacing between sensors of 10 m likely missed information along profiles A, C, and D (Figure 3). However, it is possible to assume a logical sequence of airflow processes similar to profile B in Figure 6 and approximate distances from the dune crest to different lee-side airflow zones depending on the information given by on-site sensors. Figure 9 shows alongshore variations of dirh and dirv for αC = 0+/−5°. Note that only the UAs at 35, 45, 55, and 65 m from profile B have been included in this figure as these are aligned with other sensors in the rest of the profiles. At each location, dirv (wind roses with no circular axis) have been superimposed on top of dirh (wind roses with circular axis). The sequence of lee-side airflow zones was repeated in all profiles but the distance to re-attachment (r) increased toward profile D. Sensors located at 45 m recorded re-attached airflow in profiles A-B, a mix of onshore-offshore directions characteristic of the transition zone in profile C, and reversed airflow in profile D. The AR increased slightly from profiles A to C and was largest in profile D, as a result of the increase in h (see Figure 5). Values of r were estimated by considering a range which upper limit was the position of the first sensor measuring re-attachment along a given profile and which lower limit was 5 m less (i.e. a few meters after airflow reversal or transition). The increase of r from profiles A (40–45 m) to D (50–55 m) seems to follow the AR (and hence h) along this section of the coastline and is in line with ranges given in other studies [e.g., Walker and Nickling, 2002]. Interestingly, the variability of dirh suggests complex patterns of wind steering along the beach, both within the reversed zone and beyond re-attachment. Wind directions within the reversed zone shifted from the NE in line A to the NW in line D. Similarly, dirh changed from the SE in profile A to the SW in profile D within the IBL zone. Possible explanations for this include complex submeter airflow patterns related to heterogeneities in the dune crest morphology and are discussed in section 6.2.
 Figures 8C and 8D display dirh and dirv for oblique offshore winds from the SW, corresponding to αC = −25° and αC = −50° (+/−5°) respectively. As in the cross-shore case, the distribution of lee-side airflow zones during αC = −25° (Figure 8C) did not change substantially with respect to αC = 0° (Figure 9). There was a clear zone of airflow reversal at the back beach and the distances to re-attachment were essentially similar. The average AR during αC = −25° was 0.25, and there was consistent airflow steering in the same direction within the reversed zone (from the NW) and within the IBL zone (from the SW). The largest differences in dirv were registered by UAs in positions C2 and D2, which switched from transition to reversed airflow and vice versa. Also, similar to the cross-shore case, changes in the distribution of lee-side airflow zones were clearer for αC = −50° (Figure 8D), with an average AR ≈ 0.18. The reversed zone disappeared or became quite constricted in width. The only UA that showed reversal was A1 while C1 was located within the transition zone. The change in direction at the dune crest had thus the effect of “compressing” the sequence of lee-side airflow zones (to their disappearance in some profiles) and steering the airflow parallel to the dune toe at the back beach. Finally, a strong spatial variability of upward/downward dirv movements was clear for both scenarios, especially for αC = −50°. This sequence of positive and negative β angles within the IBL zone may be related to the development of complex vortex structures, which are discussed in section 6.2
5.3 Patterns of Wind Speed at the Beach Surface
 Previous analysis conducted by Jackson et al.  indicated a strong relationship between SC and SL as measured by UAs at different locations over the beach surface, both under perpendicular and oblique offshore incident wind directions. This was confirmed by linear regression analyses conducted at all sensors locations within this study. Table 3 displays an example of some of the calculated R2 values for αC = 0°, ranging from 0.73 (D3) to 0.9 (B1) with an average of 0.81 (p-values ≤ 0.0 in all cases). Results were similar for αC = −25° and αC = −50°, with R2 values ranging from 0.72 to 0.93. Figure 10 shows the reduction of wind speed at the beach surface with respect to that measured at the dune crest (average SL/SC for each UA). Wind speed at the beach was approximately 30% of that at the dune crest for αC = 0° and 35% for αC = −25°. Wind speed patterns were more heterogeneous during αC = −50°, but SL was in average approximately 50% of SC. This is in line with results by Sweet and Kocurek , who found that SL < 30% under transverse winds with airflow separation.
Table 3. Relation Between Wind Speed at the Dune Crest and Over the Beach Surfacea
Example of R2 values (p-values ≤ 0.0 in all cases) obtained from linear regression analysis between wind speed at the dune crest (SC) and wind speed at different locations over the beach surface (SL) for perpendicular offshore winds (αC = 0°) during event 3 (see Table 1). The number of 5 min records considered in the regression analysis was 72, and the range of SC was 4.5–12.5 m s−1. Note that with the exception of D3, all R2 values were above 0.75, suggesting a strong relation between SC and SL at each of the sensors locations.
