Geoscience Reference
In-Depth Information
4.9 D-Region Turbulence
Some of the first observations of mesospheric turbulence were made at the
Jicamarca Observatory, and we choose to discuss this phenomenon first in this
chapter, even though it is a worldwide process. On average, the atmosphere is
well mixed below about 100 km, called the turbopause. Above this height the
various molecules can separate according to their mass. A detailed study of tur-
bulence per se is beyond the scope here but it does affect the small-scale structure
of the D region. Since the atmosphere in the mesosphere is very dense compared
to the ionized component, the ions and electrons are pushed around at will by
the neutral gas. The charged particles thus act as passive scalars in the vernacular
of turbulence theory. As the ionized components are pushed around by turbulent
motions, if a gradient exists in their content, as there almost always is, advection
will create structure in the ions and electrons. The resulting irregularities have
been studied using radars and rockets.
In Fig. 3.35 a typical passive scalar spectrum was shown (Tennekes and
Lumley, 1972). In turbulence theory, energy is conjectured to be injected into a
fluid at some scale
L
i
. In a laboratory experiment this might be the spacing of
grids placed in the flow. In the atmosphere the injection scale might be related
to gravity waves (buoyancy scale) or a Kelvin-Helmholtz instability (KHI). At
smaller scales, energy is passed from large eddies to smaller eddies without any
energy loss until a small enough scale is reached that viscosity becomes impor-
tant. These two ranges are called the inertial and viscous subranges, respectively.
Viscosity is important at small scales since the term
2
u
k
2
u
is large when
∇
≈
(η/ρ)
k
2
is large.
The breakpoint to a very steep spectrum occurs near the Kolmogorov
microscale given by
1
/
4
3
ν
μ
=
ε
ν
η/ρ
ε
where
is the molecular kinematic viscosity coefficient (
) and
is the energy
dissipation rate (Watts/kg). This expression shows that, as
ν
increases with
increasing altitude,
μ
increases. There is also a weak tendency for
μ
to decrease
with increasing
, but the fourth-power dependence makes this a less important
effect. Since energy is dissipated by viscosity, the dissipation rate (
ε
) is propor-
tional to the turbulent energy cascading down the spectrum. A plot of various
scales for the earth's atmosphere was presented earlier in Fig. 3.36.
In Fig. 3.36, the inner (viscous) scale was calculated following Tatarskii
(1971) as
ε
l
i
≈
7
.
4
μ
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