Geoscience Reference
In-Depth Information
The following term,
=[
1
g
2
A
DS
χ
+
−
3
g
¯
s
/
2
]¯
s
(4.47e)
describes the Dimant-Sudan instability (Dimant and Sudan, 1997) where the
parameter,
k
2
⊥
u
0
sin
θ
f
cos
θ
f
ν
e
e
0
¯
s
=
(4.47f)
D
e
⊥
k
2
η
(
1
+
T
)
θ
f
, thereby zeroing the Dimant-Sudan instability effects
at flow angles of 0
◦
and 90
◦
.
All of the thermal processes' effects andwave number dependences of the phase
velocity are included in the second term under the square root of Eq. (4.47). The
greatest effect of the flow angle on the phase velocity is in the first term in the
numerator, which describes the Dimant-Sudan instability (Dimant and Sudan,
1997). This term vanishes at 0- and 90-degree flow angles and disappears at
higher altitudes. The Dimant-Sudan instability has a cut-off at high wave num-
bers (or frequencies) so that, for example, at 430MHz, the change in the flow
angle does not affect
V
ph
. This instability occurs for negative flow angles cor-
responding to the radar looking east for a daytime equatorial electrojet. For
positive flow angles corresponding to western transmissions, the Dimant-Sudan
thermal instability might still be induced but requires significantly higher thresh-
old velocities than the ion-acoustic speed. Thus, if any radar returns are observed
at lower frequencies (
is a function of flow angle
50MHz), the phase velocity of type 1 irregularities would
be higher than for the east and vertical (if the latter are not smeared by gradient-
drift processes) transmissions. In an isothermal treatment, Eq. (4.47) reduces
to the classical expression in which the phase velocity does not depend on the
transmitted frequency.
Turning to the gradient drift instability, we must include the change of density
due to advection from the vertical perturbation electron drift in the electron
continuity equation. The term comes from
V
≤
·∇
n
, which in linearized form adds
/
=
a term 1
kL
to the first row, second column of the determinant where
L
(
)
−
1
is the zero-order vertical gradient scale length. This added
term changes only the imaginary part of
1
/
n
)(
dn
/
dz
ω
; the real part is identical. This means
that (4.43) also relates the perturbed field
n
for the gradient drift mode. To study the stability condition, consider Fig. 4.32b,
which shows daytime conditions and includes a zero-order density gradient that
is upward. From Fig. 4.32b it is clear that the gradient is a destabilizing factor
when it is upward since then the upward perturbation drift
δ
E
x
to the density perturbation
δ
n
/
δ
V
e
z
=
δ
E
x
/
B
occurs
in a region where the density is already depleted
. That is, a low-density
region is convected upward into a region of higher background density, causing
a growth in the relative value of
(δ
n
<
0
)
δ
n
/
n
. If the gradient is reversed in sign but the
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