Geomorphology of desert sand dunes: A review of recent progress

0 (2007) 239–257www.elsevier.com/locate/earscirev

Earth-Science Reviews 8

Geomorphology of desert sand dunes: A review of recent progress

Ian Livingstone a,⁎, Giles F.S. Wiggs b, Corinne M. Weaver b

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

Received 6 April 2006; accepted 29 September 2006Available online 30 November 2006

Abstract

Through the 1980s and 1990s studies of the geomorphology of desert sand dunes were dominated by field studies of wind flowand sand flow over individual dunes. Alongside these there were some attempts numerically to model dune development as well assome wind tunnel studies that investigated wind flow over dunes. As developments with equipment allowed, field measurementsbecame more sophisticated. However, by the mid-1990s it was clear that even these more complex measurements were still unableto explain the mechanisms by which sand is entrained and transported. Most importantly, the attempt to measure the stressesimposed by the wind on the sand surface proved impossible, and the use of shear (or friction) velocity as a surrogate for shear stressalso failed to deliver. At the same time it has become apparent that turbulent structures in the flow may be as or more important inexplaining sand flux. In a development paralleled in fluvial geomorphology, aeolian geomorphologists have attempted to measureand model turbulent structures over dunes. Progress has recently been made through the use of more complex numerical modelsbased on computational fluid dynamics (CFD). Some of the modelling work has also suggested that notions of dune ‘equilibrium’form may not be particularly helpful. This range of recent developments has not meant that field studies are now redundant. Forlinear dunes careful observations of individual dunes have provided important data about how the dunes develop but in thisparticular field some progress has been made through ground-penetrating radar images of the internal structure of the dunes.

The paradigm for studies of desert dune geomorphology for several decades has been that good quality empirical data aboutwind flow and sand flux will enable us to understand how dunes are created and maintain their form. At least some of the difficultyin the past arose from the plethora of undirected data generated by largely inductive field studies. More recently, attention hasshifted–although not completely–to modelling approaches, and very considerable progress has been made in developing models ofdune development. It is clear, however, that the models will continue to require accurate field observations in order for us to be ableto develop a clear understanding of desert sand dune geomorphology.© 2006 Elsevier B.V. All rights reserved.

Keywords: aeolian; geomorphology; dune; transverse dune; linear dune; turbulence

1. Introduction

Although reviews of the geomorphology of desertsand dunes routinely start with reference to the work of

⁎ Corresponding author. Fax: +44 1604 720636.E-mail address: [email protected]

(I. Livingstone).

0012-8252/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.earscirev.2006.09.004

Ralph Bagnold (e.g. 1941), Bagnold's work concentrat-ed largely on the physics associated with the movementof individual sand grains in the wind rather than on thedevelopment of landforms. His work was ground-breaking in providing systematic empirical measure-ments of wind flow, particularly velocity profiles, andof sand flux, but his work on dunes was rathermore descriptive and often speculative. A significant

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240 I. Livingstone et al. / Earth-Science Reviews 80 (2007) 239–257

speculation was his suggestion that thermally-generatedroll vortices were the origin of linear sand dunes(Bagnold, 1953). Despite his clear acknowledgment ofthe speculative nature of his theory, it became widelyquoted, and it was not until 30 years later that it waschallenged on the basis of careful field observation andmeasurement of linear dunes (e.g. Tsoar, 1983).

Tsoar's work was just one of a wave of single-dunestudies that were undertaken in the 1970s and 1980s(Table 1). These were attempts to understand the basiccontrols on the development of the form of individualdunes rather than the development of groups of dunes assand seas (e.g. Wilson, 1973) or the movement ofindividual grains (e.g. Bagnold, 1941). This trend waspart of a wider trend in geomorphology (and even morewidely in geography (Burton, 1963) and geology(Merriam, 2004)) towards the measurement of small-scale processes and the use of statistics to analyse thedata collected, frequently termed the ‘quantitativerevolution’. In fluvial geomorphology this started inthe 1950s and manifested itself as small catchmentstudies (e.g. Leopold et al., 1964). Aeolian geomorphol-ogy took rather longer to catch this wave (althoughCoursin's work (1964) was somewhat ahead of the pace)but what may be termed the single-dune studies of the1970s and 1980s were aeolian geomorphology's equiv-alent of the small catchment studies. Alongside these,there has been a number of studies based variously onsatellite and aerial photographic imagery, repeatedground survey or on a combination of imagery withsurvey that provide measurements of dune movement.

Table 1Examples of field studies of single dunes

Dune type Location Reference

Barchan dune Mauritania Coursin (1964)Various locations, USA Frank and Kocurek

(1996a,b)Salton Sea, CA, USA Lancaster et al. (1996)Tenere Desert Warren and Knott (1983)Oman Wiggs (1993); Wiggs

et al. (1996)Linear dune(longitudinal,seif)

Sinai Desert Tsoar (1982, 1983)Namib Desert, Namibia Livingstone (1989, 2003)Strzelecki Desert,Australia

Tseo (1990, 1993)

Taklimakan, China Wang et al. (2003, 2004)Others Silver Peak, NV, USA

(transverse dunes)McKenna Neuman et al.(1997, 2000)

Wahiba Sands, Oman(dune networks)

Warren (1988); Warrenand Kay (1987)

Mexico (star dune) Lancaster (1989)Algodones, CA,USA (complextransverse dunes)

Havholm and Kocurek(1988)

Single-dune studies concentrated on measurements ofwind flow and sand flux (the methods of the period aresummarised by Knott and Warren (1981)). Wind flowwas largely measured by rotating-cup anemometers,often at a single height; wind direction was measuredvariously by the orientation of ripple marks, paper flagsor by tracking meteorological balloons or kites; and sandflux was measured by using sand traps, sometimes basedon the design of Bagnold (1941). Many of these studiesbegan to provide good fundamental basic data about howthe dunes behaved. In particular, Tsoar and Livingstonewere able to show that on two very different linear dunesthere was no evidence to support Bagnold's roll-vortexhypothesis. Both their studies showed linear dunesresponding to bi-directional wind regimes, albeit withsome difference of opinion about the mechanism (e.g.Livingstone, 1988; Tsoar, 1990).

