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in this region), accounting for the intermediate-scale structuring in the cat's eye
walls.
The simulation reveals how the collisional shear instability functions. In
regions of strong retrograde plasma drift, a vertical Pedersen current flows. The
equilibrium configuration is the one in which the current has no divergence.
However, if the height of the layer is displaced vertically, appropriate polari-
zation electric fields arise to maintain quasi-neutrality. High potential regions
above low potential regions result from downward layer displacements, with
the reverse holding for upward displacements. This process is clearly evident in
the simulation by time step 16. For instability to occur, the convection driven
by the polarization electric fields must deform the plasma such that the ini-
tial upward and downward perturbations in layer height are amplified. The
growth rate depends strongly on the actual shapes of the number density, colli-
sion, and velocity profiles in a complicated way that evolves over time with the
profiles.
In KHI simulations, the waveforms that emerged first had a wavelength of
about 30 km. Over time, these transient waveforms tended to coalesce to larger
scales. A nonlocal analysis predicted the fastest steady-state growth rate for
waves with
kL
2 where
L
is the length scale of the shear. Given values of
L
of about 20 km in the postsunset bottomside, this implies dominant wavelengths
as high as 250 km. The airglow data in Fig. 4.7b show clearly how various scales
evolve. The arrow shows the bottomside of the equatorial plasma. At the top left,
the two large plumes are separated by 500 km whereas in between, finger-like
structures are separated by 100 km. By the top right-hand frame, even the finger-
like structures had grown in to major plumes. It is arguable that the largest two
plumes at the top left were given a head start by a gravity wave-induced fluctua-
tion whereas the others were seeded by KHI. Alternatively, KHI might explain all
the seeding if the twomajor plumes in the top left image were launched at the peak
altitude of the prereversal enhancement (Kudeki et al., 2007) and then drifted
overhead.
∼
1
/
4.3.3 Summary of Nonlinear Theory Results
The most important result is that plasma depletions push into the linearly stable
topside. Other results are as follows:
1. Once an initial seed occurs, subsequent growth depends very little on the scale size
of the seed.
2. Plumes can be seeded by plasma density perturbations or by spatially varying electric
fields generated by gravity wave wind fields or the collisional KHI instability.
3. Tilting of plumes with altitude is most likely caused by polarization of plumes due to
an eastward wind in the plasma reference frame.
4. Plumes with large horizontal scale can create electric fields that penetrate deep into
the E layer.
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