PHYSICS

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP80-00809A000600200284-6
• Release Decision: RIPPUB
• Original Classification: R
• Document Page Count: 13
• Document Creation Date: December 22, 2016
• Document Release Date: June 29, 2011
• Sequence Number: 284
• Publication Date: September 20, 1948
• Content Type: REPORT

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CIAS~1611 , TRTh ONLY
[FOB tD CENTRAL INTEL ! ' R f O)R
FILE INFOrI A-rg T
DATE DISTR. 20 8epteAber i94
COAGUL1& 0fi OF AERSO
Ye. 11. Tevorovokiy
Submitted by Academician A. N. IColaogorov
25 November 1946
I. DIFFUSION OF SJIVIIE IN THE GROUND. LAIR OF THE ATMOSPi ERE
The intensive dispersion of any admixture introduced into the otmosphero
is explained by the turbulence of the atmosphere.
The irregularity of turbulent motion means that the problem of the diepcr-
Sion of aerosol particles suspended in the atmosphere is solved by atatistirml
methods in the rasa manner as bba problem of vortical diffusion. In solving
this proble3e, it is seemed that the introduction of aerosol particles into the
atmosphere does not ohengo the proportiea of .be aimosphdxe.
Taylor CL7, Rioherdson j2_7, and Schmidt f3jgeneralizcd the problea
of molecular diffusion in the case of vortical diffusica.
The ooncantration of the eubstauce intorduced into the atmosphere is do-
teradved from the equation ox diffusion
,)c at a~ 1 a (gy a, 1 a(
57 TV 3Z 77
Here a is the gravis~liria wnaenrastion; x is the mean longitudinal wind direc-
tion; y 1a the 'ireotion perpendicular to this; z is the vortical direction;
u is the mean speed of the wind; and LL, i4, and D2 are the components of the
coefficient of vlartieal diffuaiti'n A.
The first solution of this equation wac given by Roberts ro, rho con-
sidered the coefficient of diffusion contain,
COUNTRY
SUBJECT
""" UYCLI!?8IFIEO
w 111 111000 OWl1 #111111 TOO 0001110 C1 1110 10.)00111 JILT TO
0. L 0:.,1 01* *L AO 11.11011. IT- 1011111-801 01 TM1 //00011011
111 ITS 160N11M II A10 1A1-q 10 10 11110111011110 M*001 III /1II.
M 11110- R 101. 110000.01101 0* 1110 0011 10 111111111110. 000?
10011: 00 00TIOQI''000101*10 111 0000 0* 101 /QON 0A0 11 0111100
A3.11011 *;N*1 00000 1* 1110 101010/10 *0010!..
No 1, 1948. (1i Per Abs =101-Translation spoai.ficelly requested.)
SOURC Russian perirodical
-1-
CLASSIFICATION !lSD
ST ATE JE N4W 7[ ~NSSRB DISiRI60TION
)ARMY. ~ rIAm Ixf RT)B
FEB 2 'gay'
JFDD
NO. OF ENCLS.
(LISTED BELOW)
FOR OFFJC1AL U$E ON6Y. SUPPLEMENT TO
THIS IS UNEVALUATED INFORMATION FOR THE RESEARCH
USE OF TRAINED INTELLIGENCE ANALYSTS
STAT
STAT
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STAT
t = 0 at a point x = y = z = 0, Roberts obtained ; 2 a
Yn ox
where g is the rate (discharges per second) of the source.
For a continually active linear source of infinite length
where t is the time from the moment of intorduction of the substance into the
atatosphere, and P is the might of the substance introduced.
For a continusll.- active point source -u( 1~,z-I)
- x . ) (3)
C c Ypz
~8Tr,Jz)
certain interval of time at an average distance A, then the coefficient of dif-
of diffusion increases rith the scale of the phenomena observed. Therefore
Roterta' assumption of the constancy of this coefficient in a turbulent atmos-
phOre is inoorrect.
