DIFFUSION IN THE UPPER ATMOSPHERE 
decreases. Thus, ¢7 can be disregarded in the atmosphere 
in view of the smallness of V In 7’. 
Table II shows experimental dy»-values when one gas 
diffuses into pure air. Observations of dy are difficult 
and are liable to experimental errors; this fact explains 
the discrepancies between the findings by different 
authors. 
Tas eE II. OBsERVvVED Dirrusion ConFFICIENTS 
(According to Chapman and Cowling [4]) 
Gaseous Mixture deere 
Been 0.616 
Oo—air 0.178 
CO.—air 0.138 
Theoretically, di. does not vary with the proportions 
of a binary mixture. There exist only approximate 
expressions for dy» , the degree of approximation being 
determined by the assumptions of the nature of molecu- 
lar encounters. For atmospheric diffusion, it is sufficient 
to study the model of rigid, elastic, spherical molecules 
of effective diameter co, . Then, the kinetic theory results 
in 
2kT (m +. Mz) 2 —1 / 
hee es a»)? / ttn ™M, Ms cm see™, ©) 
where 7 = 3.14159... . Equation (4) fails when air is 
one constituent of the binary mixture under considera- 
tion, since air itself is a mixture. It is a favorable 
circumstance that nitrogen dominates in the atmos- 
phere, and that molecular nitrogen, NV. , abounds ap- 
proximately up to 200 km above sea level. For the 
sake of clarity, atmospheric diffusion is defined as the 
motion of relatively small numbers of different gas 
molecules in the medium of an N»,-atmosphere. Only 
then can the laws of mutual diffusion be applied to the 
atmosphere, that is, the diffusion of different gases can 
be studied separately. 
Consequently, », } n;/nw, = concentration by vol- 
ume, ps & (m, — my,)/my,, and dy = dsy,. The 
Tasre III. Monecunar Properties AND DirrusiIoNn 
CoErFricIENTS OF ATMOSPHERIC CONSTITUENTS* 
| dsn, at NTP 
Ms (cm? sec“) i, = 
Gas | (relative) Ho Go MW ein | COE 
Bayeven Observed 
He 2.015 | —0.93 2.9 0.67 0.67 3.7 
He 4.00 —0.86 2.0 0.59 — 3.3 
N 14.0 —0.50 1.4 0.45 = 2.5 
O 16.0 —0.43 1.2 0.47 = 2.6 
H.O 18.0 —0.36 3.9 0.21 0.20 1.2 
Ne 20.2 —().28 2.6 0.26 — 1.4 
No 28.02 0.000 3.5 0.18 — 1 
Oz 32.0 0.14 3.3 0.19 0.18 iil 
A 39.9 0.42 3.2 0.18 = 1.0 
CO, 44.0) 0.57 4.0 0.14 0.14 0.8 
03 48.0 0.71, 4.0 0.14 = 0.8 
Kr 82.9 1.96 3.4 (O15) —- 0.8 
Xe 130.2 3.61 3.8 0.13 = 0.7 
* Mass of the molecules = m, X 1.66 X 10~*! g; o, and ob- 
served dsy, values were averaged from tables in [4] and [15]. 
It is assumed that ¢0, = %co,. The coefficient of self-dif- 
fusion dy,y, = 0.18 is taken as the atmospheric standard co- 
2ficient d in the ratio 6, = dsy,/d. 
321 
quantity vy; is a small variable number, 0 < », < 1; 
Hs is a constant for each gas, and dy, is defined by 
equation (4). Table III lists the molecular properties of 
N2 and other gases of the atmosphere. The relatively 
small differences between corresponding values of Tables 
II and III justify the foregoing assumptions at NTP. 
However, they must become dubious at levels above 
approximately 200 km. 
3. Eddy Diffusion. In consequence of the assumptions 
referred to in Section 2, the diffusion velocity of a gas 
in the atmosphere equals c, — cy, when diffusion itself 
= N;(C; — Cy.) = Ns; — NsCy,. In order to measure 
diffusion on an absolute scale, the term n,¢v, = vsNy.Cw. 
or the mean motion of the medium of diffusion must be 
investigated. For convenience, we express cy, by the 
instantaneous wind vector V; which is a function of 
space and time. 
The motion of the atmosphere is turbulent; irregu- 
lar, random movements are superposed on the regular 
or representative flow V such that 
V.=V+V. (5) 
The vector V is an average with respect to time as 
denoted by the bar: 
Ve, WV=0, (6) 
When Vp, ~ 0 in an eddying medium, turbulent fluctua- 
tions of v, are created such that 
(vs) S43 as Vs j 
If turbulent fluctuations of ny, are neglected, 
@rens fo @ 
lay >> 
NiCy, = Nx, ven, = Nv, WeV +P 3V) = nV +—3,V. (8) 
Vs 
Let the eddy diffusion-velocity be defined by 
ay (9) 
Vs 
C, = 
In order to separate the properties of the wind from the 
properties of the y,-distribution, a radius vector 1 is 
introduced which is assumed to be independent of the 
special vy, , that is, 
(10) 
dy = —1-Vr,, 
Then, 
_— Evasive 
Vs 
a = — V-ivy., or Cy = (11) 
= 
where V-1 is the coefficient of eddy diffusion. Its com- 
ponents are 
W-i) di) = Dz, (12) 
(V-j) Vj) = Dy, (13) 
(V-&) (i-k) = D. = D. (14) 
The units of D, , D, , and D are em sec ’ = length 
times velocity, the same as d,y, and d. 
Let \ and ¢ be lengths and velocities such that the 
product A¢ equals a given diffusion coefficient. In molec- 
