Mechanics of Sand Transport - Dune Worlds: How Windblown Sand Shapes Planetary Landscapes - page 45

Table 4.2 Saltation parameters, as computed by Kok et al. (2012)

They determine that the height has the same form, but
with a smaller prefactor (81 instead of 1100). This analysis
and others (e.g., White 1979; Kok et al. 2012) have con-
cluded that saltating sand on Mars quite likely achieves
horizontal lengths between lift-off and return to the surface
of from around one to some tens of meters. Note that
Eq. 4.6 shows that the saltation path length varies with
windspeed as well as other parameters—notably the path is
shorter in fluid of higher density.
These simulations can also track how effectively the
saltation cloud will build up (or not) as a function of
windspeed. If the growth of the cloud is positive (a grain
once launched into saltation will extract enough energy
from the airstream, and pass that on via splash to other
grains efficiently enough) then saltation can be self-sus-
taining. The windspeed needed to do this is termed the
'impact

Body Threshold

friction
speed (m/s)

Ratio of
impact to fluid
threshold
speed

Typical
saltation
height
(cm)

Typical
saltation
length
(cm)

Venus *0.02 [1 *0.2 *1

Earth *0.2 *0.8 *3 *30

Mars *1.5 *0.1 *10 *100

Titan *0.04 [1 *0.8 *8

discuss in a following section, this parameter may be the
principal determinant of the minimum size of sand dunes on
any given planet.
In any case, in general a saltating grain will impact the
surface both faster, and more shallowly than it was laun-
ched—the grain has extracted energy from the airstream. If
this grain can then launch other grains, they too will
accelerate and a cascading process will build up a saltating
cloud of grains. This 'splash' process (see, e.g., Gordon and
McKenna-Neuman 2011; Kok et al. 2012) depends some-
what on the particle properties: it may be that softer
materials are less efficient at splash than hard rocks. It
seems possible that the influence of impacting saltating
grains may extend beyond that of the initiation of reptation
motion through low-energy splash of surface grains from
near the impact site, perhaps also inducing a wider range of
ejection conditions than has been previously considered.
Many laboratory and theoretical studies have expanded
upon Bagnold's initial studies, including consideration of
saltation under conditions representative of present-day
Mars (Greeley et al. 1974a; White 1979; Almeida et al.
2008) and Venus (White 1981; Greeley et al. 1984a). If the
moving grain attains a high rotation rate, which is certainly
possible from the many interactions taking place during
saltation, then the grain trajectory may be significantly
influenced by lifting forces induced through the Robins-
Magnus effect (White and Schulz 1977) or electrostatic
effects (e.g., Schmidt et al. (1998) show that typical charges
of 60 lC/kg on saltating sand can modify the length of the
saltation path by some 60 %).
Calculated saltation trajectories are highly dependent
upon the many assumptions that go into any simulation
scheme but, in general, the horizontal length attained by a
saltating sand grain is much longer on Mars (meters) and
shorter on Venus (centimeters) than is typical on Earth
(*20 cm) (Fig. 4.12 ). The heights attained by the saltating
grains scale roughly similar to the differences in saltation
length noted above (Greeley and Iversen 1985, pp. 96-98).
Almeida et al. (2008) give the following expression for
saltation length at friction speeds close to the threshold as

threshold' as opposed to the classical 'fluid

threshold' in Sect. 4.4 .
Curiously, this impact threshold (Fig. 4.13 ) is higher
than the fluid threshold on Venus and Titan. On these
worlds, somewhat like sand under water on Earth, grains are
rapidly slowed by drag so splash does not help much. Thus
the classic fluid threshold is what matters.
The situation for Earth seems to be somewhat borderline,
with the impact threshold speed about 80 % of the fluid
value, as suggested by Bagnold. But on Mars, the situation
is dramatically different. Kok's simulations (2010) show
that the wind speed required to maintain on-going saltation
is lower by as much as an order of magnitude from the wind
speed needed to initiate saltation. Thus, recent documen-
tation of dune and ripple movement on Mars (Bridges et al.
2012a, b) may be more easily understood if the maintenance
of saltation requires less wind than is needed to start the
movement of the sand. Of course, like the now-proverbial
flap of a butterfly's wings over Brazil, saltation needs to get
kicked off somewhere by perhaps a meteorite impact or an
exceptional gust, but this new understanding of the hyster-
esis in saltation and the distinction between impact and fluid
thresholds may have resolved the puzzle about Mars.

4.6 Influence of Saltation on the Boundary

Layer

Since energy is now being extracted from the airstream, this
saltating cloud itself modifies the boundary layer wind
profile. Once again, Bagnold (1941, pp. 57-61) pioneered
the investigation of how a cloud of saltating sand grains
affected the wind velocity profile above a mobile surface of
loose sand. Measurements made by Bagnold in his wind
tunnel showed him that the wind profile during fully
developed saltation differed significantly from the wind
profile above a sand surface before the initiation of sand

Þ gD p 0 : 5

L salt ¼ 1100 l 2 q f g

0 : 33

ð

u u t

ð 4 : 6 Þ