Solitary wave behavior in sand dunes observed from space
Abstract Although the dynamics of individual barchan dunes are well understood, their interactions are the subject of ongoing scientific interest and debate. Numerical and analog model predictions of shape-preserving binary dune collisions have been hard to test due to the long timescales over which such processes typically occur. This paper documents ten binary dune collisions in a 45-year time sequence of satellite images from the Bodélé Depression in Chad. The observations confirm that when two barchan dunes collide, a transfer of mass occurs so that one dune appears to travel through the other unscathed, like a solitary wave. The world’s deserts contain a number of dune types, depending on the availability
of sand and the dominant wind regime (Reffet et al., 2010). Of these different types,
the barchan or crescentic dune is perhaps the best understood. Barchans are found in
areas with a relatively limited sand supply and a unimodal wind regime
(Bagnold, 1941). Under these conditions, they can be easily simulated in wind
tunnels and computer models (Wippermann and Gross, 1986). Nevertheless,
considerable controversy exists regarding an intriguing prediction of these
models, namely that barchan interactions are characterized by solitary wave
behavior (Schwämmle and Herrmann, 2003; Endo et al., 2004; Katsuki
et al., 2005; Durán et al., 2005; Durán et al., 2011). The proposed mechanism is as
follows. Because the velocity of barchan dunes is inversely proportional to their
size, small dunes eventually catch up with large ones. Computer models
indicate that when this happens, the upwind dune captures the sediment of the
downwind dune and starves it of sand. As a result, the upwind dune grows and
slows down, while the downwind dune shrinks and speeds up again. Seen
from a distance, the small dune appears to traverse right through the large
dune. Although the occurrence of small barchans at the down-wind side of big ones is
seen by some as evidence that barchan dunes could behave like solitions
(Besler, 2002), such ‘snap shot’ views are equivocal, and could also be interpreted as
barchans calved from the dune horns (Elbelrhiti et al., 2005) and blown sideways by
short term cross-winds (Livingstone et al., 2005). The only way to settle the debate
is continuous monitoring of the collision process from start to finish (Ewing and
Kocurek, 2010). Unfortunately, this is usually very difficult, because most barchan
dunes on Earth move too slowly to see dune interactions occurring on time scales of
less than a few decades. One notable exception to this is the Bodélé Depression
in northern Chad, which contains some of the world’s largest and fastest
moving barchan dunes (Vermeesch and Drake, 2008). This is due to a unique
combination of extremely strong winds and the fact that Bodélé dunes are largely
made of low density diatomite flakes, which easily break down to form the
world’s most important source of eolian dust (Giles, 2005). The Bodélé thus
forms a unique natural laboratory where eolian processes are magnified and
accelerated. Various Earth observation satellites have monitored northern
Chad from space since the mid-1960s. A time series of co-registered Landsat,
SPOT, and ASTER scenes, combined with declassified American spy satellite
images yields a 45 year record of dune migration in the Bodélé, revealing
several clear examples of solitary wave behavior (Figure 1 and Table 1). Five
of these solitons are shown as animations in the online supplement and at
http://ucl.ac.uk/~ucfbpve/solitons.
Much of the confusion and controversy regarding so-called solitary wave behavior
in dunes stems from the fact that there is no physical mechanism by which one mass
of sand could pass through another (Livingstone et al., 2005), and neither is it
possible for one dune to climb across another, as it would be destroyed by the slip
face of the latter (Durán et al., 2005). It is important to reiterate that colliding
dunes are not ‘real’ solitons, but only appear to behave like solitons, whose shape is
preserved not by a transfer of momentum, but by a transfer of mass (Hersen and
Douady, 2005). Numerical models indicate that solitary wave behavior only occurs
when the initial volume ratio (ri) of the two interacting dunes is greater than ~0.25
(Durán et al., 2005). Smaller ratios lead to either complete absorption of the small
dune, or ‘breeding’ of several little dunes (Durán et al., 2005; Durán et al., 2011).
Unfortunately, visual inspection of the two-dimensional satellite imagery used in the
time series analysis did not permit direct measurements of the relative dune
volumes. However, using the dune widths raised to the third power as a
substitute for volume, as advocated by Durán et al. (2011), yields approximate
volume ratios of 0.13-0.54, consistent with the model prediction within the
(admittedly large) analytical uncertainties (Table 1). A more rigorous and precise
quantitative validation of the soliton model would require high resolution digital
elevation models. The author is in the process of acquiring these for future
research. ‘head-on’ collision (a.k.a. ‘bedform repulsion’, sensu Kocurek et al., 2010) is just
one of the ways in which dunes can interact. When the initial lateral offset
(θi; Durán et al., 2011) between two colliding dunes is less than 0.5 a different type
of dune interaction arises. The time series of satellite images reveals a number
of these ‘off-center’ collisions (Figure 2 and Table 1). Analog models and
analytical calculations have indicated that such dune interactions may be
instrumental in maintaining the long-term stability of barchan dune fields (Hersen
et al., 2004; Hersen and Douady, 2005; Kocurek et al., 2010). Laboratory
experiments in flume tanks show that, when a small and fast barchan collides with
one of the horns of a larger and slower downwind dune, it literally ‘pushes’ away
that horn (Hersen and Douady, 2005). This results in the creation of a new
barchan and an exchange of mass between the two dunes, similar to that which
occurs as a result of the ‘head-on’ collisions discussed before. Exactly the
same kind of behavior is observed in the Bodélé Depression (Figure 2), five
further examples of which are shown as animations in the supplementary
information.
Over the past two decades or so, a series of increasingly sophisticated numerical
models have been developed in order to explain dune morphology and formation
(e.g., Wippermann and Gross, 1986; Zhang et al., 2010). Great strides have been
made in our ability to model the saltation of sand and turbulent flow of air
(Livingstone et al., 2007). The strength of scientific models, however, lies not in the
description of the natural environment, but in their ability to make testable
predictions. The observation of shape-preserving binary dune collisions in the
real world confirms the validity of the numerical and analog models that
predicted them, lending credibility to other predictions that such models might
make.
AcknowledgmentsCharlie Bristow provided useful feedback on early drafts of the paper. This research was partially funded by University of London Central Research Fund grant AR/CRF/B.
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