Modelling barchan dunes 255

Copyright © 2005 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms 30, 255–257 (2005)

Earth Surface Processes and LandformsEarth Surf. Process. Landforms 30, 255–257 (2005)Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/esp.1206

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Barchan dunes: why they cannot be treated as‘solitons’ or ‘solitary waves’Ian Livingstone1*, Giles F. S. Wiggs2 and Matthew Baddock1

1 Division of Environmental Science, University College Northampton, Northampton, NN2 7AL, UK2 School of Geography and the Environment, University of Oxford, Mansfield Road, Oxford, OX1 3TB, UK

AbstractSchwämmle and Herrmann (Nature, 2003, vol. 426, p. 619) have suggested that two sub-aerial barchan sand dunes could ‘pass through one another while still preserving theirshape’ in a manner similar to solitons or solitary waves. A wide range of published field andwind tunnel evidence suggests that this assertion should not go unchallenged. Copyright ©2005 John Wiley & Sons, Ltd.

Keywords: aeolian geomorphology; barchan dune; soliton

Introduction

Based on innovative analytical modelling solutions, Schwämmle and Herrmann (2003, p. 619) recently suggested thattwo sub-aerial barchan sand dunes could ‘pass through one another while still preserving their shape’ in a mannersimilar to solitons or solitary waves. This assertion should not go unchallenged. There is a large body of literature onthe behaviour of barchan dunes without a single report of this phenomenon. There is also much information about thedynamics of barchan dunes that suggests that there is no physical process by which this could occur.

Field and Wind Tunnel Observations

The movement of barchan dunes – the most rapidly migrating dune bedform – has been the subject of a number offield studies, many of which have used sequential air photographs and repeated ground surveys (e.g. Barnes, 2001;Hastenrath, 1968, 1987; Haynes, 1989; Slattery, 1990; Stokes et al., 1999). Whilst these studies do provide evidenceof dunes of different sizes migrating at different rates, in none of these detailed studies does one barchan pass throughanother.

There are also many observations of wind and sand flow around barchan dunes both from field observations andwind tunnel experiments (e.g. Frank and Kocurek, 1996a, b; Hesp and Hastings, 1998; Lancaster et al., 1996; Wenget al., 1991; Wiggs, 1993; Wiggs et al., 1996). These studies suggest that sand is carried over the windward slopeof the dune and deposited on the lee slope in the separation eddy created at the dune’s crest. The sand budget of abarchan dune does include some loss of sand from the ‘horns’ of the barchan and this is compensated for by sandarriving at the foot of the upwind slope of the dune. Without this input the barchan dissipates; sand supply is requiredto maintain the barchan’s mass (Andreotti et al., 2002).

There is clear evidence in field observations that dunes of a range of sizes can co-exist alongside each other andthere are well-established relationships between dune size and dune migration velocity (e.g. Long and Sharp, 1964).All other things being equal, smaller dunes move faster than larger dunes. Consequently it is not unusual for smalldunes to catch up with larger ones. When this happens the dunes either coalesce or they temporarily form a compounddune before the smaller moves off in the downwind direction (e.g. Gay, 1999). There are field observations of smallbarchans emerging from the horns in this manner (termed ‘calving’ or ‘breeding’; Norris and Norris, 1961) but no

Received 12 October 2004;Accepted 8 November 2004

*Correspondence to:I. Livingstone, Division ofEnvironmental Science,University CollegeNorthampton, NorthamptonNN2 7AL, UK. E-mail:ian.livingstone@northampton.ac.uk

256 I. Livingstone, G. F. S. Wiggs and M. Baddock

Copyright © 2005 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms 30, 255–257 (2005)

observations of dunes emerging from the slip face of a barchan. Besler’s (2002) work, cited by Schwämmle andHerrmann (2003), reports smaller barchans ‘climbing’ over the windward slope of larger compound or mega-barchans,a commonplace phenomenon also described by others (e.g. Wilson, 1972; McKee, 1979, figure 13C; El-Sayed, 2000).Notwithstanding the assertions of Schwämmle and Herrmann, there is no field evidence in Besler’s paper or elsewhereof one dune ‘passing through’ another or of a dune emerging from the slip face of another. There is no physicalprocess by which the faster moving mass of sand could ‘pass through’ the slower moving mass.

Rather than the presence of small barchans on the downwind side of larger ones being evidence of solitary wavebehaviour (see Schwämmle and Herrmann, 2003, figure 1), we would suggest that such small dunes have ‘calved’from the horns of the larger dune. The smaller size of the dune means that it has a short ‘memory’ (Warren and Kay,1987; Warren and Allison, 1998) with a morphology that is the result of shorter-term wind regimes. This means thatthe smaller dune could be blown into the path of the larger dune by lower frequency cross-winds before reverting toits original form. The location of the dune in the environment might give the impression that it must have come fromthe slip face of the upwind dune, but in fact it is just a faster responding dune form that is sensitive to non-dominantwind directions.

Schwämmle and Herrmann (2003) draw an analogy with waves in water that can pass through one another. Thismechanism is completely different from the ‘wave pattern’ sub-aerially created in sand. Despite the superficial similar-ity, noted in early work by Cornish (1914) and others, waves in fluids are propagated by momentum transfer betweenmolecules whereas the wave form of dunes is created in granular material. There is no evidence to suggest that sanddunes are energy waves, as is the case with solitons.

In fact, in earlier modelling work Herrmann and Sauermann (2000) argued that because barchan dunes lose sandfrom the horns and require an input of sand from upwind this was ‘a good argument against the hypothesis thatbarchan dunes are solitary waves’ (p. 28), and more recently Schwämmle and Herrmann (2004, p. 783) stated that‘these dunes do not behave exactly like solitons because of their loss of volume’. A study with co-workers (Lima etal., 2002) spoke of ‘coalescence’ and ‘merging’ of dunes.

Considerable effort is currently being expended to produce reliable mathematically based models of the behaviourof barchan dunes, including three-dimensional models that consider the controls on a barchan dune’s shape (e.g.Hersen, 2004). One recent study has modelled barchan collisions and suggested that the outcomes are either ‘coales-cence’ or ‘reorganization’ (i.e. calving), controlled by the offset (how far from a ‘direct hit’ the collision is) and themass ratio between the two barchans (Katsuki et al., 2004). Subaqueous physical modelling of dunes (Endo et al.,2004) identified other collision outcomes, but they were cautious about the application of these results to subaerialenvironments.

Conclusions

There is no empirical evidence from field or wind tunnel observations that barchan dunes behave like solitary waves.When a smaller dune catches up with a larger dune it will either: (i) coalesce with it; or (ii) merge to form a compounddune before subsequently separating to progress downwind; or (iii) migrate over the windward slope of the largermega-dune. Barchan dunes do not ‘pass through one another while still preserving their shape’ in a manner similar tosolitons.

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