αC = 0°
6.1 Thresholds for Changes in Lee-side Airflows and Implications for Potential Leeward Transport
 Analyses conducted in this paper suggest that airflow separation at the dune crest and reversal at the back beach occurred at a SC as low as 1 to 4 m s−1 (Figure 7). Despite the large range of incident SC, results did not indicate a minimum threshold of SC at which no airflow separation occurs, which is in line with previous observations by Sweet and Kocurek , Walker and Nickling , and Delgado-Fernandez et al. 
 Thresholds in wind direction were, however, different from values reported in the literature. Sweet and Kocurek  suggested that αC = 0° to 20° result in separated airflows for AR > 0.2 under neutral atmospheric conditions, and αC = 20° to 80° result in attached airflow independently of the dune shape (Figure 1C). Allen  suggested the formation of closed loop roller vortexes with αC = 0° to 45° and helical vortexes with αC > 45° (Figure 1D). Figure 8 shows that there were no substantial changes in the location of lee-side airflow zones at the beach surface as αC switched from 0 to −25°, but reversal almost completely disappeared from the back beach with αC = −50°. In order to refine the exact moment in dirh associated with these changes, two sensors at 35 m in profiles B and D were selected (see Figure 3 for UAs locations). These recorded reversed airflows when αC = 0° and αC = −25° but switched to reattached airflows when αC = −50°. Figure 11 shows scatter plots of αC versus β and α. At this point, all wind records have been included in the graphs, including those for onshore winds to enrich the discussion (i.e., αC = −90° to −180°). Changes in β for both sensors were clear at approximately αC = −30° to −40°, with a change from reversed onshore (β > +/−90°) to re-attached airflow (β < +/−90°). The wind remained re-attached for αC = −40° to αC ≈ −100°, when it “reversed” due to incident onshore winds. Changes in α showed the same trends but were more gradual. Interestingly, the airflow was never perfectly offshore at these two locations but remained steered alongshore during αC ≈ −35° to αC ≈ 120°. The threshold of αC ≈ −30° to −40° separating reversed versus re-attached airflows at 35 m found in this study is hence half way between values reported by Sweet and Kocurek  and Allen  (note that comparisons are made based on absolute values, as the previous authors reported angles with no sign). Figure 8 suggests, however, that a clear distinction between separated versus attached airflow in the field may be difficult. Sensors at A1 and B1 recorded streamline slopes typical of separated and reversed airflows even under αC = −50°, suggesting complex mix of lee-side airflow patterns with possible coexistence of areas of separated airflow and areas of attached-deflected airflows.
 On average, r ≈ 45 m for αC = 0°, which means that there was a relatively wide area (≈ 15 m from the embryo dune toe) of beach surface where bare sediment could have been entrained and transported back to the dune by reversed airflows (Figure 10). This area was less defined and much narrower in the case of αC = −50° but contained stronger winds compared to the perpendicular case. Winds of αC = −25° also resulted in a wide reversed zone, with slightly faster wind speeds compared to the perpendicular case, and containing a more “steered” airflow behavior. This is there seems to be a trade-off between the size of the area containing reversed airflows and how fast they are depending on αC. Sweet and Kocurek  suggested that SL could be calculated from SC by using a cosine function of the incident αC. This paper proposes an exponential rather the cosine function because the latest results in SL = 0 m s−1 for αC = 0°. Data from sensors at 35 m used in section 6.1 (B2 and D1) were used again as an example to examine the relationship between SL, SC, and αC. Figure 12 shows scatter plots of relative airflow speed (SL/SC) versus αC, with the best achieved by an exponential trend line with the following general form:
Jackson et al.  calculated the threshold shear velocity for dry sand of 0.17 mm at the site as ≈ 0.19 m s−1 and used this to speculate over calculations of threshold wind velocities at different heights assuming a logarithmic profile close to the surface. Details can be found in Jackson et al.'s section on “Geomorphological implications”. Their procedure allows approximating a mean wind threshold value for dry sand at 0.5 m over the beach surface of ≈ 2.8 m s−1. This corresponds to SC = 10.8 m s−1 for αC = 0°, SC = 8.4 m s−1 for αC = −25°, and SC = 6.5 m s−1 for αC = −50° following equation (4). Reversed airflows at Magilligan therefore have the potential to transport sediment onshore as offshore directed winds at the dune crest often exceed the calculated threshold values. This suggests that sediment budget calculations should include offshore winds at locations where dune morphology introduces airflow separation and fine sediment sizes dictate relatively lower wind thresholds for grain entrainment.