These single-dune studies spawned a series of rathermore sophisticated studies (e.g. Wiggs, 1993; Frank andKocurek, 1996a,b; Lancaster et al., 1996; Wiggs et al.,1996; McKenna Neuman et al., 1997). This increasingsophistication was partly a consequence of rapidlyimproving computer technology; the data loggers usedto collect and store information from anemometersimproved very rapidly through the 1980s and 1990s.Loggers became able to store much more data from alarger number of devices and laptop computers wereavailable for downloading and analysing data. Moreaccurate anemometers were developed including hotwire anemometers although there was an issue ofrobustness in field situations. Equipment such as theSaltiphone (Spaan and Van den Abele, 1991) and theSensit probe (Stockton and Gillette, 1990) weredeveloped to count the impacts of saltating grains intransport. Often this trend for field monitoring andmeasurement meant that large amounts of hardwarewere installed for these single-dune studies (Fig. 1).

Although enabled by improving technology, theincreased sophistication was driven more fundamentallyby the realisation that simple wind-speed measurementsat a single height were not enough to characterise thewind flow over the dune. Even though Bagnold (1941)and others had related sand transport rates to wind speed,sand transport has been more commonly related to thestress imparted at the sand surface by the wind. Usingwind speed as a surrogate for shear stress was apragmatic response to the difficulty of measuring shearstress directly. Many single-dune studies in the 1990sattempted to measure wind speeds at different heights inorder to produce a velocity profile from which shearstresses could be inferred via the calculation of shear (orfriction) velocity, u⁎.

Fig. 1. Anemometers and sand traps on a dune in the Salton Sea, California, USA. Measurement of airflow on the windward slopes of sand dunesoften resulted in spectacular arrays of equipment on dune surfaces (photo: Nick Lancaster).

241I. Livingstone et al. / Earth-Science Reviews 80 (2007) 239–257

In recent years the number of single-dune studies hasdropped considerably. There are two main reasons forthis. The first was the realisation that links between windand sand flow around dune forms are more complicatedthan perhaps was envisaged 20 or 30 years ago andinstrumentation in real-world environments was notdelivering the link between the essentially turbulentnature of the wind and sand flux. Even on the mostfundamental of ‘free’ dunes–transverse dunes–it wasnot possible to make measurements of wind speed usinganemometers that would give reliable values of surfaceshear stress. The second realisation was that single-dunestudies were oversimplifying dune systems where thereare frequently complicated combinations of a variety ofsingle-dune forms. It became apparent that single-dunestudies could only take us so far in our understanding ofdune dynamics and development.

As a consequence the international conference onaeolian research (ICAR) held every 4 years saw a dropin the number of papers reporting single-dune studiesmore or less to zero in 1998 and 2002 (see editorials byLivingstone, 1999; Livingstone and Nickling, 2004).They were replaced by a burgeoning interest in dustentrainment and transport and in palaeoenvironmentalstudies of aeolian environments driven in part by theexplosion of interest in luminescence dating which hasrevolutionised dating of aeolian sediments.

Furthermore, aeolian geomorphology has seen some-thing of the wider methodological debate about whether‘reductionist’ studies can deliver explanations of duneform and pattern. The argument has been that

understanding the physical processes at the grain scalewill not deliver an explanation of what is happening atthe dune scale because the relationships are complex;equally dune-scale processes do not help us to under-stand patterns at the dunefield or sand sea scale. Thecomplexity is a result of a number of factors, not leastthe non-linearity of the physical relationships. Theclearest general explanation of the thinking behind non-linearity and complex systems is provided by Phillips(1999, 2003). Most straightforwardly, “a system is non-linear if the outputs are not proportional to the inputsacross the entire range of inputs” (Phillips, 1999, p.4).

More than a decade agoWerner (1995) suggested thatdunes provided good examples of complex systems andhe showed that he could model the development ofdunefield patterns without reference to the small-scalegrain-to-grain processes that have been the focus ofmany single-dune studies. More recently, Kocurek andEwing (2005) suggested that we should view dunes asself-organised complex systems and argued that reduc-tionism breaks down because the relationships are non-linear. Yet non-linearity in itself is not sufficient toeschew so-called reductionist studies; the most reduc-tionist studies at the grain scale are able to deal with non-linearity in threshold equations for grain entrainment.

Kocurek and Ewing suggested that viewing dunes ascomplex systems represented a paradigm shift but it isprobably fairer to suggest that there has been a paradigmreappraisal. It is not the case that geomorphologists haveceased to be interested in questions associated with howdunes develop as landforms. While single-dune studies

Fig. 3. The search for flow-form equilibrium. A summary of bedformdynamic processes linking flow field, sand flux and bedform change inthe fluvial environment (modified from Leeder, 1983). These dynamiclinkages also formed the basis for experimental design in many aeoliandune studies in the 1980s and 1990s.


continue, other approaches are being explored, inparticular those in which there is greater control on thevariables in the system. Modelling approaches–bothhardware in wind tunnels and software–provide thisoption. This paper now considers how the complexity ofdesert dunes is being examined.

2. Transverse dunes

2.1. Field studies of transverse dunes

The most actively studied dune type in terms ofprocesses and dynamics is the barchan dune. Theapparent simplicity of the barchan form, its reflectionof an aerodynamic structure, the limited sand supplyinvolved, and its existence within a uni-directional windregime all provide motivation to generate interest and thedesire for measurement. During the 1980s and 1990s thismotivation was prompted by the improved understand-ing that sand dune dynamics was not a simple response toregional wind patterns but a complex interaction be-tween dune morphology and wind flow. The data gen-erated from process studies at this time (e.g. Lancaster,1985, 1987; Watson, 1987; Wiggs, 1993; Frank andKocurek, 1996a,b; Lancaster et al., 1996; Wiggs et al.,1996) highlighted the role of secondary flow regimes indune maintenance and dynamics whereby the compres-sion of streamlines on the windward slope of a dune, andthe separation of airflow at the brink and in the lee-sidecreated airflow structures that impacted upon thesedimentary processes acting on the dune (Fig. 2).Dunes were thus not just responding to the wind regime,

Fig. 2. Field measurements of wind speed over a 10m high barchan dunein Oman, represented as fractional speed-up ratios (from Wiggs et al.,1996).

but creating their own secondary flow regimes thatinteracted with the dune and had a significant role to playin the dynamics of the dune and its development. Thisimproved understanding lent itself to the continueddevelopment of the concept of dynamic equilibrium, firstexpounded in the aeolian case by Wilson (1972), butwith a particular emphasis on investigating the notion ofthe ‘equilibrium dune'.

