Numerical Models - Dune Worlds: How Windblown Sand Shapes Planetary Landscapes - page 238

Fig. 19.11 Simulation of a barchan field. Note the trailing arms, with
downstream barchans often near-centered on the sand streams from the
arms of the upwind ones. Such interactions can be explored with pure

CA models, continuum models, and (ideally) coupled sand/flow

models. This is a CA example, courtesy of Jo Nield

a field of mixed size barchans would see the small ones
shrink and the large ones grow.
However, the barchans will interact with each other.
Smaller barchans propagate faster, and so will overtake, or
collide with, their larger counterparts. A crucial issue is
what happens during these collisions. If the barchans are of
very different sizes, then the smaller one is simply absorbed
into the larger one, but more interesting effects occur on
more similarly-sized dunes (Fig. 19.11 ).
Hersen and Douady (2005) performed water tank
experiments with small barchans, using glass beads of dif-
ferent colors to trace the fate of the sand from the two
colliding dunes. The dunes could not be 'too' equal in size,
as then the differential speed is too low and it takes too long
to practically perform the experiment. Their elegant
experiment (similar experiments in a water flume have been
done by Endo et al. 2004) showed that one barchan (green)
hitting another (red) about twice its size slightly off-center,
merges with the larger dune but causes it to spawn another
barchan downstream, not much smaller than the original
'impactor'. The sand color showed that it was not the
impactor barchan propagating through the large one—the
spawned dune was all red sand from the original target
dune. Numerical simulations of the same 'tunneling' pro-
cess were reported by Schwammle and Herrmann (2003).
These experiments can inform efforts to understand the
apparent organization of barchan dunes into corridors (e.g.,
Hersen et al. 2004; Elbelrhiti et al. 2008), wherein across a
barchan field there may be significant variation of dune size,
but along the downwind direction the dunes tend to have a
somewhat constant size.
Exploration of pattern formation began with ripples.
Initially, ripples form at a small scale, but can progressively
grow in spacing and amplitude ('pattern-coarsening'); this
behavior was noted in early work by Werner and Gillespie

(1993). In Pelletier's (2009) simulation, with a domain of
N = 256 points across in each direction (each point sepa-
rated by the saltation length), the pattern coarsens to a
steady-state value over about 1000 N 2 timesteps.
This coarsening has been observed in field measurements
and wind tunnel experiments: the bedform spacing (nor-
malized by particle diameter) grows as the square root of
time until the steady-state is reached. This square-root
growth is also observed in the numerical model.
An interesting behavior in aeolian transport is that an
initially-irregular ripple or dune pattern, with many 'defects'
(i.e., free ends of dunes, or Y-junctions; see Fig. 19.12 )
becomes progressively more and more regular. The
dynamics of individual defects were considered by Werner
and Kocurek (1999) in an analytical way. That simple model
showed the growth of spacing with time (initially linearly,
then logarithmically, until leveling off at an asymptote) and
the associated decrease in defect density. The progressive
elimination of defects from the pattern is also seen in Wer-
ner-type models; e.g., in Pelletier's simulation, the defect
density decreases to zero over about 10000 N 2 timesteps.
In this evolution scenario, all dune systems should evolve
to be free of defects. Many of the oldest dune systems are
relatively free of them (or at least have areas where this is the
case): the Namib and Arabian deserts for one, and Titan's
Belet sand sea is another example. On the other hand, when
climate change (e.g., due to Croll-Milankovich cycles) leads
to a change in wind regime, the dune pattern must adjust
(e.g., Werner and Kocurek 1997), and in so doing (essen-
tially a new dune/ripple system builds on top of the old one)
many defects can be created, thus the defect density is seen
as a kind of clock that might measure the age of a system.
General dune patterns, and dune-dune interactions, have
been well-documented (e.g., Kocurek and Ewing 2005;
Ewing and Kocurek 2010). However, it is only now that