6.2 Causes of 3D Airflow Patterns
 Although general patterns of lee-side airflow strength and direction can be roughly depicted (previous section), results here indicate not only that the extent of the separation zone was different alongshore but also that the wind was consistently steered in opposite directions at certain locations within the similar lee-side airflow zones (section 5.3). The long distances between sensors (10 m cross-shore by 30 m alongshore) hampers a general interpretation of opposing wind directions within the reversed zone and beyond re-attachment. However, it is possible to hypothesize the origin of these complex flow patterns if we assume that the field results are point measurements in the CFD map of wind velocity vector simulated by Jackson et al. . Figure 7 of their paper contains a 3D simulation of airflow at the same location as this field study. This map of surface velocity shows areas of flow convergence and divergence related with zones of flow reversal and no-reversal, respectively. This is opposite to the patterns associated with lobe and saddle fluvial features [Venditti, 2003], where flow convergence is associated with weak or absent reversal. While more research is needed, this study suggests that spatial variations of the recirculation zone may be related to both small topographic irregularities at the dune crest and with physical roughness elements introduced by the presence of vegetation. Our hypothesis suggests that relatively small protrusions on the lee-side of the dune crest that do not affect the approaching wind could have created lee-side wind pressure differentials rather than windward flow deflections. Longer recirculation lengths could therefore have been created by delayed flow separation at the crest. Shorter circulation lengths could have been caused by maintaining attached flow on the crest between protrusions. These “protrusions” are created by the presence of vegetation able to hold hummocks of sand together at slopes that would be aerodynamically unstable in bare sand. This introduces even more complexities at the lee side of coastal dunes, and could be an important factor in many deserts and rivers, where vegetation and other form of roughness elements are found.
 The sequences of upward/downward airflow movements (positive/negative β) within the new IBL zone may be related to the formation of complex airflow structures such as corkscrew, spiral, or hairpin vortices [Allen, 1985; Ellis, 2006]. Corkscrew vortices have been identified in many aeolian settings, from blowouts [Hesp and Hyde, 1996; Smyth et al., 2011] and desert dunes [Greeley and Iversen, 1985], to wind tunnel simulations [Sutton and McKenna-Neuman, 2008] and fluvial environments [Best, 2005b]. The passage of corkscrew or spiral vortices, for example, could result in alternate zones of differently pitched airflow while maintaining a fairly constant wind direction downstream (e.g., Figures 8B–C).
6.3 Logistical and Theoretical Limitations for Lee-Side Experiments
 As mentioned in the previous section, different beach transects showed different degrees of airflow reversal and even opposite airflow horizontal directions (e.g., compare lines a and d in Figure 9). In the absence of spatial homogeneity, 2D field experiments could provide very different results depending on the particular choice of instrument transects. This supports the need to validate powerful modelling techniques such as CFD which are able to provide a flow field over entire dune systems [Beyers et al., 2010; Jackson et al., 2011; Smyth et al., 2011, 2012].
 The processing of wind data recorded by UAs continues to be a matter of debate in the aeolian literature, with some authors choosing to calculate turbulent parameters both over rotated and nonrotated data [e.g., Baddock et al., 2011]. The complexity of α and β flow angles in this work supports nonrotation of lee-side airflows [in line with Roy et al., 1996, and Walker, 2005], which has consequences for the type of turbulence analyses that can be conducted in these environments. Data rotation may be applied in scenarios where it is possible to assume that the streamlines are parallel to the surface [Roy et al., 1996] and to each other [Wyngaard, 1981]. Under these conditions, it is possible to align the sensors into the streamlines, to reduce the wind spanwise (v) and vertical (w) components, and then correct the data by removing possible sensor tilts using data rotation [Roy et al., 1996; Walker, 2005]. This is important because it strongly affects the accuracy of quadrant analysis and calculated turbulent parameters such as Reynolds stress [van Boxel et al., 2004; Baddock et al., 2011; Chapman et al., 2012; Lee and Baas, 2012]. It is not possible to perform data rotation in complex situations where secondary flows induce vertical velocities different from zero because the streamlines (not the sensor) are at an angle with the surface, and where the mean vector orientation presents large spatial variability. This limits the applicability of findings in flat surfaces or at the windward slope of dunes, because the links between sediment transport and RS-quadrant analysis [Weaver and Wiggs, 2011] rely on the assumption that the mean vertical (normal to the bed) velocity is zero. Take, for example, the sensor located at 45 m in Figure 6, where αC = 0+/−5°. Previous knowledge of flow behavior at this particular location could be gathered using qualitative flow visualization techniques (e.g., smokers) or quantitative flow visualization techniques such as the one conducted in this study. According to dirh and dirv in Figure 6, a sensor “aligned” with the streamlines should be physically rotated roughly 50° to the right in the horizontal plane and tilted about 30° toward the beach surface. Assuming that this is possible, the calculated yaw and the pitch angles [see van Boxel et al., 2004; Walker, 2005] should be used to correct the variability between the sensor's frame of reference and the streamlines, which is roughly 70° in the uv plane and roughly 10° in the uw plane. Assuming that this is possible, the question remains as to the meaning of calculated turbulent parameters such as Reynolds stress and quadrant analysis. As Roy et al. point out, “what does a quadrant IV event indicate if the frame of reference adjusted to the streamline is at a 45° angle with the bed? How would these turbulent motions act with the bed sediments?” [Roy et al., 1996, pp. 825]. In the absence of data rotation and the presence of non-log linear velocity profiles that cannot be used to estimate friction velocity [Sweet and Kocurek, 1990], the lee side of aeolian dunes need new relations between transport and other turbulent parameters, such as turbulent kinetic energy, instantaneous variations in wind speed, or standard deviations of the three components of the wind vector in relation to a fixed co-ordinate system.