Many investigations in the 1980s and 1990s focusedon determining the inter-relationships and feedbacksbetween airflow structures, sediment transport and dunegeomorphological change in an effort to identify thebalance between these dynamic parameters that mightexplicate the equilibrium dune form. Such investiga-tions were allied to those researching sedimentarybedforms in fluvial environments and the researchstructure that was used in both aeolian and fluvial workis well summarised by Best (1996) (see Fig. 3).

The aspiration of these single-dune studies was that themeasurement of shear velocity (u⁎), rather than the previ-ously relied upon wind speed, would enable a far greaterunderstanding of downwind changes in sediment fluxacross dune surfaces. This expectation of shear velocitymeasurements was generated by successes in wind tunnelexperiments where the shear velocity exerted by the windhad been recognised as a primary driving force for theaeolian transport of sand (e.g. Butterfield, 1993).

Fig. 4. Mean wind speed profiles from a Namib Desert sandy plain (Weaver, unpublished) demonstrating the characteristic log–linear relationshipwith height. Such profiles allow the straightforward calculation of mean shear velocity (u⁎) using the ‘law-of-the-wall’.

Fig. 5. Field measurements of sand flux on the windward slope of abarchan dune (from Wiggs, 2001).


Shear velocity (u⁎) is proportional to the gradient ofthe wind velocity profile plotted on a logarithmic heightscale (Fig. 4) and is associated with surface shear stress(that is the driving force of erosion) by:

s ¼ qu2⁎ ð1Þ

where s=the surface shear stress, ρ=the density of airand u⁎=the shear velocity.

Numerous sediment transport formulae have beendeveloped from wind tunnel investigations that relatethe sediment flux (q) to the third power of shear velocityq α u⁎

3 (e.g. Bagnold, 1941; Kawamura, 1951; Zingg,1953; Owen, 1964; Lettau and Lettau, 1977; White,1979). The discussions between Lancaster (1985, 1987)and Watson (1987) therefore promoted the idea thatstudies of dune dynamics should be focussed onattempting to measure wind velocity profiles on dunesurfaces. From these data shear velocities could bedetermined in order to predict sediment flux and thelocal surface height change on a dune (Δh/Δt) could thenbe determined from downwind changes in sand flux(Δq(x)):

Dq xð Þ ¼ Dh=Dt ð2Þ

Such research designs were popularly adopted andwere frequently directed at exemplifying the processeshighlighted in Fig. 3 based on measurement of two-dimensional transects along barchan dune centre-lines.Such studies were highly successful in demonstratingthat velocity acceleration up dune windward slopes (e.g.Frank and Kocurek, 1996a,b; Lancaster et al., 1996;

Wiggs et al., 1996) due to streamline compression wasanalogous to wind flow over low hills (Jackson andHunt, 1975). Measurements of sand flux gained fromsand traps were also highly informative concerning therelationships between velocity acceleration, dune shapeand rate of change of sediment transport rates (Wiggs etal., 1996; Fig. 5). However, the studies demonstrablyfailed in the correct determination of shear velocityacross dune surfaces, and so they failed successfully tolink the processes controlling wind velocity to those ofsand flux. The reasons for this failure were two-fold.

First, due to the varied acceleration of velocity withheight as flow approaches the dune crest, velocityprofiles become increasingly non-log-linear up wind-ward slopes (Fig. 6). This prevents the successful

Fig. 7. The imperfect measured relationship between shear velocity(u⁎) and the distance up the stoss slope of a barchan dune (fromLancaster et al., 1996).


calculation of u⁎, which requires a log–linear velocityprofile (Mulligan, 1988; Frank and Kocurek, 1996a,b).

Second, wind tunnel data indicate that the velocityacceleration also produces a gradient of shear stressclose to the surface toward the crests of dunes that isextremely strong (Wiggs et al., 1996). The consequenceof this is that in order to determine wind parameters thatare relevant to sand flux, measurements must be madevery close to the surface (b∼10 cm). Such measure-ments are difficult in the natural dune environment onoccasions where saltation is active and attempts tomeasure u⁎ above this critical layer result in dataindicating a reduction in mean u⁎ from toe to crest(Lancaster et al., 1996; Fig. 7). Such data are illogical tothe natural dynamics of sand dunes.

These difficulties initiated a rapid demise in fieldinvestigations of aeolian dune processes. The failure ofsuch process studies adequately to determine sandtransport rates on single dunes led to some researchersabandoning measurements of flow parameters andresorting to direct measurement of sand flux usingsand traps. Additionally, some questioned the relevanceof mean values of shear velocity and wind speed to thetransport of sand on dunes. For example, Wiggs et al.(1996) noted that the decrease in mean wind speedupwind of dunes due to an increasing pressure gradientwas not associated with a commensurate decrease insand flux. Wind tunnel investigations by the authorsresulted in the suggestion that observed increases inwind turbulence due to streamline curvature in this toeregion of the dune might counteract the influence of thewind-speed reduction (Fig. 8). The potential role ofturbulence in sand transport was also highlighted inwind tunnel investigations where naturally occurring

Fig. 6. The non-log-linear characteristics of a velocity profile measuredat the crest of a sand dune (from Mulligan, 1988). Streamlinecompression and flow acceleration result in a curved profile that makesthe calculation of shear velocity (u⁎) problematic.

gusts with cyclical velocity variations and periodicitiesless than 20 seconds that might be expected to givehigher sand transport rates than steady winds of thesame mean wind speed have been observed (Butterfield,1998). Mounting empirical evidence for the role ofturbulence in sediment transport by water (e.g. Lapointe,1992; Bennett and Best, 1995, 1996; Buffin-Bélangeret al., 2000), where high levels of instantaneous stresswere thought to be the driving mechanism behind thedetachment and transport of sediment (Nearing andParker, 1994), has also led to a change in the emphasisof aeolian studies from investigations of mean windparameters to those of higher frequency turbulence.

Fig. 8. Turbulent intensities measured over a model barchan in a windtunnel. Data indicate increased turbulent mixing at the toe and upwindof the dune (from Wiggs et al., 1996).

Fig. 9. Quadrant plot of the four coherent turbulent flow structures,based on horizontal (u′) and vertical (w′) velocity fluctuations (fromBest, 1993).


2.2. The potential role of turbulence

Throughout the 1980s and 1990s, following thedevelopment of turbulence instrumentation such aselectromagnetic current meters and laser Doppleranemometers, turbulence has been recognised as thedriving force behind sediment transport in river flows

Fig. 10. Characteristics of three streamer patterns in plan view (lef

(e.g. Lapointe, 1992, 1996; Bennett and Best, 1995,1996; Kostaschuk and Villard, 1996), tidal estuaries(e.g. Simpson et al., 2004) and ocean currents (e.g.Heathershaw and Thorne, 1985; Thorne et al., 1989) andis believed to be a key component for the formation andstability of subaqueous bedforms (e.g. Nelson et al.,1993, 1995; Best and Kostaschuk, 2002; Best, 2005;Venditti and Bauer, 2005).

