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opposite to the Hall current observed. A westward wind of over 100m/s is
required by the data in Fig. 3.17b. The winds cannot be measured during the
day using the TMA method, but two days after these data were taken, the wind
speeds measured just after sunset were of this magnitude (Larsen and Odom,
1997).
At still lower levels, a very interesting feature of the mesospheric temperature
field is shown in Fig. 3.34. This solstice view of the earth's atmospheric tempera-
ture shows the curious feature that the polar summer mesosphere, in full sunlight
for 24 hours a day, is nearly 100K colder than its winter counterpart (Geller,
1983). Radiative equilibrium theory predicts just the opposite, and the expla-
nation must involve a dynamic effect. This too requires a discussion of gravity
waves and their profound effect on the system, and we revisit the polar summer
mesosphere in detail in Chapter 7.
3.6.2 A Primer on Turbulence and the Turbopause
Neutral turbulence has been studied for many years in both the atmosphere
and the laboratory. The crucial parameter is the Reynolds number, which is a
measure of the importance of the different terms in the momentum equation.
The momentum equation, also called the Navier-Stokes equation, for a neutral
gas (ignoring gravity) is
ρ
(∂
U
)
2
U
+
(
U
·∇
)ρ
U
=−∇
p
+
η
∇
∂
t
If we compare the second and fourth terms we get
2
ρ
|
U
|
η
|
U
|
:
L
L
2
Their ratio yields the Reynolds number
=
|
U
|
L
R
ν
where
is the kinematic viscosity. In the atmosphere
L
is quite large (com-
pared to the laboratory), and high Reynolds numbers are common (
R
ν
=
η/ρ
1000).
In laboratory experiments energy is generated at some scale by, for exam-
ple, flowing through a grid. The eddies generated at the grid scale
≥
generate
smaller-scale waves in the inertial subrange where energy is passed from scale to
scale without losses. Ultimately, a scale is eventually reached at which viscosity
damps out the structure. That this must occur at small scales can be understood
from the viscosity term
(
L
)
2
U
. When viewed in the Fourier domain this
(η/ρ)
∇
becomes
2
U
k
2
(η/ρ)
∇
≈
(η/ρ)
U
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