Geoscience Reference
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many ways the flow affecting dunes can be thought of not as
the flow of an infinite atmosphere that progressively thins
upwards into space, but rather like a layer of fixed depth as
if it were a liquid held under an elastic sheet. Airflow
encountering an obstacle that is small compared with the
PBL thickness can go over and around. However, if the
obstacle is thick (i.e., an appreciable fraction of the PBL),
the air flow must accelerate strongly to get over it, and this
acceleration at the top will increase the shear velocity
enough to prevent sand from accumulating at the crest. Thus
dunes cannot grow to be higher than some fraction of the
PBL thickness and, given that dunes have a constant max-
imum height-to-wavelength ratio, limits the ultimate size
and spacing of sand dunes to approximately the PBL depth
(Andreotti et al. 2008).
Over the oceans on Earth, where the heat capacity of the
sea is large, the PBL is typically a few hundred meters
thick. Over the continents, and in large deserts especially,
the PBL can grow to be 2-3 km deep. This difference is
made visible in mature coastal dune fields such as the
Namib, where coastal dunes are somewhat small but,
further inland, much larger and higher dunes are seen where
the PBL is thicker.
On Titan, the PBL (controlled in part by the length of the
day, the solar heating, and the heat capacity of the land and
atmosphere) is about 2-3 km deep. This may account for
the general uniformity in dune size observed—on Titan the
seas of hydrocarbon liquid are found only near the poles—
and thus the boundary layer is not likely to vary dramati-
cally in thickness across the equatorial areas where dunes
are found.
On Mars, the thin atmosphere needs little heat to be
warmed appreciably, and so the PBL can grow to be quite
deep—as much as 10 km. One way in which the depth of
the PBL is sometimes indicated on Mars and Earth is that
dust devils can rise up to the PBL depth; Martian dust devils
have been observed to reach much greater heights than their
terrestrial counterparts.
On Venus, the PBL depth is not constrained by obser-
vations. Even more so than Titan, the thick atmosphere
takes a lot of heat to stir, although the length of the solar day
(*120 Earth days) on Venus gives the PBL time to grow.
Thus a depth of the order of a few hundred meters to
*1 km seems plausible.
review briefly the models used to simulate flow at the global
With the possible exception of the role of gravitational
tides in shaping Titan's near-surface winds, the ultimate
power behind wind, and thus dune-building and migration,
comes from the sun. In a nutshell, solar heating is stronger
in some places than others, and causes air to rise. Continuity
requires a horizontal movement of air to replace this rising
cell causing winds, and this horizontal motion can be
affected by the planetary rotation and by topographic
obstacles. This process occurs at a range of different scales
that are superposed. First is the natural result of planets
being spheres, such that some parts geometrically receive
more sunlight than others: this is a function of the tilt of
their equator with respect to their orbit around their parent
star, as recognized by Edmond Halley in the 1600 s. In fact,
all the dune worlds have modest obliquities so that the polar
regions on average receive less sunlight (which is not true
for worlds with obliquities above 40). With modest
obliquity, solar heating is concentrated at low latitude and
leads to rising air over the equator. Where it comes down—
the mean meridional circulation, sometimes referred to as
the Hadley circulation—depends on planetary rotation, and
the downwelling flow is typically dry and thus is where
deserts tend to form. On Earth, this occurs in two bands
roughly 20-30 from the equator (Fig.
3.1
). On slowly-
rotating Titan, a wide equatorial band tends to dry out.
The interaction of planetary rotation with the meridional
flow leads to overall surface wind patterns which, because
of their utility for exploration and commerce, are named the
'trade winds'. The first global map of these was published
by Halley. They are belts of diagonal winds where the
upwelling and downwelling flows (which are statistical
averages—the air does not move in one large coherent
global way) meet the surface and go north or south, but are
diverted by the so-called Coriolis effect due to the planet's
rotation.
Because of Titan's slow rotation, the meridional circu-
lation is pole-to-pole for each half of the year (reversing
each equinox), without the intermediate cells seen on Earth
(Fig.
3.2
).
Note that even subtle changes in these astronomical
drivers of the atmosphere can drive climate change. The
Croll-Milankovich variations in the rotational and orbital
parameters of a planet (and their arrangement with respect
to each other—specifically the timing of perihelion with
respect to the seasonal cycle) play a role, perhaps even a
dominant one, in forcing change in the extent of ice sheets,
sea level, and the extent of deserts on Earth. These changes,
on timescales of tens to hundreds of thousands of years (i.e.,
large compared with the construction time of a typical dune)
can therefore form and leave dunes in locations where
present conditions do not allow them to form. Thus dunes
3.3
Planetary Wind Patterns
Clearly, no discussion of planetary dunes can be complete
without consideration of the winds that form these features.
A variety of factors affects winds at different temporal and
spatial scales; these variations are superposed, and how they
interact is well beyond the scope of this topic (although we
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