This recognition has spurred a move away from theempirical approach of using mean flow properties forpredicting sediment transport toward investigations ofhigh-frequency events where instantaneous flow veloc-ities exceed and fall below the time-averaged flowvelocity. These stress excursions are commonly detectedusing quadrant analysis after Lu and Willmarth (1973)(Fig. 9). Depending on the relative sign of thesedeviations, four discrete turbulent events have beenidentified. Sweeps and ejections act as positivecontributions to the shear stress and outward and inwardinteractions act as negative contributions.

In the aeolian domain, research into the role ofturbulent flow in sediment mobility has somewhatlagged behind that of its fluvial counterpart. This isprimarily due to the fundamental difference in the fluiddynamics of sediment transport between that of air andthat of water. Buoyancy effects are orders of magnitude

t) and cross section (right) (from Baas and Sherman, 2005).

Fig. 11. A model of dune dynamics that emphasises the influence of streamline curvature on shear stress (from Wiggs et al., 1996).


lower in air than in water and so the overall effectivenessof vertical motions in entraining and transportingsediment is inherently less in aeolian environments(Walker, 2005). Moreover, the problems involved inmeasuring such small-scale motions in the airstream inthe presence of high energy saltation have resulted in theabsence of literature detailing the role and importance ofturbulence within the aeolian sediment transport system.

The aeolian literature does make reference tostructural, event-like phenomena such as ‘sand snakes’,‘streamers’ and ‘saltation pulses’ (Butterfield, 1991;Baas and Sherman, 2005). These are believed toconstitute individual eddies of high and low windvelocities that subsequently result in spatially discretesediment transport events (Fig. 10). Wind tunnel workcarried out by Butterfield in the early 1990s revealedthat temporally varying winds, of the order of seconds,could potentially induce unsteady, or even discontinu-ous, two-dimensional behaviour in saltation throughtime (Butterfield, 1991, 1993, 1998). This marked thebeginning of a shift in the aeolian research communityaway from the accepted traditional ‘mean’ approach,towards investigating the role of instantaneous windvelocity, shear stress and turbulent structures insediment transport (Walker, 2005) and wind flowstructure (Hommema and Adrian, 2003a,b).

Only a handful of aeolian field researchers has beensuccessful in measuring sediment transport and windspeed at a frequency high enough to determine theexistence of turbulence within the wind flow. This has

been made possible by the recent advances in thedevelopment of high-frequency instrumentation capableof simultaneously measuring the three-dimensionalnature of the wind flow (e.g. ultrasonic anemometry;see Walker, 2005 for a review) and sediment flux (e.g.grain impact sensors; see Baas, 2004). Studies con-ducted by Sterk et al. (1998, 2002), Schönfeldt and vonLöwis (2003), Van Boxel et al. (2004), Baas andSherman (2005) and Leenders et al. (2005) haveattempted to relate sediment flux events to the turbulentbursting process. Sterk et al. (1998) failed to find a well-defined relationship between the instantaneous shearstress and saltation flux. Rather, they observed that flowevents (sweeps and outward interactions) that wereassociated with high saltation fluxes had an instanta-neous horizontal wind speed that was higher thanaverage (u′ N0).

Results presented by recent field studies involvingmore robust experimental set-ups (e.g. Schönfeldt andvon Löwis, 2003; Leenders et al., 2005) are in agreementwith the original findings by Sterk et al. and highlight theimportance of the instantaneous horizontal wind speedfor sediment transport. This supports the conclusionmade by a number of researchers, both in the aeolian andfluvial environments (e.g. Heathershaw and Thorne,1985; Jackson and McCloskey, 1997; Butterfield, 1998;Stout, 1998; Baas and Sherman, 2005), that in theintermittent case, sediment transport should not bepredicted on the basis of mean shear stress (or frictionvelocity) alone, unlike the majority of the current

Fig. 12. A conceptual model of lee-side flow regions over a transverse dune. Labelled regions represent: A, outer flow; B, overflow; C, upper wake;D, lower wake; E, separation cell; F, turbulent shear layer; G, turbulent stress maximum; H, turbulent shear zone; I, internal boundary layer (fromWalker and Nickling, 2002).


transport equations. Rather, it is more useful toincorporate some aspect of the instantaneous horizontalwind speed as a driving variable.

The small number of investigations concerningproperties of aeolian turbulence and sediment flux isinsufficient to draw firm conclusions and there is muchscope for development. What is also lacking is thecoherent application of our embryonic understanding ofturbulent flow and sediment flux to the dynamics ofdunes. The wind tunnel studies such as those of Finniganet al. (1990), Castro and Wiggs (1994) and Wiggs et al.(1996) attribute much significance to the impact ofstreamline curvature and changes in Reynolds’ stressesand turbulence intensity to the maintenance of shear andsediment transport on the windward slopes of sanddunes, particularly in the toe region where velocitystagnation occurs (Fig. 11). In contrast, further windtunnel experiments conducted by Walker and Nickling(2002, 2003) over both isolated and closely spaced dunesfound little evidence for the maintenance of shear stress

in this region. However, despite the apparent decline intime-averaged shear stress measurements observed byWalker and Nickling (2002, 2003), the variability in theshear stress signal increased to the dune toe indicatingflow unsteadiness and increased turbulence. Such resultsmight be attributed to the effect of streamline curvaturegenerating increased instantaneous and higher frequencyfluctuating horizontal and vertical velocity componentsthat are not apparent in time-averaged estimates of shearstress (Walker and Nickling, 2003).

Results presented by Walker and Nickling (2003)show the existence of a direct link between near-surfaceflow acceleration and increasing steadiness in surfaceshear stress up the stoss or windward slope of a dune.Similar wind tunnel results showing a decline inturbulence intensity up the windward slopes of duneswere presented by Wiggs et al. (1996). These datasuggest that mean streamwise accelerations, rather thanturbulent structures or eddies, contribute more to stossslope dynamics toward the crestal region of the dune.