Richardson shoved that if one examines the dispersion of particles over a
in question. This is explained by the fact that eddies of varying magnitude
6s..M;t in a ttlcatiantt ayl40WT-)r6.' as a result', tl'1?9m?gnituds of the cOetl'iciont
within wide Units, and that its magnitude depends on the scale of the phenomenon
Richardson f5j showed that the coefficient of turbulent diffusion varies
C a (7r d' X) ji 'Y W
where Q is the discharge per second per unit of length of the source.
fusion for this scale of dispersion is
n_.falY/j
D. Y u,
. (6)
Bore S L the constant specific intensity of diffusion; m is a dimensionless
parameter related to the vertical distribution of the telozstures and vary-
ing from 1 to 2 (with the isotherm m2),
tween the COW left of diffusion and the time of mc7ement of the clouds
t
I n X 7
pate in its dispersion.
On the basis of Taylor's correlation theory, Sitton shows a relation be-
In proportion to the increase of the cloud, all larger eddies Till pbrtici-
cloud.
When the volume of the released cloud is small, it will be dispersed by
smell eddies which are roughly commensurate with the dimension of the o!oud.
Sittan f6 7, taking Richardaon's concepts as a basis, considered that the
coefficient of turbulent diffusion is related to tie time of movement of the
The magnitude of a as determined by Richardson is equal to 0.2 am 2/3/see.
_ fX -ut) *Y tz
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I.
For a continually active point source
For a continually active linear source of infinite length
7r V2 S.x
For a continually active linear source with width 29,
9 + ~~~ e sxx'~
where j (y) is Oramp'a function.
Iaykhtmen [7_7, starting with the hypothesis that the magnitude of the
coefficient of turbulent diffusion in the ground layer of the atmosphere All
depend on the height, determined this relation from the equation for the "mixing
length" Which he proposed in a now forms
a
(10)
where d, is the "mixing length"; x is a constant equal to 0.38; a is the
is the roughness of the surface (the
height Dove the surface of the earth; z
~
height above the surface of the earth at which the speed of the wind is assumed
equal to zero); p is the pensmster c mursoterizing the stability of the atmosphere
vertically, in which p varies from 1 to ca.
With an adiabatic vertical distribution of temperatures (isotherms) r -.-
equation (10) develops into the usual formula of Prandtl for the "mixing length"
In the flow of an inoompreasible fluid, closo to the boundary.
-/s x z (1Oa)
The magnitude of parameter p may be determined from laykhtman's formrila
for the distribution of speeds of wind by height:
i4! Sri/' i~(!r
The relation of the vertical comp-.neat of the coefficient of turbulent
diffusion D. to the height is presented by Isykhtman in the form
l-1
Where Dry is the ooefficioat of turbulent diffusion at height zl. Equation
(12) is Er* only for the ground layer of the atmosphere (aaproxinutoly to a
height of 10-15 meters:.
The horizontal oomponents of the ooofficieut of turbulent diffusion D.
and re usually not considered to be related to the height and not equal in
mega!
The equations obtained by Sitton were verified by us experimontal-'q.
S^oke from a continually active linear source was :introduced into the ground
mitle~l.
The results of the measurements showed that Sittor.'s formula (9) is essen-
tially correct in its representation of the feu for variation of concentration
Q
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of sucks due to the intensity of the scuts, the speed of the wind, and the
distance.
Together with Ta. L. Zabosbinsl r Z9_7 we showed that in the came of
a obaage of the average concentration at the cater of the awoke wave at the
ground suming that the surface of the earth vin reflect the aloud of aroko,
the aoaesntration should be doubled-along the irvtherm (m is assumed equal to
tae) equation (9) may be written in the form
C. ' 11 (33)
The agmbol Se above that only the dispersion upnard is taken into consideration
for a 34;;W source; the symbol u2 indiaates that the speed of the wind tea
moswared at a height of 2 asters.
Table 1 givos the values 8a (of the vertical a nt S), calculated from
eogmriasntal data.
