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10
21
k
23.5
V
0
5
100 m/sec
10
22
10
23
10
24
10
25
10
26
1
2
3
4
10
20
k/k
s
120
64
32
12.8
(m)
Figure 4.38
Spectra (dots) from the numerical simulation of Keskinen et al. (1979)
compared with the theory (solid curve). The curve was normalized at the point marked
with the cross and the dissipative cutoff wave number
k
d
was chosen for the best fit to be
15
k
s
, where
k
s
is determined by the size of the numerical grid and is somewhat analogous
to (but in practice considerably larger than) the long-wavelength
k
c
discussed in the
text. [After Sudan (1983). Reproduced with permission of the American Geophysical
Union.]
Two-dimensional simulations of equatorial Farley-Buneman waves have
enabled researchers to understand a number of key electrojet observations. They
show that the dominant nonlinearity arises when the perturbed electric fields
interact with the density perturbations and drive energy into modes that are lin-
early stable or damped. This wave-wave interaction modifies the linear behavior
of the waves in a number of observable ways. It leads to mode coupling that
saturates the waves when
is the average amplitude of
the perturbed electric field generated by the waves. This causes a broadening
of the turbulent spectrum and also reduces the expected dominant phase veloc-
ity below that predicted by linear theory (Oppenheim and Otani, 1996). This
results from mode coupling when the perturbed fields of secondary modes, on
average, reduce or cancel the driving field,
E
0
, of the primary modes. This model
and the two-dimensional simulations do not predict a strict saturation of the
phase velocity at the sound-speed as was inferred from the data by Hanuise and
Crochet (1981), Makarevitch et al. (2002), and others. Rather, they predict a
saturated phase velocity traveling at roughly the sound speed times the cosine
|
δ
E
| ∼
E
0
where
|
δ
E
|
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