Winds and Atmospheres - Dune Worlds: How Windblown Sand Shapes Planetary Landscapes - page 24

3

Winds and Atmospheres

Essentially, all solid bodies in the solar system, and likely
most of those in other planetary systems, have some fine-
grained materials on their surface. But few have atmo-
spheres to blow these grains around to make dunes. Entire
libraries exist on the subject of meteorology; here, we can
only highlight the principal characteristics of these atmo-
spheres and their winds. For further reading, the text on
desert meteorology by Warner (2004) is recommended for
the Earth, while students of Mars should refer to Read and
Lewis (2004).

Density and pressure P are related. For ideal gases, this
relationship is simple: qa = PM/R o T, where R o is the uni-
versal gas constant 8314 J/K/mole, T is the temperature in
Kelvin, g is gravity and M is the relative molecular mass
(28 for nitrogen, 29 for air, 44 for CO 2 ). If we kept the total
mass of the atmosphere (and thus the pressure) the same,
but raised the temperature, then the density will get lower.
Substituting values for the summit of Mauna Kea on Hawaii
(a familiar location to astronomers, with an altitude of
4200 m) P = 611mb, T = 260 K, we find the density to be
about 0.8 kg/m 3 , or a third less than at sea level, which
accounts for the symptoms of altitude sickness often

3.1 Atmospheres

encountered there.
Note that on Titan, the atmosphere is thick and cold
enough to be somewhat close to partial condensation (the
air on Titan is only 100 times denser than the methane-
nitrogen-ethane liquids there which have a density of
450-700 kg/m 3 ) and the ideal gas law is several percent
off and a more complex equation of state should be used
for accurate calculations. For most aeolian studies, a few
percent accuracy is good enough, however.
This 10 km column mentioned above is the 'scale height'
of the atmosphere. Because, unlike liquids, gases tend to be
compressible, the density declines gradually with height and
there is no sudden 'top of the atmosphere'. The decline is
usually an exponential function of height, and is usually
written q(z) = q o exp(-z/H) where q(z) is the density at
height z, qo = q(0), the density at the surface, and H is the
height distance over which the density falls by a factor of
e = 2.718. It can be shown that for an isothermal atmo-
sphere in hydrostatic equilibrium, H = R o T/gM, with defi-
nitions as above. Thus for Earth, T * 287 K, g = 9.81 m/s 2
and M = 28, we have H * 9000 m. The values for other
worlds are similar, although for Titan with its low gravity,
H * 21 km. We see that the scale height is proportional to
temperature; thus, if we warmed the atmosphere up and
made the density lower as above, the scale height increases
by the same factor, so the product of column height and

The principal parameters of interest in aeolian studies are
the air density rho_a, and its viscosity. Density is by far the
more important of these. On Earth at sea level, air has a
density of 1.25 kg/m 3 —your lungs hold about 5 grams of
air. This density is 800 times less than that of water, and
thus about 2000 times less than that of sand-forming
materials. The density of Titan air is a factor of 4 higher
than Earth's, but the planetary range on dune worlds is quite
dramatic—from torrid Venus with air 50 times denser than
Earth, to the whistling thin atmosphere of Mars 50 times (or
in places, several hundred times) less dense (Table 3.1 ).
The atmospheric pressure is an indication of the total
amount of gas in the atmosphere; it is the weight of the
column of gas (and hence has dimensions of force per unit
area). Indeed, we used to determine our atmospheric pres-
sure by balancing it against the weight of a column of a
different fluid—mercury. The weight of a *10 km column
of air with a density of 1.25 kg/m 3 is the same as a 760 mm
column of mercury with a density of 13,600 kg/m 3 (or, of
interest to divers, a 10 m column of water with a density of
1000 kg/m 3 ). These are equivalent to one 'atmosphere', or
1 bar (= 1000 mb): the formal SI unit of pressure is the
Pascal (Pa) and 1 bar = 101325 Pa (or 1013 hPa, a hect-
opascal being about the same as 1 millibar).