 The application of UAs in aeolian research has focused predominantly on the calculation of turbulent parameters [van Boxel et al., 2004; Walker, 2005; Baddock et al., 2011; Weaver and Wiggs, 2011; Chapman et al., 2012; Lee and Baas, 2012], the comparison of wind components in the uv plane [Delgado-Fernandez et al., 2011], and/or the calculation of wind speed and direction [Leenders et al., 2005; Jackson et al., 2011] over 2D transects. The recent work by Smyth et al.  showing averaged measured 3D flow vectors in coastal blowouts supports the use of UAs to explore the variability of the airflow both in the uv (horizontal direction) and the uw (vertical direction) planes. This manuscript takes a step further and presents the full variability 5 min averages of wind 3D directional data at sensors' locations over an extensive grid with a spatial coverage and resolution not attempted before within the lee side of a dune. The conclusions and implications of the findings can be summarized as follow:
 In general terms, the average distance to re-attachment (r ≈ 4hr) and the location of other lee-side airflow zones was relatively constant for winds approaching the dune crest at an angle of αC = 0° to −30° and incident wind speeds of 1 to 13 m s−1. This suggests that the extent of the separation zone could remain very similar for winds blowing from a 60° window of wind directions (0+/−30°), independent of their wind speed.
 The threshold for incident wind angle at which clear changes occurred at the beach surface was approximately at αC = −30° to −40°, which is slightly larger than the one reported in desert dune studies. Reversed flows were stronger during oblique incident offshore winds compared to transverse offshore, winds but the size of the reversed zone was narrower. The change from transverse to oblique incident wind direction at the dune crest “compressed” the sequence of lee-side airflow zones and steered the airflow more parallel to the dune toe at the back beach.
 The lee-side 5 min wind vector showed considerable spatial variations over the beach surface, with complex alongshore patterns of wind steering both within the reversed zone and beyond re-attachment. This suggests limited meaningfulness of data collected over 2D transects, as airflow patterns across a given profile differed substantially from those measured at another profile a few meters away alongshore, even under similar incident wind directions.
 The location and extent of lee-side airflow zones were relatively constant under similar incident wind directions. This favors the application of CFD tools, which are capable of providing steady-state solutions of the wind field over a complex topography in three dimensions. The large number of UAs deployed in this study allowed a spatial coverage of the 3D wind vector not attempted at the lee side of a subaerial dune before. However, and despite the large grid, results highlight some of the limitations associated with measuring complex flows in the field, where sensor placement, elevation, and distance between each other limit results interpretation. CFD simulations help fill in the gaps found with point measurements and allow full sampling of coherent structures and complex airflow patterns.
 The large variability of horizontal and vertical wind directions and the complexity of near-surface airflow vectors, with vertical flow angles of up to 30° towards the surface at the re-attachment zone, confirm the unfeasibility of performing data rotation. This precludes application of findings from windward slopes based on quadrant analysis and calculated Reynolds stress and suggests the need to investigate alternative relationships between sediment transport and turbulence at the lee side of aeolian dunes.
 Alternative areas of airflow convergence and divergence, also visible in previous CFD simulations conducted at the same location, were associated with reversed and re-attached airflow, respectively. This is different from fluvial dunes, where flow convergence has been associated with weak or absent reversal, or from transverse desert dunes, where deflection has been reported only in one direction. Differences seem to be related to the role played by vegetation in creating topographic irregularities that are not present on bare sand dunes, and that introduce complex heterogeneities in the airflow regime.
 We wish to thank Robert Stewart, Sam Smyth, Peter Devlin, and Marianne O'Connor for their DGPS field surveying efforts. Thanks are also extended to Colin Anderson (electronics workshop), Nigel Macauley (mechanical workshop), and Thomas Smyth for providing invaluable assistance in mounting the equipment and conducting the experiment. A number of people sporadically participated and helped in the field: Ursule Boyer-Villemaire, Henk van Rein, Alexander Callaway, and Lluis Gomez-Pujol. LIDAR information was used with the permission of Geological Survey Ireland and access to the field site was kindly provided by Defence Estates UK. This work is funded through the UK Natural Environment Research Council grant NE/F019483/1.