Table 1. Values of 9bgnitude
0* 41
Espal-
Speed of Uind at
Altitande of 2 m,
Difference of
Tomperaturea at
D1so argo of
Source on a
Average
Roughness
82
out
in Wsec
Altitudes of 20
and 250 cm,, in 40
Motor l'ioat
per Minute, in 0
ac, in m
1
5.2
_?.3
56
0.005
0.030
2
6.4
0.9
16
0.005
0.026
3
7.4
.,x.0.4
47
0.005
0.024
4
8.0
0.2
18
0.005
0,023
Slightly Broken Terrain Covered With Ztgh Grade
.5
1.15
-0.4
18
0.1
0.086
6
2.8
0.0
a8
0.1
0.094
7
3.2
-0.4
27
0..t
0.088
8
3.75
?(?0.1
27
0...
0.092
9
3. s
+0.2
18
0.1
0,380
10
5,0
?x,0.4
18
0.1
0.090
-31
5.9
?.0.1
.18
0.1
0.712
Tae rot seas s taw determined from data on the distribui.ian of the speed
of teind abooading teha3,lht in accordance pith egaation (11); it was elm aseumrt1
that for the isotherm p -a.. In this ease (U) takes the form
(tla)
An -it
Prom this the "lug so ie'BZeo calculated.
'% `. .~ C.. .
Prom Table ? it is evident that the nagnitude S, is essantia119 related to
the Sagree of r ass so.
For the isotbaao it may be assuaged
S IQs ?
The value of Dg my, ; c + ott'eined i'aomea_mastion u8),. which takes the Dorm
for the iaot r.m
C: Y (Loa)
Rio have assumed n s al M.
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tton the fact that Sy wee determtr.efl Acnor41 no 1 o the detn of o.ha r,Knerinrnr i~+
which the speed of wind was measured at a height of 2 m, must be looreased to
when zo . 10 cm DL1 , O.C63 al z1'
when zo a 0.5 cm Dzi a 0.027 ul zL.
Consequently, Dzl corresponds to the
The value of the horizontal component of the coefficient of diffusion D. D1 may be found from the hypothesis that at a certain height above the earth
t e components of the coefficient of diffusion become the same: Dx o Dy Z Dz,
that Is, an isotropic turbulence appears. (The determination of the magnitude
of the harizogtcl component, which has been cited, was done together with D.
L. iaykhtman and L. S. Boriebanskiy.)
At this height the, brake action of the surface of the earth ceases to
affect Dz.
The measurements of vortical energy cited to Brent (9_7 have been used
for the determination of the height at which isotropic turbulence is reached.
To Figure 1 a curve is given showing the relationw'f' according to the
data of various authors (W to the component of vortical speed in a vertical
direction, V , is a horizontal).
Height in meters e A. ft *1 if to
Figure 1
o skr,yz
+ Brent
4Taylor
A. evident from the graph, the most probable assumption is that the height
at which isotropic turbulence let reached along the isotherm will be equal to 12-
leasters. We assumed this height to be equal to 13 meters. At this heigi;t
? DR a DYn .e,, s 03 a.,.
For rOugheeee zo - 5 om, Ltl . 0.C5u1e1. Consequently, for this height
Dr. DY_ ass ?i.~.
It till be in.eresting to estimate the average value of the over-all co
efficleut of diffusion at a height of' L meter (D1). The magnitude Dl may be
calculated as the geometric moan 3
40 R 4r 1)R , (1)t )
In this case O.Ry~
p,=ssyot, R.,
40
(14a)
When to - 10 cm Dl Q.35uItL
When zo s 5 cm DL = 0.27u1z1
Whom zo a 0.5 cm DL c o. L5ulzl
rt. COACALATIOB OF SMXK PARTICLES IN A TURBULENT ATMd8PBh3E
ilith the aid of ultramicroscopes specially adapt, for field measurements,
eas change in magnitude of smoke particles in a cloud of smoke expanding in the
ground layer of the atmosphere was investigated. The number of particles and tile
lift
STAT
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weight concentration of the smoke were 'Aeasured at various points of the smoke
wave. From. the given measurements the average radius of the parttclor of.3moko
was calculated.
