Mechanics of Sand Transport - Dune Worlds: How Windblown Sand Shapes Planetary Landscapes - page 47

Fig. 4.14 Wind velocity
distributions for loose sand, both
prior to the start of motion, and
after sand-driving has become
fully developed (modified from
Fig. 18 of Bagnold 1941)

wind tunnel, and he was able to document that sand was
removed from those areas where the drag effect was not
fully developed while sand was deposited downwind of the
place where the drag effect was fully developed. This led
him to conclude that sand patches less than *6 m in width
will tend to lose sand, whereas sand patches larger than this
size will tend to gain sand, gradually growing to the point of
becoming a regular sand dune.
Andreotti et al. (2010) have measured the saturation
length Lsat in careful wind tunnel experiments, and find a
value of 0.55 m, essentially independent of wind speed.
They suggest that Bagnold erred in that he estimated the
removal rate (by weighing) averaging over distances com-
parable with the length they measured Lsat to be. Field
measurements by Elbelrhiti et al. (2005) suggest L sat to be
1-1.7 m. These and other measurements seem to suggest
Lsat being at least a little shorter than Bagnold's pioneering
measurement. Andreotti et al. (2010) evaluate Lsat for
sediments of different size and windspeed, and find that
within 50 %, L sat * 2L d .
Claudin and Andreotti (2006) have argued that the drag
length similarly (perhaps via the saturation length) defines
the scale at which a flat sand bed will destabilize—essen-
tially, the wavelength of perturbation that will grow the
fastest and thus the size of 'typical' dunes that form first.
Plotting (Fig. 4.15 ) the wavelength k of the smallest dunes
in snow and sand on Earth, as well as dunes on Mars and
seen in the Venus wind tunnel (see Chap. 14 ) , they suggest
a global scaling of
k 53L drag 53D p q a q p

Fig. 4.15 The length scale of 'elemental' dunes in a wide range of
fluid mechanical settings seems to relate to the drag length. Data from
Claudin and Andreotti (2006)

This scaling suggests that, unlike on Mars, where the
smallest 'proper' dunes (see next section) are many meters
across, the smallest dunes on Titan will be tiny. However,
once dunes form, they can grow, probably until they reach a
wavelength roughly equal to the height of the planetary
boundary layer ( Sect. 3.2 ) .
Equation 4.8 implies a scaling (for a given sediment size
and density) with atmospheric density; this effect is nicely
seen not only in the difference between typical ripples on

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