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The requirement (4.54) seems to be met only in the 100-105 km height range,
but (4.55) is less stringent and it seems quite possible for secondary gradient
drift waves to be generated below 100 km. Such waves were detected during the
CONDOR rocket flight with radar and in situ probes.
4.8.2 On the Observations That the Phase Velocity of Type I
Equatorial Waves Is Independent of Angle
In Chapter 10 we describe the results of auroral zone studies of type 1 electrojet
echoes. With a near vertical magnetic field and highly variable flow direction, it
is possible to measure the phase velocity as a function of angle. Bahcivan et al.
(2005) have conclusively shown that the relation
V
ph
=
is the best match
to the observations. The implication is that the waves travel at the threshold for
instability. This result seems at odds with the classic observation in the equatorial
electrojet that the phase velocity is
C
s
, independent of the angle to the flow. In
addition, this result is in disagreement with linear theory, which, for
C
s
cos
θ
ψ
small,
predicts a wave phase velocity equal to
V
D
cos
is the angle between
the current and the radar beam and
V
D
is the flow velocity.
The key to understanding the equatorial results is based on two important
factors (Kelley et al., 2008). First, the drift velocity of importance is the total
drift velocity, which is equal to the vector sum of the zero-order horizontal
drift and the drift induced by intense, large-scale waves. Second, a radar will
respond to the most intense wave in the field of view, so it will detect a narrow
Doppler shift at the value
C
s
cos
θ
where
θ
, corresponding to the projection of the largest
line-of-sight velocity. The horizontal wavelength of daytime large scale waves
is in the range of 2-3 km (Kudeki et al., 1987) and is coherent over an altitude
range of 4 km. The vertical drift data presented in Fig. 4.35a can be used along
a horizontal drift, based on the rocket data in Fig. 3.17b, to create a vector
drift velocity on a two-dimensional grid. Figure 4.35b shows how this region
would be interrogated by the JULIA radar at two different zenith angles for
the system beam width and range resolution and the same for the AMISR-P
at its maximum zenith angle of 20
◦
. The red crosses in the figure correspond
to regions in which the total velocity exceeded the factor (1
θ
+
0
)
C
s
and for
which the value of cos
is the angle between the beam
and the total flow velocity. For this purpose we used the isothermal value for
C
s
.
The first criterion assures that the total drift velocity exceeds the threshold for
instability. Now almost certainly, the most intense waves are those with a phase
velocity vector nearest the flow angle, implying that the radar will preferentially
detect such waves if they are in the range gate and will thus register their Doppler
velocity. By our criterion, this echo will be registered at a phase velocity in excess
of 0
θ
exceeded 0.9, where
θ
9
C
s
. At the equator, clearly the radars will always see a near constant
Doppler shift as a function of angle when the horizontal drift velocity is large
and intense, large scale waves are present. The long-standing problem thus seems
resolved.
.
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