The measurements showed that the average radius of the particles increases
quickly in proportion to the advance of the smoke cloud, and increases from 2 to
4.10 om upon reaching a distance of 1,000 meters.
The number of particles in the experiments was of the order of 104 106
per 00.
Two processes occur in the cloud of smoke moving in turbulent atmosphere:
the dispersion of the particles and their coagulation.,.
coagulation is equal to o K4J j _dAe where N is the number of particles in a unit volume; t is the time; K is the
constant of speed of coagulation.
According to $molukhnvskty 5oJ, the change of the number as a result of
The decrease in number of particles with ,the distance will be equivalent to
Idw
_ - N
pressed by the equation dAi.
Hence for the constant of speed of coagulation we obtain:
Hgeation (21) may also be expressed by the dimensions of the
distance x; ro and co, norreapoadtngly, at distance x0.
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particles,
where x is The distance traversed by the cloud on the wind; A .,.3+,5aprJw
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0
Table 2.
Values of K
No of
p/p
Speed of Wind
U21 in m/sec
Ss
1
1.15
0.086
2
2.8
0.094
3
3.2
0.088
4
3.75
0.092
5
5.0
0.09
6
5.9
0.072
7
5.2
0.03
8
6.4
0.026
9
7.4
0.024
K. 108
in cc /see
0.5
19.1
10.0
13.4
188.0
177.0
4.5
10.8
16.4
As is apparent from Table 2, the constant of speed coagulation depends
greatly on the speed of the wind and the vertical component of the coefficient
of transfer (S.).
This relation may be expressed by the fcllniing equation:
In Figure 2 the relation of 1?g K to 1?g (Sou) is represented
''1(J
Yt /
The relation of K to 8 and U indicates that in turbulent atmusphore, in
addition to coagulation pro&meed by a theraal nrvement of mrloonlea, there also
oeeurc coagulation of partiu2os rwoduced by turbulent agitation.
Ths ragnitude of the oonrtant of speed of oongnlation proau byy_mloou1ar
notion, according to the experiment 9t !!aitely-Grey and Paterson 1LJ, far
partiolaa with a radius of 2 - 3.10'5 oa is apparmt ntoly erual to 5.14"'10 ao/sae.
The adYa3m~ valve of K fomad by va exceeds this by almost tan time, tIa
MXIW14 by 4,000 titre".
M. OA1UTATIO,I OF TIE COLSTAUI OF S= r OF TUI UI} IC OnAGUTATI01U
DO phamonm of,.coaplation of partia:tos in a flow we first investigated
by Sw2mIMAv*kLY 10.j... He examined ooayvlation in a lami,r flan along o plane.
In this ease as a result of varying speed of the flow at distr::m a 1ror:
that plane, the number of eaml73siono of particles inc eases, and the spool of
ooa&nlation
diV 3~; x a d!
3 (23)
STAT
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Is
.Troller C10? J considered that in a flow in rotary motion the particles,
from ' inertia,- oil diverge from the linos of flow, and the 6pood of coagulation
will increase in proportion to the dimensions of the coagulating particles?
Wind C1 7, assuming that the speed of turbulent agitation is propor-
tional to the speed of the wind, and considering the factor of proportiomlilp
sejualto 0.25, accepted the equations of Smol.ukhovskiy for the calculation or
the speed of coagulation in a turbulent flow.
In this case (23) takes the fort
d,y K
do j YN slj
(24)
and the constant of speed of coagulation is also found to be proportional to
the cubs of the radius of the particles.
T h e ealculati~on according t h e h and', formula for our odes (the radius
of particles of the order 3.10"Som) siowe that the constant of speed of c:oaga-
lation with a wind speed of 6 m/eec is equal to 5.10.-1-1 cm/sec, that is, one-
tenth of the constant of speed of moll-,War coagulation.