These results support the findings of McKenna Neumanet al. (2000). These authors investigated the effects ofnon-uniform airflow on the magnitude and intermittencyof sediment transport on the stoss slope of a lowtransverse dune and their results represent one of thevery few field studies of the impact of unsteady winds orturbulence on dune dynamics. Their results suggestedthat wind gusts of short duration, that are in the range ofthose associated with turbulent fluctuations in theatmospheric boundary layer, were relatively inconse-quential in terms of the total amount of sedimenttransport and therefore the modification of the stossslope.

Similarly, turbulence may have an important role toplay in the lee of sand dunes (Fig. 12). It has beenrecognised that lee-side flow patterns may exert asignificant influence on the dynamics of the stoss slopeand may play a larger role in dune morphology thansimply recycling sediment back toward the dune (e.g.Hoyt, 1966; Sweet and Kocurek, 1990). Walker andNickling (2003) discovered that complex secondaryflow patterns exert control on boundary layer develop-ment in the lee and hence, on surface shear stress andsediment transport. In their wind tunnel experimentsover isolated and closely spaced transverse dunes,reversed flows within the separation cell generatedsignificant stresses of approximately 30–40% of themaximum, despite the existence of flow expansion anddeceleration in this region. Shear stress variabilitycontinued to increase until a peak value at the point offlow reattachment. This feature is indicative of theimpact of turbulent eddies on the surface generated byflow separation. Consequently, although streamwiseshear stress at the point of reattachment appears to be ata low level, the gustiness of the flow in this area of thedune will ultimately inhibit sediment deposition.Additionally, the characteristics of flow in the lee sideof aeolian dunes bear many similarities to the flow in thewake of fluvial bedforms (see the recent review by Best(2005)). Investigations carried out by Nelson et al.(1993), McLean et al. (1994) and Venditti and Bauer(2005) found that turbulence created in the wake regionof fixed two-dimensional bedforms occasionally im-pinged on the boundary layer, thereby profoundlyaffecting the near-bed sediment dynamics.

Evidently, research into the effects of turbulence andcoherent flow structures on sediment transport is in itsinfancy. The role of turbulence in dune dynamics is notat all clear and there is enormous scope for more fieldstudies that effectively test the conclusions of Wiggset al. (1996) and Walker and Nickling (2002, 2003).Before this can be accomplished, however, we require a

far greater understanding of the linkages between graintransport mechanics and aeolian sediment transport atsuch short time scales. Opportunities abound fordeveloping strong research links with fluvial investiga-tions where recent studies have provided evidence thatfluid turbulence may be very sensitive to changes intopography, and that connections exist between turbu-lence generation, sediment transport and evolvingtopography (e.g. Best, 2005; Jerolmack and Mohrig,2005).

2.3. Computer simulations

Numerical modelling of dune dynamics has a longhistory. Based on the early analytical approach ofJackson and Hunt (1975), models developed by Howardet al. (1977, 1978), Walmsley and Howard (1985),Wippermann and Gross (1986) and Weng et al. (1991)combined geomorphological understanding of sandtransport with computer models of wind flow overbarchan dunes. However, few studies successfullymodelled completely the patterns of erosion anddeposition on sand dunes and the models were generallyunable to provide reliable predictions of dune movementand growth (Wiggs, 2001). Early models showed atendency to develop instabilities that were believed toresult from the strong sensitivity of the transport rate tovariations in wind velocity coupled with a strong andexaggerated sensitivity of the flow model to small-scaletopographic perturbations (Walmsley and Howard,1985).

In addition, the early studies suffered from aninability to simulate the highly turbulent flow in thelee of dunes (Stam, 1997). This artefact of numericalmodelling limited the calculation of flow structures tolow angle dunes where lee-side eddies were not present(Parsons et al., 2004a). Recently, however, sophisticatedcomputational fluid dynamics (CFD) models havebegun to be applied to modelling flow over aeoliandunes.

Although research on computational models has hada mainly fluvial focus (e.g. Hardy et al., 2003), there hasbeen heightened interest in the complex interactionsbetween sand dune morphology, windflow and sedimenttransport. With the recent proliferation of field and windtunnel data concerning dune processes, it is nowappropriate to apply new refinements in numericalcalculations of flow fields over bedforms using CFD toprovide new insights into dune flow dynamics andrelated sand transport mechanisms (Parsons et al.,2004a,b; Fig. 13). Parsons et al. (2004a) outlined anumerical model that was able to simulate areas of flow

Fig. 13. An example of an isovel contour plot of streamwise velocity calculated using computational fluid dynamics (from Parsons et al., 2004b).


stagnation at the dune toe, flow acceleration up the stossslope and flow reversal in the lee. They developed thisinitial model and determined the effect of simple dunegeometry variations on streamwise and vertical velocityflow fields and additionally, secondary flow structures.

The results from the application of CFD to a modelsand dune demonstrated that up the windward slope aprogressive acceleration of flow to a crestal maximumoccurs. This is in accordance with field measurements ofmaximum wind velocities at the dune crest (Lancasteret al., 1996; Wiggs et al., 1996). The majority of earlynumerical models failed to simulate this feature of dunedynamics primarily because previous models could notaccommodate the highly turbulent flows in the lee-sideseparation zone; hence wind velocities were subse-quently suppressed at the crest (Stam, 1997; Parsonset al., 2004a).

A particular advantage of the application of CFD toaeolian dunes is in the lee where the highly turbulentreverse flow region has traditionally posed problems formodellers. The leeward wind flow is very difficult tocalculate correctly because of the wind separation at thedune crest and multiple scales of flow (Momiji andBishop, 2002). However, the zone of separated flowimmediately in the lee of a dune creates a region ofnegative pressure that was adequately modelled in theinvestigation by Parsons et al. (2004a). The modelapplied by Parsons et al. demonstrated a shear zone inthe lee of a dune expanding towards the point ofreattachment and then dissipating as an internalboundary layer developed downwind. Such modelresults are broadly consistent with the limited numberof field observations in the lee of dunes (e.g. Sweet andKocurek, 1990). Significantly, the model of Parsons etal. (2004a) allowed a quantification of the downwinddistance required for full boundary layer recovery.Results suggested that it may occur at a downwinddistance equivalent to between 40–45 times dune height(h). This exceeds the figure of 10–15 h put forward by

Lancaster (1989) and is perhaps more in line with therecent wind tunnel measurements by Walker andNickling (2002, 2003) of 25–30 h.

