Ionospheric Alfvén Resonator (IAR) - Ultra and Extremely Low Frequency Electromagnetic Fields - page 184

loss. In an isotropic homogeneous medium the omnidirectional spectral density of
the mechanical energy of the turbulent flow has a power law spectrum / k 5=3 .The
typical frequencies of turbulent pulsations are evaluated as ! kV , where V is
the smoothed mean velocity that slowly varies along the flow. Hence we find that
the Kolmogorov spectrum is localized in the frequency range given by

V
!

V
Re 3=4 ;

(5.72)

where the lower margin corresponds to large-scale pulsations whereas the upper
one stands for the dissipative turbulence scale, i.e., for the smallest pulsations in the
turbulent flux. For instance, taking the parameters V D 100 m/s, V D 50 m/s and
D 10 km one obtains 0:01 ! 4 Hz. These estimates show that the typical
frequency band of the gas flow turbulence can be close to the eigenfrequencies of
the ionospheric resonance cavity that results in the most effective transfer of the gas
kinetic energy into the Alfvén and FMS wave energy.
The analysis has demonstrated that, in principle, the wind-driven ionospheric
currents are capable of producing IAR excitation and observable perturbations at
the ground level. One test of this theory can use the fact that the SRS signature
should be sensitive to the magnitude of the wind velocity at the ionospheric altitudes.
A standard technique for measuring the wind velocity is based on the Doppler shift
of electromagnetic waves reflected from the ionosphere. When this topic is being
prepared, these tests have not been carried out.
In summary, the principal results of this section are as follows:

1. The IAR dispersion relation is split into two coupled modes, the shear Alfvén
mode and the FMS mode. The eigenfrequencies of the Alfvén mode practically
do not depend on the perpendicular wave number k ? , whereas the eigenfrequen-
cies of the FMS mode approximately follow the linear dependence on k ? .The
FMS mode damping rate decreases with the increase in k ?

while the Alfvén

mode exhibits the opposite tendency.
2. It follows from the theory that the IAR power spectra exhibit the SRS only during
the nighttime conditions. This conclusion agrees with the observations both at
middle and low latitudes. The nighttime conditions are thus more preferable for
the IAR spectrum observation.
3. Overall, the predicted IAR spectra are consistent in magnitude and resonant
frequencies with observations. The typical IAR eigenfrequencies lie in the
range of 0:5-5 Hz depending on the magnetic latitude and the ionospheric
parameters. The average frequency difference f between two adjacent peaks
in the spectrum is about 0:2-0:5 Hz.
4. The predicted shape of the IAR spectrum is practically independent of the shape
of single lightning spectrum while the IAR spectrum magnitude depends on
both the mean number of lightning discharges per second and the magnitude of
low-frequency part of the lightning spectrum. This implies that the CC of return
strokes can greatly affect the magnitude of IAR spectra.