Mechanics of Sand Transport - Dune Worlds: How Windblown Sand Shapes Planetary Landscapes - page 44

Fig. 4.11 Beautiful high-speed
photography of saltating sand
grains in a wind tunnel. The
grains (about 350 lm in size) are
illuminated by a laser sheet,
strobing at 380 flashes/s. The
rotation of the grains can be
clearly seen—some are spinning
at least at 100 revs/s, which may
affect their dynamics. The arrows
show the direction of motion—
the downwind flight results in a
rather shallower angle of impact
than their steep launch. Image
courtesy of Susan McKenna-
Neuman

oxygen). Thus the dynamics of sugar sprinkled onto the food
of astronauts or space tourists may be rather similar to the
mechanics of sand on Titan (see Fig. 1.4 ).
The perspective afforded by this plot is all very well; the
overall mobility of material is reasonably well conveyed.
This analysis also forms the principal basis for assuming
that Titan's sand dunes are made of particles of 0.3 mm
diameter (they have not been measured!). For Titan and
Venus, the approach above is probably about right even if
the cohesion may need adjusting, since the atmospheres on
these worlds are dense and so fluid stresses really determine
the mobility. However, a vexing problem for some time is
that the threshold winds it predicts are necessary to move
sand on Mars are rather high, and yet sand (and even larger
granules) sometimes move.
The resolution to this paradox was somewhat anticipated
by Bagnold, who pointed out that the threshold under static
conditions (where no saltating grains are impacting the
surface) is higher than the threshold observed when active
saltation is under way; the so-called impact threshold is
about 80 % of the static threshold value. The difference
between starting saltation and sustaining it turns out to be
critical at Mars (e.g., Kok 2010) and relies on understanding
what happens to grains once they do get moving.

raise the grain from the surface, but as the grain moves
higher into the wind profile, it steadily picks up horizontal
velocity obtained at the expense of the wind. Bagnold
(1941) considered the initial movement of the sand grains
when lifted off the surface to be essentially vertical, but
high-speed photography of sand motion in wind tunnels
(e.g., Fig. 4.11 ) has demonstrated that the average ejection
angle ranged between 34 and 41 (from horizontal) for
sand of from 90 to 300 lm in diameter (Table 1 of Nalpanis
et al. 1993). It appears that even deep within the boundary
layer of the wind, sand grains lifted from the surface very
quickly

acquire a horizontal velocity derived from the

particle's interaction with the wind.
In the absence of forces other than gravity, the height
achieved by a saltating sand grain is directly related to the
square of the ejection velocity divided by twice the accel-
eration of gravity, a straightforward ballistic relationship,
and the time of flight is just twice the vertical component of
speed divided by gravity. Aerodynamic lift and drag can
modify these times and heights somewhat (more for Venus/
Titan than Earth/Mars), see below. The sand grain is
accelerated horizontally by the drag induced by the wind,
and if the grain climbs appreciably through the boundary
layer, it experiences ever stronger winds.
The grain may attain a high fraction of the windspeed if
it remains aloft long enough. One simple metric is the so-
called 'drag length' L d , the horizontal distance required to
achieve this, which is written simply as L d *D p (q p /q a ).
Bigger particles have more inertia (D 3 ) compared to their
drag area (D 2 ), and so take further to accelerate. Similarly,
thinner atmospheres and denser particles take longer to
accelerate. Some numbers are indicated in Table 4.2 ;aswe

4.5 Sand Grain Trajectories

The trajectory followed by a saltating sand grain is the
result of the interplay between the various aerodynamic and
inertial forces acting on the sand grain. In broad terms, the
initial part of the trajectory is dominated by lift forces that