Whilst some recent progress has beenmade in the 3-Dsimulation by CFD of flow over ripples and bedforms inthe fluvial environment (Zedler and Street, 2003; Yueet al., 2005) no such advances have yet been made in theaeolian field. Results from CFD modelling of flow overaeolian sand dunes are therefore currently restricted to2-D. However, recent 3-D modelling of dune dynamicshas been achieved using an alternative approach toCFD. With regard to the difficulties of adequatelyaccounting for the highly turbulent reverse flow regionin analytical models, Zeman and Jensen (1987)suggested a heuristic approach to modelling airflowover a dune. They introduced a ‘false’ separation bubblethat comprised the recirculating flow in the wake of thedune and extended from the brink to the point ofreattachment, thereby negating the requirement to modelthe flow in this region of highly turbulent flow.Sauermann et al. (2003) concluded from field measure-ments carried out on barchan dunes in Morocco thatlinear expansion models comprising the heuristicapproach to the separation bubble, combined with theanalytical expression for flow over a low hill afterJackson and Hunt (1975), provided a reasonableapproximation for the wind field around the dune.

The linear expansion models developed by Andreottiet al. (2002a,b), Lima et al. (2002), Schwämmle andHerrmann (2003) and Hersen (2004) successfullyrecreated barchan dune shapes and migration patterns.The model applied by Hersen (2004) carved up abarchan dune into a succession of independentlymodelled 2-D ‘slices’ aligned parallel to the winddirection. Each slice was linked to its neighbour via asand flux that redistributed the sand laterally from thecentral slice towards the horns. Hersen proposed theprocess of reptation as a suitable physical mechanismfor this redistribution of sand across the dune surface. In

Fig. 14. Instability of barchan dunes caused by variations in received and output flux for dunes of differing size. The small dune is under-supplied andcan only shrink. The bigger dune receives more sand than it loses and so grows. The time evolution of their volume V, calculated from simulations ofthe Hersen et al. (2004) model, is also shown (from Hersen et al., 2004).


this way the model successfully recreated the charac-teristic barchanoid form and Hersen (2004) discoveredthat the degree of reptation linkage between individual‘slices’ controlled the barchan shape. A high degree oflinkage resulted in a wide dune, whilst a low degree oflinkage via reptation resulted in a sharp and streamlinedshape.

Such linear expansion models have also been used togood effect in increasing our understanding of theinteraction between dunes as barchans are rarely foundin isolation and frequently propagate as a group,interacting with one another through collisions andindirect sand exchange (Katsuki et al., 2004). Suchinteractions are difficult to investigate in the fieldbecause of the long time scales involved in geomor-phological change (e.g. Gay, 1999) but now flumeexperiments (Endo et al., 2004) and modelling (e.g.Schwammle and Herrmann, 2003; Hersen, 2004) havebegun to shed light on the possible processes involved.Endo et al. (2004) and Katsuki et al. (2004) recognised‘collision’, ‘splitting’, ‘absorption’, ‘re-organisation’and ‘side-swiping’ of dunes, the precise mechanismoccurring depending upon the mass-ratio of the dunesinvolved and their relative positions.

Endo et al. (2004) also described the controversialprocess of ‘ejection’ that is similar to the idea of ‘solitarywave behaviour’ of sand dunes as proposed bySchwammle and Herrmann (2003). In this case, dunesact as solitary waves where, on approaching a slowermoving large dune, a fast moving small dune absorbsthe upwind sand flux. This has the effect of enlargingand slowing the migration rate of the upwind dune,whilst also forcing the contraction and acceleration ofthe downwind dune, increasing the distance between thetwo dunes. The smaller dune therefore appears to ‘passthrough’ the larger dune in a manner similar to a‘soliton’. However, geomorphological evidence for theexistence of such a process is lacking (Livingstone et al.,

2005) and our understanding of airflow in the lee ofbarchan dunes (Walker and Nickling, 2002, 2003;Parsons et al., 2004a,b) discounts the possibility of adune emerging from within the reverse flow region inthe lee of an upwind dune.

In contrast to the model used by Schwammle andHerrmann (2003), Hersen et al. (2004) employed aconstant upwind sand supply in their model (rather thana constant sand volume, where sand leaving themodelling space downwind is re-introduced upwind).Results using this approach have provided a significantcriticism for the suggestion, long employed bygeomorphologists, of barchan dunes existing as anequilibrium form. In the model of Hersen et al., theconcept of a constant upwind sand supply resulted insolitary dunes becoming unstable. This is because theamount of sand a dune receives from upwind is pro-portional to the width of the dune (i.e. a wider dunereceives more sand at its upwind toe). However,the amount of sand loss from a dune is proportionalto the width of its downwind-facing horns because thisis the only place where sand is lost from a barchan. Thedifference between upwind sand flux received bythe dune and downwind sand flux losses from thehorns therefore determines the change in dune mass.Hersen et al. (2004) argued that horn width (determin-ing sand flux loss) is not proportional to dune width.They stated that smaller dunes (with small bedformwidths) demonstrated a relatively larger horn width,and consequently greater relative sand loss, than largerdunes (with large bedform width). That is to say theratio of horn width to barchan width decreases withincreasing dune width and so output sand flux is alsorelatively reduced. Whilst there are no published fieldmeasurements of this geomorphological occurrence,the result in the model of Hersen et al. is that, withincreasing time, small dunes get smaller and big dunesget bigger (Fig. 14).


Hersen et al. (2004) therefore argued that barchandunes were not in a strict equilibrium when solitary.However, morphological measurements of dune devel-opment over time (e.g. Gay, 1999) also suggested thatbarchan dunes do not grow or disappear with a strictinstability. Hersen et al. (2004) suggested that there mustbe other processes at work that we are not aware of or donot completely understand that explain this disparitybetween equilibrium and dis-equilibrium for barchandunes. Some possible contenders might include sedi-ment transfer between dunes as a result of the collisionof two or more dunes, or via the impact of non-uniform(i.e. non-unidirectional) wind directions (Hersen et al.,2004; Hersen, 2005; Hersen and Douady, 2005). Suchprocesses would alter sediment transfer between dunesand also impact upon the input/output fluxes ofindividual dunes. Equilibrium in sand dune geomor-phology may therefore be recognised at a dunefieldscale at greater than annual time scales, rather than at thesolitary dune scale. However, the number of studiesdevoted to the dynamics of, and the processes operatingin, dunefields is limited and consequently the majorityof questions at this scale remain unanswered (Hersenet al., 2004). A start toward addressing these issueswould be a greater understanding of the 3-D dynamicsof sand transport on dune surfaces under varying winds.Furthermore, field measurements are required toquantify the relationships between dune geomorphologyand the upwind input sand flux and associated outputsand flux from dune horns.