Like Sitton, we assumed that in turbulent agitation atr sphere eddies cf
random dimensions are formed, that is, that along with large eddies dot mined
by diffusion, "microeddies" also exist. Those small eddies (more truly, the
ablM of smell volnmas of air at all points of space, produced by vortical
novemeat) increase the senior of collisions of particles, and determine the
rphens,f'emon of h++.bule!rF cosg a1nt!on_, Peoei+4. of the iremon"l io of ttlrbo1eut
movement, an asset solution of the prcblem of turbulent coagulation may be ob-
tained only by statistical methodej ho:ever; an attemist is being made in the
preoen: work to solve the given problem proceeding from the dimensions.
The constant of Speed of ooaguloti:n of particles in a turbulent atmoe-
here best be equivalent to X a B1 - & (25)
where K1 is the constant of oongnlatIon of particles produced by turbulent
molecular movement and K2 to the oonat:wt of coagulation of partioloo by
turbulent movement.
Since the rdcvamant of particler in a turbulent flow is irregular, we may
assume that in turbulent coagulation it vitl be determined by the coefficient
of turbulent diffusion of the particles as za the ?rob' of, molecular coagu-
lation. Consequently, using Smolukhevskiy'n equation ,/l0, which relates the
oonr*ant of coagulation to thecoefS:icient of diffusion, we may write
x = 41rr (Di -l-' ), (26)
where D, is the coefficient of diffusion of particles, depending on their re-
spectiv tranaforense produced b:r wolsoular movement, and D2 is the ceeffiaiert
of diffusion of particles depending on these respective transference produced
by turbulent movement.
As indicated. above, the coagulation of particles in a turbulent atmoarhure
due to raising produced by turbulence is much greater than their coagulation
due to the t6ermnl movement of molecules.
Therefore, for a turbulent etmoephore It may be assumed that
A e 4 -rD . (25e)
It is also possible, using aqua%ion (2:ia), to eatimato the evorage value
of the coefrioiont of diffusion particles.
:-aeoading +o Table 2, with a wind of average force, of the order of 3
xe/sea, K = ;r.0.10" S cm2 lsea. Than, with thi ever, e r diuo cf te .rttalss
r ; 3.30'5 cm, we find D2 = 0,6.10"3 rm2/s ic.
The coefficient of diffusion of rti.lsa of given dimension; depending
on molaeolar movement, is Dl^"i0"b /ear.; that is, Dl is auc.uer then Pc by
20 time.
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The coefficient of turbulent diffusion of a flow in the Mund layer of
the atmosphere D, an was indicated above, in of the order of 104 oin2/see
and
,
is therefore larger than D2 by 107 times. The relation between the coefficient
of diffusion of particles of smoke at a distance of the order of he distances
between particles , and.the coefficient of diffusion of the total cloud of
smoke I), may be fouRd from the following:
It is evident that the larger D is., the larger D must be; on the other
band, the coefficient of diffusion of particles moat diminish with an increase
in the kinematic viscosity of the medium, since an increase in the kinematic
viscosity tooreasas the dimonaione of the "mioroeddiss," and consequently re-
laces the relative transference of particles. Therefore, starting with the con-
tention of dimension, we may write;
(27)
where A is the dimensionlesa constant.
The expression for the constant of speed of turbulent coagulation w:'ll
assume the following form:
~P'yx-e/f";I (28)
Pweoeedi9 from the dimensions, we may also find the relation of the con-
otattt of speed of coagulation to kinematic viscosity.
The particles in a turbulent flow will collide only in the avant that they
are .eetod to movements relative to one another from the direction of the
flow. The smeller these movements are, the greeter the probability that they
will eoiveege; for with large movements (larger than the distance between
particles) all the particles will merely move together with the moving part of
the flow without approaching one another. On the other band, the meter the
speed of movement produced by turbulent movements the greater the probability of
a collision of particles.
