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Figure 4.9b
Sequential sketches made from photos of the hydrodynamic Rayleigh-
Taylor instability. A heavy fluid is initially supported by a transparent lighter fluid.
the surface grow “in place,” pushing the lighter fluid upward. In the ionospheric
case the “light fluid” is the low-density plasma, which carries a gravity-driven
current that provides the
J
B
force, preventing the plasma from freely falling.
The system is unstable when
g
and
×
n
are oppositely directed. We discuss the
E
0
term shown at the top right of Fig. 4.9a following.
We now calculate more formally the growth rate of the RT instability, assum-
ing a small initial perturbation in plasma density and electric field. Inertial terms
are dropped, which corresponds to the condition
∇
t
. This approximation
breaks down at high altitudes but is certainly valid on the bottomside and up
to 450 km or so. Using (2.37b) and ignoring neutral winds for now, the steady
velocity of each species under the influence of electric and gravitational fields is
given by
ν
in
∂/∂
1
1
j
W
j
⊥
+
κ
j
1
j
W
j
⊥
×
B
2
2
V
j
⊥
=
+
κ
+
κ
(4.1)
where
W
j
=
b
j
E
+
g
/ν
j
n
−
D
j
∇
n
/
n
(4.2)
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