2.4. Transverse dunes: some conclusions

Concurrent with advances in understanding dunedynamics based on the empirical measurement ofprocesses in the field, significant progress has beenaccomplished in the mathematical simulation andphysical modelling of airflow over dune forms and inthe understanding of interactions between dunes (Wiggs,2001). Numerical modelling has the advantage of beingable to provide an overall picture of the flow structure,which is spatially much more complete than the resultsobtained by experiments both in the field and in the windtunnel. More specifically, it offers the flexibility torepresent an array of complex geometries observedwithin the natural environment (Badr and Harion,2005). However, even with the advent of these modellinginvestigations the amount of field-based empirical dataagainst which to verify these models and simulations hasbeen severely limited (Wiggs, 2001). Consequently, bothnumerical and physical modelling must be viewed ascomplementary to field investigations.

One issue that recurs in all types of investigationdiscussed in this review is the effect of turbulence on theairflow and sediment transport dynamics over a dune.Within all regions of the dune form, turbulence has beenpromoted as having some influence on sedimenttransport. Flow acceleration/deceleration and streamlinecurvature have been advocated as having an impact onturbulence experienced at the dune toe and on thewindward slope. Within the lee, secondary flow patternsincluding gusts have been suggested as being importantin sediment transport and consequently dune dynamics.In tandem with research aimed at understanding thecomplex interactions between dune forms within adunefield, attention should therefore also be paidtowards understanding how turbulence affects dunedynamics at the single-dune scale.

3. Linear dunes

Given the difficulty experienced in elucidatingprocesses on relatively simple transverse forms, it isnot surprising that more complex dunes have proveneven more difficult to explain. While transverse dunesare formed in uni-modal wind regimes, other forms suchas linear and star dunes are formed in more variablewind regimes. Tsoar et al. (2004) recently consolidatedthe classification of dune forms based on morphody-namics by proposing a three-fold division: migratingdunes (exemplified by transverse forms); elongatingdunes (exemplified by linear dunes); and accumulatingdunes (exemplified by star dunes). Broadly speakingthese equate, respectively, to dunes formed in uni-modalwind regimes, those formed in bi-modal wind regimesand those formed in annual wind regimes with morethan two modes, sometimes called ‘complex’.

The dissatisfaction with empirical studies has beenkeenly felt in the study of linear dunes. Studies in the1970s and 1980s by Tsoar (e.g. 1983) and Livingstone(e.g. 1989) showed that both of their study dunes haddeveloped in bi-modal wind regimes and they reportedno evidence to support Bagnold's (1953) roll-vortexhypothesis. Although the detail of their explanationvaried, both Tsoar and Livingstone argued that lineardunes extended along some resultant of the winds fromthe two directions. Some of the difference between themconcerned the importance of the separation vortexcreated in the lee of the dune: for Tsoar the lee sidewas essential to the dynamics of the dunes; forLivingstone the separation vortex was incidental andthe variability of wind speed (as a surrogate for shearstress) was seen as the fundamental control. Tseo (1993)provided some observations of the trajectories of

Fig. 15. Dune alignments created in flume experiments simulating bi-directional flows. Full arrows are the vectors of flow, the length of the arrowsrepresenting the relative energy from the two directions. Shaded bars represent the resulting bedform alignment (from Rubin and Ikeda, 1990).


tethered kites from the Strzelecki Desert which heclaimed supported the roll-vortex theory but which couldequally be attributed to the secondary flow patternsgenerated by the intrusion of the dune into the boundarylayer described by Tsoar (1983) and Livingstone (1986).Some measurements of wind flow and sand flux onlinear dunes continue to be undertaken in the TaklimakanDesert in China (e.g. Wang et al., 2003, 2004).

One issue that recurs in the study of linear dunes is thequestion of whether linear dunes migrate laterally. Boththose supporting roll-vortex origin and those whobelieve linear dunes to be formed in bi-modal windregimes agree that the overall movement of sand is alongthe dune (creating the elongating form of Tsoar et al.,2004). There is a widespread belief, however, that thereis also a lateral component of movement of linear dunes.

Much of this belief emanates for the work ofsedimentologists, concerned to explain why lineardunes seem to be poorly represented in the rock record.The expectation has been that if linear dunes areresponding to winds from either side of the crest, a slipface would be built sometimes on one side of the crestand at other times on the other. This would lead to sets ofavalanche beds at around 32–34° (the angle of repose ofdry sand) which are often taken as diagnostic of anaeolian origin. Bagnold (1941) provided a simplerepresentation of this case based entirely on suppositionrather than field evidence but the rock record lacksdeposits demonstrating this pattern.

Rubin and Hunter (1985) argued that linear dunes(they termed them ‘longitudinal’ dunes) rarely developin symmetrically bi-modal wind regimes so that oneregime dominates in the development of the dune. As aconsequence the dune tends to migrate more strongly inthe direction of the stronger mode and therefore todevelop asymmetry. Asymmetry of linear dune form iswell-documented from many of the major sand seas.Rubin and Hunter, whose primary focus was what lineardune deposits would look like in the rock record, wereable to use computer simulations to show that inasymmetrical wind regimes, linear dunes would produceinternal structures where the dips were predominantly inone direction (see Rubin's website at http://walrus.wr.usgs.gov/seds/). Their observation was that opposedbeds were rarely found in the rock record. Theysuggested a terminology based on morphodynamics toreflect this: transverse dunes that are roughly (within15°) normal to long-term sand transport direction; lon-gitudinal dunes that are roughly parallel to long-termsand transport (again within 15°); and oblique dunesthat are the intermediate at 15° to 75° to the resultantsand transport direction.

The most compelling evidence that linear dunesmigrate laterally was provided by the experiments ofRubin and Ikeda (1990). They created dunes in asubaqueous flume by simulating flows from twodifferent directions by turning a turntable. They variedthe angle of divergence between the two modes and the

http://walrus.wr.usgs.gov/seds/

http://walrus.wr.usgs.gov/seds/

Fig. 16. Internal structure of a Namib linear dune showing bounding surfaces elucidated by ground-penetrating radar (from Bristow et al., 2005).


relative amount of energy from the two modes. Theirexperiments showed that in a bi-directional flow withdivergence between the modes of 135° and transportratio of 1:1, a longitudinal dune developed aligned withthe resultant transport direction (Fig. 15). However,once the transport ratio was varied from 1:1, obliquedunes were formed. Rubin and Hunter suggested thatthis was why linear dunes were not recognised in therock record. Of course, the implication of their work isthat there probably are some dunes created wheretransport ratios are roughly 1:1 and we might expect tofind dunes of this type in the rock record.

