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4.2.4 Role of Velocity Shear in Convective Ionospheric Storms
The question of gravity wave seeding and the general problem of the very long
wavelengths that occur in equatorial spread F must be viewed in a context,
which includes the velocity shear that we now know exists in and below the
F layer (e.g., see Chapter 3 and Fig. 4.2). Extending earlier work dealing with
the
E
B
instability (Perkins and Doles, 1975), Satyanarayana et al. (1984)
showed that velocity shear acts to stabilize the Rayleigh-Taylor instability. This is
illustrated in Fig. 4.15, where the normalized growth rate
×
γ
=
γν
in
L
N
/
g
is plotted
versus the normalized wave number
k
=
2
π
L
N
/λ
for various values of the shear
parameter
dV
/
dz
V
0
/
L
S
=
≈
g
L
N
1
/
2
g
L
1
/
2
/
/
where
L
N
is the vertical density scale length,
V
0
is the maximum in the plasma
flow velocity, and the scale length
L
characterizes both the velocity shear and
the density gradient scale length.
S
0 corresponds to no shear, and the corres-
ponding curve yields the dependence of the Rayleigh-Taylor growth rate on
k
.
This result differs from the simple analysis given earlier, for which
=
1 for all
values of
k
(until diffusion sets in). This more accurate linear theory shows that
γ
γ
=
k
equals unity only for
≥
10 or
λ
≤
2
π
L
/
10
0
.
6
L
. Since
L
=
15 km, the
pure RT growth rate is small for
λ
≥
10 km, where, experimentally, much of the
k
,
but
a
largest perturbation occurs. For
S
>
0 the growth rate decreases at all
begins to evolve for small values of
k
. This means that velocity shear
is stabilizing but that it does push the most unstable waves to long wavelengths.
It is interesting to note that for
peak in
γ
S
>
2 the growth rate begins to rise again,
1.2
ˆ
S
5
0
0.8
0.4
ˆ
ˆ
S
5 0.25
S
5
1
ˆ
ˆ
S
5
4
S
5
2
0
0.1
1
10
ˆ
k
Figure 4.15
Normalized growth rate plotted versus normalized wave number for various
shear strengths. [After Satyanarayana et al. (1984). Reproduced with permission of the
American Geophysical Union.]
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