Geoscience Reference
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of the spikes. This follows from the fact that the denominator in Eq. (
5.68
) contains
LJ
3
(
5.31
) which includes the exponential functions of k
0
d, so that if k
0
d
1,the
signals become practically undetectable on the ground.
The fluctuations of the neutral wind can lead to the resonant amplification of
the energy flux flowing from the wind into the resonance cavity if the fluctuation
frequency range is close to the IAR eigenfrequencies. Such fluctuations caused by
the gas turbulence are usually observed in the vicinity of turbopause and we assume
that they can occur in the E-layer. The gas flow pattern is characterized by the
Reynolds number Re
D
V =, where is the mass density of the neutral gas, is
the coefficient of gas viscosity due to molecular collisions, V denotes the variation
of the mean gas velocity, and is the characteristic scale of the variations. In order to
find the frequency range typical for the turbulent pulsations we need to
es
timate the
Reynolds number. The value of can roughly be estimated as
.k
B
Tm
n
/
1=2
=
c
,
where k
B
is Boltzmann constant, T is the gas temperature, m
n
denotes the mean
molecule mass, and
c
is the collisional cross-section of the neutral particles. At
the altitudes range of 100-130 km the
ni
trogen molecules are predominant. So, at
the E-layer the average molecule mass m
n
is equal to
27-28 units of proton mass
that approximately corresponds to nitrogen molecules while the typical collisional
cross-section
c
0:8
10
18
m
2
. Using these parameters one can find the rough
estimate
1:6
10
5
Pa s. It should be noted that the effective gas viscosity
can be much larger than the molecular viscosity calculated above, for example, due
to the interaction between eddies in the gas flow located below turbopause (Kelley
1989
). Our estimation is rather relevant to the E-layer where the turbulent mixing
gradually decreases.
The mass density and the neutrals number density fall off approximately
exponentially with altitude in the atmosphere. Inside the ionospheric E-layer
n
m
7
10
17
-10
19
m
3
depending on the
a
ltitude. Choosing n
m
D
2
10
18
m
3
as an average value one obtains
D
n
m
m
n
9
10
8
kg/m
3
. The altitude
profile of the wind velocity is subject to diurnal and seasonal variations. Typically,
the diurnal wind variations increase with altitude from 10-30 m/s at 95 km up to
100-150 m/s at 200 km. So, the value V
.10
100/ m/s seems to be a relevant
estimate for the wind velocity fluctuations at the altitudes of 100-130 km. Taking
.1
10/ km as a characteristic spatial scale of such fluctuations, we finally
obtain Re
60
6
10
3
.
In this picture, one can assume that such a great value of the Reynolds number
exceeds the critical value which is necessary for transition from the laminar to
turbulent gas flow. To study the possible effect of the gas turbulence in a little
more detail we consider a scaling law for turbulent gas flow. The Kolmogorov
theory (e.g., see Landau and Lifshits
1986
) assumes that if a neutral flow is
stirred at some wavelength , the certain structures will be formed in a so-called
inertial subrange in k space, where the energy will cascade to larger and larger
values of k, i.e., from the large- to the small scales. The cascade is bounded from
below by the value
1
and from above by the so-called Kolmogorov dissipative
scale k
m
D
1
Re
3=4
, where the influence of the molecular viscosity becomes
significant and the energy dissipation occurs. So within the interval
1
k
1
Re
3=4
the energy is transferred from eddy to eddy with no net energy gain or
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