The difficulty for geomorphologists is that there arevery few records of linear dune movement with whichto test the assertion that they move laterally. Threemain types of evidence have been put forward tosupport the lateral migration hypothesis: morphology,direct measurements of movement, and sedimentology.

The morphological evidence used to support thelateral movement hypothesis is the marked asymmetryof the cross-profile of many linear dunes. In theSimpson Desert in Australia, Rubin (1990) explicitlytook this asymmetry as evidence that the sand transportvector was not exactly parallel to the dune trend. Thesecond body of evidence is direct measurements of dunemovement but these are sparse. Hesp et al. (1989), forexample, were able to provide some circumstantialevidence plus some aerial photography data thatsuggested that linear dunes in Qaidam Pendi, NWChina, were migrating laterally at 1–3 m yr−1. The thirdsource of evidence is sedimentological. Rubin (1990)noted the distribution of sediment on the surface of theSimpson Desert dunes and in particular that loose sandwas more abundant on east-facing slopes. This wasdeemed a consequence of lateral migration. He alsoreported that the internal structure demonstrated east-dipping beds at the base of west flanks implying that theeast flanks were 50 to 100 m west of their presentpositions when these foresets were deposited.

Ascertaining internal structures has always beentricky in contemporary desert dune sands because ofthe difficulty of maintaining cut sections in dry sand.

Consequently, reports of pits dug in the surface oflinear dunes have only provided data from the upperfew tens of cms (e.g. McKee 1982) and have seemedrather unsatisfactory. Recently, however, Bristow et al.(2000, 2005) have demonstrated that ground-penetrat-ing radar (GPR) enables us to see internal structures toa much greater depth in dunes. Their preliminary work(Bristow et al., 2000) on a small linear dune in theNamib Desert showed that internal dips on a dune crosssection were often predominantly in one directionalthough not necessarily in the same direction in allsections. Their view was that there was sufficientevidence to support a belief that this dune was mi-grating laterally as well as elongating. In this part of theNamib sand sea the divergence angle between themajor wind regime modes is approximately 135° andthe transport ratio between the modes is roughly 3:1 soaccording to Rubin and Ikeda this would produce alaterally migrating ‘oblique’ dune (cf. Fig. 15). Furtherevidence for lateral migration came from the southernend of a larger linear dune in the same area (Bristowet al., 2005). Here the radar penetrated to depths of 10–15 m and confirmed sizeable cross-sets of bedssuggesting east-to-west migration (Fig. 16). Morecompelling evidence has been provided by an as yetunpublished study taken from the main body of a lineardune.

Notwithstanding the work of Bristow et al.,Livingstone's studies in the same area in the Namibshowed that in 21 years of observations there had beenno perceptible lateral shift of the study dune althoughthere had been considerable movement of the dune'ssurface (Livingstone, 2003). Tsoar et al. (2004) werealso unable to find evidence for lateral movement inaerial photographs from Sinai (taken in 1973, 1982 and1999) and field measurements from vegetated lineardunes and from sharp crested, unvegetated linear duneswith slip faces (which Tsoar et al. term ‘seif’ dunes).They argued that lateral movement could only occurwhen the dune's slip face reached the inter-dunesurface but on their dunes, and the Namib dunes, slipfaces are restricted to the upper slopes.


The work of Bristow et al. (2000, 2005) providedclear sedimentological evidence of migration, yetneither Livingstone (2003) nor Tsoar et al. (2004)could find evidence in field measurements of lateralshift. It is likely that dunes that are over 70 m high likethose in the Namib move so slowly that two decadesmay not be enough to see such a lateral shift and it maybe possible that the lateral shift evident in thesedimentological record is no longer occurring althoughwe must guard against resorting to palaeoenvironmentalexplanations for apparently contradictory evidence.Nonetheless, the difficulty remains that two detailedmonitoring programmes on linear dunes have failed torecognise a lateral shift. Undoubtedly continued GPRsurvey work will further elucidate this conundrum.

4. Conclusion

There is no doubt that field-based studies ofindividual dunes–complemented by theoretical andnumerical investigations–have moved our understand-ing of dune dynamics forward. Despite the difficultiesof obtaining field measurements that allow us toascertain the shear at the sand surface, it remains thecase that field evidence is important. However, in thepast many of the single-dune studies described alargely inductive approach: that is, they collected fielddata, generally about wind flow and sand flux, and thentried to make sense of those data. It may well be that inthe future, now that we have more robust mathematicalmodels, a more deductive approach can be adopted.With this approach the models would provide someidealised version of wind flow, sand flux and dunemovement that could act as a normative model tosuggest areas of field investigation and even act as thebasis for the generation of hypotheses.

The measurements we have of airflow structurearound sand dunes are improving, both as a result offield studies and as a result of the hardware andmathematical models. However, much of the importantrecent work, both in aeolian and fluvial domains, hassuggested that improved understanding of turbulentstructures and their impact on sediment transport mayprove a fruitful way forward in the near future.Increasingly, field studies will be important for thecalibration of computational models that enable greaterunderstanding of these flow-form interactions. Whereasin the past single-dune studies were necessarily by theirnature rather isolated snapshots of very small parts of thedune story, in the future the field studies will validatemodels that allow us to ask a rather wider range of ‘whatif?’ questions.

Some of the results of recent analytical modellingsuggest that we may have to re-evaluate the idea of‘equilibrium’ dunes. Dune patterns at the dunefield orsand sea scale may demonstrate ‘equilibrium’, but at thedune scale future investigations will focus on thedynamics of sediment transfers at the dune and inter-dune scale and longer time-series measurements of duneevolution.

The paradigm for dune studies for several decadeshas been that good quality empirical data about windflow and sand flux will enable us to understand howdunes are created and maintain their form. At least someof the difficulty in the past arose from the plethora ofundirected data generated in single-dune field studies. Inaddition, it proved very difficult to measure theprocesses of sand entrainment and transport at thedune scale. Consequently, some dissatisfaction wasexpressed with field studies during the 1990s. Morerecently, attention has shifted–although not complete-ly–to modelling approaches, and very considerableprogress has been made in developing models of dunedevelopment. It is clear, however, that the models willcontinue to require accurate field observation in orderfor us to be able to develop a fuller understanding ofdesert sand dune geomorphology.

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Documents

Geomorphology of desert sand dunes: A review of recent progress