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particularly strong if the plasma drift speed matched the phase velocity of the
wave, since in such a case the perturbation would always act in the same sense
on a given parcel of plasma. This is a variation on the so-called spatial resonance
theory suggested first by Whitehead (1971). Wave-like modulations of ordinary
tropospheric clouds are created by this effect as the local temperature is raised
above or lowered below the dew point by a gravity wave. Beer's idea has not
passed the test of time, but other gravity wave effects have been proposed, as
discussed next.
Klostermeyer (1978) also appealed to the spatial resonance effect but pointed
out that the internal wind field,
δ
U
in a gravity wave must also drive electrical cur-
rents,
J
. Due to the finite wavelength of the gravity waves, the associated winds
are not uniform in space. The divergence of the wind-driven electrical current
is therefore not zero, and an electric field,
δ
E
, must build up with a wavelength
equal to that of the gravity wave. This process is illustrated in Fig. 4.13. If the E
region is a perfect insulator, no field-aligned currents can flow and the
δ
∇·
J
=
0
equation may be replaced by the more restrictive equation
J
has
components due to the gravity wave wind and the electric field. This require-
ment has been used to generate the diagram. The resulting electric field pattern
has alternating eastward and westward components, which, due to the
δ
J
=
0, where
δ
B
drift, will cause portions of the ionosphere to rise and portions to fall. Now,
if the plasma has a zero-order vertical density gradient, the
V
δ
E
×
n
term in the
continuity equation will lead to a sinusoidal density pattern with the same hori-
zontal wavelength as the gravity wave. These east-west oscillations may then act
as an initial perturbation, which is amplified by the Rayleigh-Taylor process (see
Fig. 4.1). An additional attractive feature of the gravity wave theory is that after
sunset the ionosphere begins to descend. This is also the direction of the phase
velocity of a gravity wave carrying energy upward from below (an upward grav-
ity wave energy flux has a downward phase velocity, as discussed in Chapter 6).
·∇
a
z
ˆ
B
a
x
ˆ
J
J
u
k
Figure 4.13a
Schematic diagram showing how the perturbation winds in a gravity wave
generate electric fields.
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