Geoscience Reference
In-Depth Information
has been used. This operation yields the time rate of change of a quantity—
in
this case—moving with the flow. Equation (2.4) states that the rate of change of
ρ
ρ
moving with the flow is determined only by the divergence of the velocity field.
For an incompressible fluid the mass density of a parcel cannot change as it moves
(
d
0. In an incompressible
fluid the velocity field is divergence free. The advective derivative (
U
ρ/
dt
=
0), and so from (2.4) it follows that
∇·
U
=
) in (2.5)
is important, since it describes the temporal variation of a quantity, at a point
in space, due to the transport of that quantity into the region. For example, in
the case of incompressible flow, the mass density can only change with time at a
fixed point in space via this term, since
·∇
∂ρ/∂
t
=−
(
U
·∇
ρ)
(2.6)
In the case of a partially ionized medium, ion and electron pairs may be pro-
duced by impact of a photon or energetic particle or lost through recombination
between positively and negatively charged particles. These processes are very
important for the ionospheric plasma. If
P
j
denotes the rate of production of
ions (and electrons) per cubic meter per second and
L
j
is the rate of loss, then
the mass conservation equation for each of the ionized species is
+∇·
ρ
j
V
j
=
P
j
−
L
j
M
j
∂ρ
j
/∂
t
(2.7)
where
M
j
is the mass of each species. Notice that we use the notation
V
j
to
represent the velocity of the charged species, reserving
U
for the velocity of the
neutral gas. Since electric charge is a conserved quantity, it must be the case that
the total number of electrons (e) gained or lost equals the sum of all the different
types of ions gained or lost—that is,
P
j
−
L
j
=
N
P
e
−
L
e
j
=
1
We ignore negative ions because their formation is unimportant above about
80 km altitude. Because the number density of the neutral gas far exceeds that
of the ion and electron gas for heights below several thousand kilometers, we
can ignore the loss of neutral particles when ion-electron pairs are formed. Fur-
thermore, if we are not interested in the possible neutral mass density changes
due to composition changes of the neutrals (e.g., formation of atomic oxygen by
photodissociation), we may use (2.2) for the neutral atmosphere, while for the
ionized particles we need (2.7).
The most important photoionization sources are illustrated in Figs. 2.1a and
2.1b in two different styles. In Fig. 2.1a the penetration depth of solar radiation
is plotted versus wavelength. Except for absorption bands and some scattering,
visible light reaches the ground, but shorter wavelengths are absorbed by the
Search WWH ::
Custom Search