Dynamics and Electrodynamics of the Equatorial Zone - The Earth's Ionosphere: Plasma Physics and Electrodynamics - page 90

The height dependence of these normal modes is a crucial factor in tidal the-
ory, since when forcing (e.g., solar heating) is included in the equations, the only
modes excited are those having a vertical structure that matches the vertical struc-
ture of the forcing. Although the mathematical models were well developed by
1900, controversy raged over the actual nature of atmospheric tides until defini-
tive measurements of the temperature structure of the earth's upper atmosphere
became available from sounding rockets. The features of these temperature pro-
files, which are of most relevance to tidal theory, are due to the absorption of
sunlight by ozone in the stratosphere and by water vapor in the troposphere.
When both the

θ

and z dependences of forcing functions and the normal modes
are taken into account, many of the dominant features of tidal oscillations can
be explained. For our purposes we summarize these features as follows:

1. As tidal oscillations propagate upward, the associated wind speed amplitude also
grows up to F-region heights, where the amplitude becomes constant. (This ampli-
fication is due to the decreasing density of the atmosphere and is a consequence of
energy conservation. This important feature of vertical wave propagation is discussed
in detail in Chapter 5, where gravity waves are studied.)
2. Diurnal tides can propagate vertically only below 30 ◦ latitude. At higher latitudes

they remain trapped in the stratosphere.
3. With the decreasing importance of the diurnal tide, the semidiurnal tide becomes
dominant at latitudes higher than 30 ◦ .

Armed with this modest understanding of tidal theory, we may now investigate
some aspects of the E-region dynamo.
In the E region of the ionosphere, the conductivity tensor is not diagonal, and
the Hall terms must also be considered. Furthermore, the electric field cannot
be taken as being entirely self-generated by local wind fields, as we assumed for
the nighttime F-layer dynamo. This can be understood as follows. The entire
dayside ionosphere is a good electrical conductor in which currents are driven
by lower thermospheric tides. The tidal E-region wind field U ( r , t ) is global in

nature and will drive a global current system given by J w = σ ( r , t ) ·[ U ( r , t ) × B ] .

σ ( ) ( )

Now, because both depend on r , the current J w is not, in

general, divergence free. Thus, an electric field E

r , t and U r , t

( )

r , t must build up such that

the divergence of the total current is zero and

∇·[ σ ( E ( r , t ) + U ( r , t ) × B ) ]= 0 (3.12)

The resulting E is as rich and complex as the driving wind field and the

conductivity pattern that produce it. The latter has a primarily diurnal variation
over the earth's surface, whereas the dominant tidal winds change from diurnal
to semidiurnal, depending on latitude and altitude. As a first approximation we
might then expect a diurnal electric field pattern at low latitudes and a mixture
of diurnal and semidiurnal electric fields at higher latitudes. This crude analysis
actually describes the situation fairly well.

( r , t )