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simulated; probably one of the most important factors,
especially in ripple formation, is the launch speed of a
saltating particle. The recent book by Zheng (2009) dis-
cusses these factors and the application of trajectory simu-
lations to aeolian studies; this topic also discusses at some
length the cellular automation and continuum dune and
ripple modest that we introduce later in this chapter. A
recent development is the COMSALT (Comprehensive
Saltation) model (Kok and Renno 2009) which systemati-
cally treats the various factors and finds, for example, that
because the kinetic energy of a particle 'splashed' from the
bed is high compared with the additional energy the particle
gains in the thin Martian air (unlike on Earth), that there is
an order-of-magnitude difference between the wind speed
needed to initiate saltation on Mars and that needed to
sustain it once it has started (Kok 2010), and that this may
account for the seeming paradox that predicted windspeeds
on Mars are often too low to permit saltation. A crucial
distinction between Mars/Earth and Venus/Titan emerges
from this study, namely that splash is inefficient on the latter
two worlds, where particles must be generally mobilized by
direct fluid lifting (and in that sense movement is qualita-
tively more similar to terrestrial underwater rather than
subaerial transport).
The COMSALT model finds hop distances of 0.15-
0.2 m for shear velocities (friction speeds) of 0-1 m/s on
Earth. On Mars, for shear velocities of 0.5-3 m/s, the hop
lengths are 1-4 m. These results are more-or-less com-
mensurate with the typical scale of ripples on the two
worlds. The corresponding hop heights are 1.5-2 cm and
10-35 cm (Kok, 2010). On the other hand, for conditions
of only twice the threshold on Venus and Titan, the hop
length is 1 cm and 8 cm respectively, compared with
*30 cm and 1 m on Earth and Mars. Thus Venus hops are
invisibly short and visible ripples are unlikely to be seen
ples on Titan may be present (and conceivably could affect
radar reflectivity via Bragg scattering), but would be rather
smaller than on Earth.
In principle, the evolution of a dune could be calculated
by applying the flowfield from a CFD model or similar as
the inputs to such grain trajectory simulations. However,
modeling the migration of a dune grain by explicitly-sim-
ulated excruciating grain is not an efficient way to proceed.
Various attempts to parameterize the airflow over a dune
and compute the resultant sand transport with conventional
equations have been made, and these efforts (see also later
in this section) have tended to focus on isolated barchans, as
both beautiful and somewhat simple but perhaps surprising
shapes. Perhaps the first such effort, and a paper still worth
reading today as it crisply outlines the problem, is that by
Howard et al. (1978). A description of wind speed and
direction from field measurements at different places on a
Salton Sea barchan were applied to Bagnold-type sand
transport formulae, and the evolution of the dune deter-
mined by book-keeping the sand. They went on to suggest
what factors may control barchan form, but the first result to
look for is essentially that the dune does not evolve—iso-
lated barchans simply retain their shape and move down-
wind. Wipperman and Gross (1986) investigate a similar
approach: one nice result (seen also in the revival of bar-
chan models in the last decade—see later) is the evolution
of a simple conical sand pile into a two-horned barchan.
For understanding the general relationship of wind
direction to dune form, some quite compelling simulations
of dune dynamics can be generated by applying rather
simple rules over and over again to rather elementary
description of the terrain (a grid of discrete heights, with
perhaps only a dozen or two cells across a dune: in some
cases). The seminal work in applying such Cellular
Automaton (CA) models was that of Werner (1995),
building on Landry and Werner (1994), and Nishimori and
Ouchi (1993) have a similar approach.
The most famous example of a cellular automaton is the
'Game of Life' devised by mathematician Simon Conway.
Here, there is a square grid of cells each of which can be
either dead or alive (0 or 1). The status of each cell at the
next timestep depends on its present status and that of the
eight cells adjacent to it. If a cell has 0 or 1 or more than
three live neighbours, it dies from starvation or over-
crowding, but if it has two or three, it lives. A dead cell with
three live neighbors will bcome live. That's it. Despite the
simplicity of such rules a bewildering array of structures
can exist-constant (e.g., a square of four cells), oscillating
(e.g., a line of three cells), propagating (the 'glider', a set of
six cells that cycles through a set of four configurations, but
displaces itself by one cell over that cycle) and so on. Not
only are remarkable structures possible (e.g., the glider gun,
a cyclic structure which launches a glider every 30 steps)
but it can be shown that the game can act as a Turing
machine, i.e., in principle, any computable problem could
be expressed in the game. More generally, the application of
CA models to a wide range of situations has been espoused
by Stephen Wolfram.
The way Werner's model works is that a grid of surface
heights is set up (essentially as stacks of discrete slabs of
sand), and simple rules describe the transport of slabs from
one stack to another. A cell is selected at random and it is
determined whether the top slab in the cell (if there are any
slabs) is in the shadow of upwind slabs—i.e., it is less than
15 degrees below them (e.g., Fig.
19.5
). If not, then the slab
is moved in the downwind direction by some distance (the
saltation hop length). Then the grid is checked to see if the
angle
of
repose
is
exceeded;
if
so,
slabs
are
shuffled
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