Numerical Models - Dune Worlds: How Windblown Sand Shapes Planetary Landscapes - page 235

Fig. 19.7 In a coupled model,
the flow field is computed using
the topography as a boundary
condition, then the surface wind
stress and thus the resultant
sediment flux is computed. This
is then used to modify the
topography and the system
begins the loop again. This
example is courtesy of Clement
Narteau

Fig. 19.8 A cellular automaton
model incorporating vegetation.
These transverse and barchan
dunes are moving up towards the
top right, where vegetation
modifies the transport rules (cells
with vegetation have small
vertical stalks, and thus appear
dark in this representation).
Image courtesy of Jo Nield

implementations of this type of CA model available on the
web, e.g., Barchyn and Hugenholtz (2012).
Another approach, somewhat distinct from the cellular
automaton flavor of model, is to consider the sand surface
height as a continuous variable, and to model the evolution
of a height profile algebraically. This type of morphody-
namic model was invoked by Kroy et al. (2002); a recent
review is by Duran et al. (2010). Essentially, a shear stress
field is calculated, taking the surface slopes into account
(i.e., the topography causes the flow to accelerate at the

crest). Simplistically, this would prevent dunes from
growing—sand would be least likely to accumulate at the
crest. However, several factors break the symmetry of the
problem. First, hydrodynamic effects cause the shear stress
to be maximized upwind of the crest. This would cause
deposition at the crest, leading to growth of a dune.
However, a finite distance (the 'saturation length') is
needed for sand transport to build up to a steady-state value.
This has the effect (see Fig. 4.17 ) that the sand flux reaches
a peak downwind of the peak shear stress and means that a