Mechanics of Sand Transport - Dune Worlds: How Windblown Sand Shapes Planetary Landscapes - page 41

Fig. 4.6 a Image mosaic from the Mars Pathfinder Lander, showing
the three dangling metal cones that made the Windsock Experiment.
Wind tunnel calibrations allowed the orientation of these to be related
to windspeed (U. Arizona/NASA). b The three measurements at three

separate heights follow the Prandtl-von Karman equation (a straight
line on a plot of speed against logarithm of height). The slope of this
line is the shear velocity (or friction speed) and the intercept at zero
velocity is the roughness length. (Data from Sullivan et al. 2000)

in which the airflow is laminar. Such a laminar, horizontal
flow has little hope of lifting particles up, and so dust par-
ticles must be somehow lifted off or pushed through this
layer in order to get into suspension. Due to the low Rey-
nolds number typically encountered at Mars (compared with
the Earth, where the air is 50 times denser) this viscous
sublayer is rather thicker—and thus more important—at
Mars. Its importance depends on the particle size on the
surface, if these are large compared with the viscous sub-
layer thickness then the surface is considered 'aerodynami-
cally rough' and the flow can impart stress on the particles.
When particles are small (like silt on Earth), the particles can
hide in the sublayer and do not feel the full force of the flow.
On Earth the dividing line is usually taken to be about 80 l.
Of course, dust is raised from surfaces on Earth, despite
this effect. This can happen when there are even a few
roughness elements (e.g., rocks) that are large compared
with the viscous sublayer, and stir the flow into the ground
in their wake. There is speculation that pressure drops in
dust devils can suck particles out of the ground, or even
other factors like solar heating and electrostatic effects can
loft the dust to the point where turbulent suspension can
take over. But possibly the most significant mechanism is
where sand or larger particles smash into the ground and
splash dust upwards. This still leaves us with how to get the
sand moving, however.

4.4 Launching the Sand

Sand grains poking out through the viscous sublayer will
see wind stresses. If these can overcome weight, friction
and adhesion, then they can get the ball rolling—literally.
Rigorous treatments will consider the direction of the forces
(and the turning moments) acting on a grain sitting among
other grains, but we will avoid bogging ourselves down in
these distinctions.
Shear velocity (also known as friction velocity) u * is
proportional to the slope of the wind velocity profile when
plotted on a logarithmic height scale (Fig. 4.7 ); it is also
directly related to the shear stress s at the bed surface and to
the air density q f :

Þ 0 : 5 u ¼ s = q f ð ð 4 : 5 Þ

where q a is the air density. While u * has units of velocity, it
is actually related to the rate at which the velocity is
changing within the boundary conditions expressed by the
Prandtl-von Karman expression in Eq. 4.1 .
u* is a less intuitive quantity than the actual windspeed
U. The two are connected, via the stress exerted on the
surface (working through the equation above) in a some-
what convoluted way. A simpler way to at least get a feel
for the numbers is to consider that the stress on a surface