Geoscience Reference
In-Depth Information
p
D
X
n
n
n
kT
(4.6)
c
v
Œ@T=@t
C
.
V
;
r
/T
C
p
rV Dr
.
n
r
T/
C
P
UV
nQ
C
P
nQ
C
P
nQ
P
nL
(4.7)
In these equations,
n
n
is the concentration of the
n
-th neutral component;
V
is
the neutral wind velocity vector;
V
d
n
is the diffusion velocity vector, which has only
a vertical component equal to the sum of molecular and eddy diffusion velocities;
Q
n
,
L
n
are the production and loss rates of the
n
-th neutral component taking into
account the dissociation of O
2
and the reactions of recombination for O and O
2
;
the index “hor” stands for horizontal vector components; ,
p
are the mean mass
density and pressure of the neutral gas;
˝
is the Earth's angular velocity vector;
ni
,
ni
are the reduced mass and frequency of collisions between the neutral
and ion components of the atmosphere;
V
i
is the ion velocity vector; is the
coefficient of viscosity;
g
is the sum of gravity and centrifugal accelerations;
r
is
the geocentric distance;
m
n
is the mass of the
n
-th neutral component;
k
is the
Boltzmann's constant;
T
is the temperature of the neutral gas;
c
v
is the specific
heat at constant volume;
n
is the thermal conductivity coefficient of the neutral
gas; P
UV
nQ
, P
nQ
,andP
nQ
are the rates of heating of the neutral gas by ultraviolet
(UV) and extra-ultraviolet (EUV) solar radiation, Joule heating, and heating by
precipitating energetic particles; and
P
n
L
is the rate of heat loss of the neutral gas
resulting from radiation. The detailed expressions for all coefficients and terms of
Eqs.
4.1
,
4.2
,
4.3
,
4.4
,
4.5
,
4.6
,and
4.7
and their form in a spherical geomagnetic
coordinate system can be found in Namgaladze et al. (
1988
) and in Brunelli and
Namgaladze (
1988
).
We use Eq.
4.1
to compute the O and O
2
concentrations; the total mass density
is calculated from the hydrostatic equilibrium equation, Eq.
4.3
.AsfortheN
2
concentration, the barometric law for the molecular nitrogen density is used to
calculate it above the turbopause level instead of calculating it as difference between
the total mass density and mass density of molecular and atomic oxygen (Eq.
4.5
)
because of great errors that arise when this difference is small. Equations
4.2
are
used to calculate the horizontal meridional (
V
x
) and zonal (
V
y
) components of the
neutral wind velocity. To obtain the vertical wind velocity we use the continuity
equation, Eq.
4.4
, because the vertical component of the momentum equation for
the neutral gas is reduced to Eq.
4.3
, which does not contain the vertical component
of the neutral wind velocity. At last, the heat balance equation (Eq.
4.7
)isusedto
compute the neutral temperature
T
.
The system of Eqs.
4.1
,
4.2
,
4.3
,
4.4
,
4.5
,
4.6
,and
4.7
is completed by initial and
boundary conditions. At the upper boundary (
h
D
520 km) we assume that
@
V
=@r
D
@T=@r
D
0
and all neutral components are in the diffusion equilibrium there. At the lower
boundary (
h
D
60 km) the wind velocity is taken according to the geostrophic
