Geoscience Reference
In-Depth Information
the region where the density gradient vanishes or reverses sign, but only for the
CONDOR data. Such waves are weak in the middle data set and are not seen at
all in the lowest set of data. In the center data set the conditions were close to
two-stream instability and the wave activity was stronger than in the case of the
lowest data set. However, in both the center and lowest data set the waves were
restricted primarily to the region of upward vertical density gradient. Those data
are thus in excellent detailed agreement with linear theory.
The fluid theory discussed thus far breaks down at short wavelengths and
a kinetic approach is necessary. Such calculations have been carried out by
Farley (1963) and more recently by Schmidt and Gary (1973). Pfaff et al.
(1987b) compared Schmidt and Gary's calculation of
with the spectrum
of electric field fluctuations measured in the CONDOR rocket flight during pure
two-stream conditions (above the density gradient) as shown in Fig. 4.34. The
two plots are remarkably similar. This strongly suggests that pure two-stream
waves grow in a narrow range of wave numbers near the peak in their linear
growth rate.
To summarize, the linear theory explains (a) the acoustic speed drift velocity
threshold for type 1 irregularities, (b) the low drift velocity threshold for type
2 waves, (c) the association of waves with upward density gradients during the
day and downward ones at night, (d) the wavelength and angular dependence
of the phase velocity of type 2 waves, (e) the slow phase velocity of large-scale
waves, and (f) the peak in the two-stream threshold spectrum.
The linear theory does not explain, among other things, (a) 3m wave genera-
tion by the gradient drift process (since it is linearly stable at that wavelength),
γ(
k
)
Primary two-stream waves
Punta Lobos, Peru
Primary two-stream waves
Punta Lobos, Peru
10
10
108.3 km
V
5
Schmidt and Gary
(1973)
N
o
5 10
5
e/cm
3
T
e
5 T
i
5 2308
V
e
5
507 m/s
8
8
500 m/s
6
6
4
4
2
2
0
0
0.1
1
10
0.1
1
10
Wave number (m
21
)
Wave number (m
21
)
Figure 4.34
Comparisons of the measured electric field wave spectrum and two-stream
growth rate calculations for daytime equatorial conditions by Schmidt and Gary (1973).
The dotted line in the growth rate calculation is the result of the fluid theory and the solid
line represents the kinetic results. [After Pfaff et al. (1987b). Reproduced with permission
of the American Geophysical Union.]
Search WWH ::
Custom Search