Numerical Models - Dune Worlds: How Windblown Sand Shapes Planetary Landscapes - page 231

Fig. 19.2 Output from a
mesoscale model: the plot
indicates a region about
1000 km 2 centered on Arsia
Mons, a volcano that rises some
9 km above the surrounding
plain. Here, night-time winds are
shown, with a strong katabatic
flow of cool air downhill. From
Spiga and Lewis (2010, CC
License)

Fenton et al. (2005) used a mesoscale model to consider
the airflow in Proctor crater, Mars. Kok (2010) showed that
even though the hourly averaged winds are below the fluid
(initiation) threshold for sand transport, the lower threshold
for sustaining transport (see later) means that as long as
there are occasional gusts that can cause saltation (however
briefly), the probability of sand transport during winter days
is in fact quite high. This explains why seasonal shifts in
slip faces can be observed on Proctor dunes, even though
the hourly mean speeds are below the initation threshold.
Spiga and Lewis (2010) have used a mesoscale model to
explore the wind variability and its effect on sediment
mobilization; some example output from their model is
shown in Fig. 19.2 .
With a cell size that may be of the order of l km in such
models, transient turbulent structures are not usually
resolved, and subscale transport must still be parameterized.
The reader will be unsurprised to learn that yet smaller-scale
models also exist, so-called Large Eddy Simulations (LES)
with typical grid scales of a few meters or less, which are
able to explicitly model turbulent eddies such as dust devils.
Moving to an even smaller scale, with *0.1 m or less
grids, it is possible to simulate the airflow over an individual
dune. The language used to describe such models tends to be
a little different, for historical reasons. Although internally it
is still the Navier-Stokes equations, this scale of model was
developed not for meteorology but for aeronautics, to model
the drag on aeroplanes and other vehicles. The codes here

are referred to as CFD (Computational Fluid Dynamics), and
typically do not bother with such aspects as radiative
schemes or clouds, but pay much more attention to surface
shape, and the treatment of friction (Fig. 19.3 ). With this
type of model, one can simulate such features of aeolian
interest as the separation of the airflow at the crest of the
dune and the recirculating eddy behind it.
A significant complication, not yet explored widely with
CFD, is the effect of saltating sand. In other words, for
accuracy at this small scale, the interaction of the air flow
with the suspended or saltating material needs to be con-
sidered, in that the effective surface friction felt by the wind
changes once sand is lofted. This coupling is an outstanding
area for further work.
Finally, a rather distinct class of flow models has
emerged in recent years for certain applications, called
lattice-gas or Lattice-Boltzmann (LB) models, see, e.g.,
Frisch et al. (1986). These are somewhat similar to cellular
automata (CA—see below). Like CFD, LB models consider
a flowfield as a set of cells within which the flow is assumed
to have uniform properties, being considered in effect as a
set of particles. However, in an LB model, these properties
(usually flow direction) can have one of only a small set of
discrete values; for example, in a hexagonal grid, the flow
direction can have only one of six values, and the speed has
only one value. The interaction between cells is considered
analogously to colliding particles. While this simplification
sounds primitive, the aggregate behavior across large