Geoscience Reference
In-Depth Information
indicated species. Figure 2.1b shows the variability in the solar photon emission
at short wavelengths for quiet and active solar conditions, as well as for solar flare
events. EUV radiation is absorbed at high altitudes, both heating and ionizing
the E and F regions. X-rays penetrated quite deeply and, along with Lyman
α
(ionizing NO), control the D region ion densities. UV is absorbed by ozone,
creating the temperature rise in the stratosphere.
2.1.2 Equation of State
For an ideal gas, the mass density and pressure,
p
j
, are related by
p
j
=
ρ
j
k
B
T
j
/
M
j
=
n
j
k
B
T
j
(2.8)
This is the equation of state for each of the fluids we consider (ions, electrons,
neutrals), and we relate the mass density
ρ
j
to the number density
n
j
through
ρ
j
n
j
M
j
. In this text we use
k
B
to represent Boltzmann's constant. The letter
k
used alone or with any other subscript represents a wave number.
=
2.1.3 Momentum Equation for the Neutral Fluid
The continuity equations and the equation of state must be supplemented by a
dynamical equation relating the fluid velocity to the forces acting on the fluid.
This is derived from the principle of conservation of momentum, which requires
that the change of momentum per unit time within a volume be equal to the
pressure gradient force and the total external force field
F
acting on the material
inside the volume plus the momentum flux carried across the surface bound-
ing the volume by viscosity, advection, or wave flux. We first treat the neu-
tral gas. Here, as in most ionospheric and upper atmospheric studies, the wind
direction is indicated by where the wind is going—in other words, an eastward
wind is a wind toward the east. (In meteorology an easterly wind comes
from
the east.)
Advection of a vector quantity such as momentum across a boundary by
flow is conceptually no more difficult than previously discussed for the scalar
mass density. However, the mathematical description is more complex and is
most readily accomplished by the use of tensor notation as employed here.
The equation equivalent to (2.1) for the time rate of momentum change in a
volume is
−∇
p
dV
∂
∂
t
(ρ
U
)
dV
=
+
F
dV
V
V
V
−
π
m
·
d
a
−
π
w
·
d
a
(2.9)
Search WWH ::
Custom Search