DIFFUSION IN THE UPPER ATMOSPHERE 
lar and eddy diffusion and the forces acting on the s- 
molecules: 
Ovs a vsQs(usgm ar ms fs) 
Qey 
=0 23 
dz kT ndsns pee) 
when 
ds 
Ss 24 
Q: din» 7s 1D? ( ) 
and equation (22) is reduced to 
Sate pet Nea) 12 oe: (25) 
ot Oz Oz 
Permanent gases are characterized by yo = 0 in both 
steady and unsteady states; unsteady states are caused 
by time variations of 7, Q, , and/or f, . Sources and 
sinks of nonpermanent gases can be external when 
matter enters one and leaves the other boundary of the 
atmosphere (or of the layer under consideration), and 
internal when production and destruction of matter 
(as measured by q‘” and q‘”’) are height functions in 
the layer under consideration. In steady states of non- 
permanent gases with external sources and sinks, 
Y = yo = const + 0, (26) 
Where yo measures the strength of the continuous 
external source which equals the negative strength of 
the corresponding sink. In steady states of nonper- 
manent gases with internal sources and sinks, which 
are independent of x and y, 
0 = 
= 2 eg tq =O (27) 
or diffusion balances the effects of internal production 
and destruction. Unsteady states of nonpermanent gases 
result, mainly, from time variations of y, g, and 
q ’. Complications arise when the production of matter 
influences the physical state of the atmosphere (temper- 
ature, motion, turbulence), and when the ejection from 
sources causes an initial movement of matiter, as in case 
of eruptions or explosions. Further details will be dis- 
cussed in Section 12. 
Atmospheric diffusion can also be studied in connec- 
tion with the motion and distribution of particles (dust, 
nuclei, droplets, etc.). Let a; be the diameter and n; the 
number of particles per cubic centimeter. The kinetic 
theory represented by equation (4) fails in defining a 
coefficient of particle diffusion when a; is large in com- 
parison with oy, © 10° cm. There will be a Brownian 
movement of such particles, which becomes less intense 
as the size of the particles increases. When a; is large in 
comparison with the free path of nitrogen molecules 
(10 ° cm at NTP), the integrated effect of the continu- 
ous action of numerous collisions with the molecules of 
the atmosphere is called the viscosity. If gravity is the 
only force acting on the particles, the motion reduces to 
a simple fall in a hypothetical atmosphere without wind 
and turbulence. For instance, spherical particles with 
323 
10° < a; < 10 em attain a rate of descent 
—— —gai(p; a p)/9n, (28) 
according to Stokes’ law, where p; = density of the 
particle and 1 = dynamic viscosity of the atmosphere = 
0.00017 g em‘ sec! at T = 273K. 
The equation of particle diffusion in a turbulent 
atmosphere becomes 
me; = —nick + nC; + niV, (29) 
where C; is defined by (11) when », = »; = n:/ny, = 
n/N. 
DIFFUSION IN THE VERTICAL—STEADY 
CONDITIONS 
5. The General Solution. One of the possible causes 
of forced diffusion is electromagnetic fields. The heat 
transfer in gases—which is very similar to the process 
of diffusion—is perceptibly affected at NTP by electric 
fields greater than 10‘ vy em’, as was shown experi- 
mentally by Senftleben and Gladisch [34]; the effect 
becomes less intense when pressure decreases. The mag- 
nitude of electric fields in the upper atmosphere nor- 
mally is smaller than the value given above when 
ionospheric layers are electrically neutral. The possible 
influence of the earth’s magnetic field on the diffusion 
of ions was found to be dubious by Ferraro [10]. Thus, 
we assume f; = 0 in the following computations, based 
on equation (23). 
The linear differential equation 
~ +. yo(@) + ya) = 0 (30) 
Ab 
has the solution 
y= E - [vex (fe a) az Jexo(—fe a), (31) 
when yp = const. 
We define the scale height (height of the homogene- 
ous atmosphere) as 
H = kT\/mq . (82) 
When N> is the medium of atmospheric diffusion, m = 
mn, = 28.02 X 1.66 X 10-4 g. Normally, the scale 
height is expressed in terms of mm , the average molecu- 
lar weight of pure dry air (7/my, = 1.033). In the 
following computations, the value of H = 8 km is 
used. 
When y = yw, that is, when internal sources and 
sinks do not exist between 0 and z, the solution of (23) 
with the aid of (81) and (32) is 
Vs = Vso EXP (- A z 0, a) 
yo [? Qs fe fp? Gein ) | 
. = c = = BN) OF Ne 
E Vs0 i ndsn» ae G 0 gol’ Q : 
If T = T) and g = go throughout the layer under 
consideration, then ¢/y = const in equation (30), and 
(33) 
3. Some investigators may prefer to omit the assumption 
g = 9 by measuring the vertical scale in dynamic meters rather 
than in geometric meters. 
