Numerical Models - Dune Worlds: How Windblown Sand Shapes Planetary Landscapes - page 236

Fig. 19.9 Flow separation in a
lattice gas/cellular automaton
model of a star dune. Image
courtesy of Clement Narteau

bump will not grow unless its length is large compared with
the saturation length. In other words, the saturation length
defines a minimum scale for dunes to grow—a concept
discussed in Chap. 5 .
Two further effects on the downwind side of the dune are
important. Sand cannot sustain slopes greater than the angle
of repose. Thus a slope condition is imposed on the slip face
of the model. Also (and while generally true even for
rounded dunes (Fig. 5.1 ), it is particularly true of the sharp
change of slope at the top of the slip face), if the downwind
surface slope bends downwards sharply, the airflow can
detach, forming a separation bubble with a recirculating
flow. Flow vectors in such a bubble, estimated using CFD
by Hermann et al. (2005), are shown in Fig. 5.2 ; the
empirical size of this bubble is introduced into the contin-
uum model. (As with CFD, lattice gas models calculate the
flow and thus the bubble explicitly—e.g., Fig. 19.9 .)
In the original one-dimensional incarnation of the model,
an initial low sand mound can progressively grow until its
height becomes such as to perturb the flow, and a slip face
develops. More recently 2-dimensional variants have been
explored, and models of this type have been rather suc-
cessfully compared with water tank experiments (e.g.,
Reffet et al. 2010) and with barchan morphology on both
Earth and Mars (Fig. 19.10 ). In particular, a range of bar-
chan morphologies can be produced by changing the angle
between bimodal winds: in unidirectional winds a conven-
tional two-horned barchan is formed, but as bimodality is
introduced the dune becomes more dome-like with the gap
between the horns filling for an opening angle of *40.

When the opening angle is increased to 90 or more, the
dune takes on a more wedge-like appearance with a single
trailing tail (essentially, a linear dune with a head.) Reffet
et al.'s (2010) study also shows that a single linear sand
streak (whether transversely-oriented or longitudinally)

breaks up into a string of barchans when bimodality

(20-30) is introduced.
These modeling approaches can be somewhat hybrid-
ized. Pelletier (2009) combines a Werner-type model,
modified with Jackson and Hunt's (1975) description of the
boundary layer airflow over a hill, to consider aeolian rip-
ples, transverse dunes, and megadunes, in the same hierar-
chical framework. In essence, the character of the airflow
and ultimately the wavelength of the bedform pattern is
influenced by a roughness scale, which for ripples, he
argues, is determined by the (upper 20th percentile) particle
size and the length scale for the transverse dunes is in turn
set by the ripple amplitude. Note, however, that very dif-
ferent interpretations of the determining length scales (e.g.,
the atmospheric boundary layer thickness as an upper limit
for dune spacing and the saturation length for initial dune
forms, as advocated by Andreotti and others, see Sect. 5.5 ).

19.3 Dynamics at the Dune and Ripple Level:

Pattern Formation

Modeling has now reached a level where not only the for-
mation of an individual dune morphology but the interac-
tion between dunes is being captured. Models now can