Let us now examine the relation of the distance at which particles may
oonverge and at their speed of movement to viscosity.
The distance S will be greater, the greater the viscosity; for, the greater
the viscosity, the greater will be the distance from one another ant these
movements will be extinguished, 5according to Reynolds criterion, (29)
The speed of movement of the particles will decrease with the viscosity
according to Stokes' le%t v.. i
V. ' (30)
Time, the time Of collision of panicles, that is, the time of their coagula-
tion, is r s - a
. (,1)
it ona_asoumee that the constant of speed of coagulation is invorsel;,+
(32)
Hangs (28) viii assume the form ~' y~rA'? i y (34)
that is, the *onstant of speed of turbulent coagulation is proportional to the
cubs o: the coefficient of diffusion.
as. a
a j,?
j,J s.
STAT
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The values of A are given in Table 3, where r is considered equivalent to
3.10'7 cm, and al M I pier;
Table 3. Values of A
No
Speed of Wind
U
i
V
Roughness Zo,
Averqge Value
'
K. 108
A.105
P /P
n n
soo
13
in em
oaf/D
, in
880
co /see
1
0.89
10
0.35
0.5
0.22
2
2.15
10
0.35
19.1
0.30
3
2.5
10
0.35
10.0
0.21
4
2.9
10
0.35
13.4
0.20
5
3.9
10
0.35.
328.0
0.36
6
4.6
10
0.35
177.0
0.30
7
4.7
0.5
0.15
4.3
0.20
s
5.7
0.5
0.15
10.8
0.22
9
6.6
0.5
0.15
16,4
0.22
The 'wage value of A r 0.25.10-5. The constancy of A may serve as a
proof of the accuracy of the equations cited,
Equation (34) may also be obtained from an examination of the mrchaniam
of a turbulent flow.
Gontesioorary idwea nn t, Leal uotere..of t=bm'Unt s,-.- ---- r, _~
.rwvw.v i xra~
forted by Richardson 1-5 aw -U
J. It is assumed that the smallest dimension of
pulsations in a tntnlent stream A, is determined by the viscosity of tile radium
on the condition that. Reynolds8 number Re A. Is of the order of unity L 13.
Dissipation of the energy of the turbulent flow occurs in these pulsations,
It is also assumed that turbulent pulsations cannot exist on a scalp less
than A? since they Mat quickly be a.ingnished baoa?me of the viscosity; and
at these scales only lemii,er (viscous) flow is possible.
Small scale pulsations, however, not only are extinguished but constantly
regenerate, and, consequently they always exist in a turbulent flow,
The asetuoption of the pressnee of such pulsations may serve as an oxpluna-
tio>y of the cameos of turbulent coagulation in a flow. Under the action of these
fluotuetions, the particles all be subjected to email covenants at abort die-
taness A(A4 k,,. Inasanuah as these fluctuetion;n are produced by the turbulence,
ON ny asame that the coefficient of diffusion o particles oven in this no
of megzitulee A will obey the function found by Richardson DA a d 1(A)?!.
The calculation of U ford of the order of t'n average distance between
particles (with the average nne,er or pay Ciolos in our experiments N r 5.105
pea cs, the distances between particles A= Ir""/3 s 1.3.10-2om) gives a value
D; %w 2/sec. This agrees weal with tare value of the ooofticient of
diffusion of particles D2, calculated from the data for On coagulation of
particles in the atae,ihera.
L. bs theory of ],gaal,,isotropie turblenoe was worked out by Rolmc~gorov
trabnlenndst 15_J They showed that the dissipation of energy of a
whirs E Is the dissipation of energy per unit of volume per unit of time; Q"is
the change In speed of the flow at distance of the order 1; and 1 is the scale
of the turbuleree of thu flow.
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I
obuleuov Lrl3, 16j showed that the average quadratic
in a turbulent flow ~(!f> Xa)
E. 3
Let us use equation (35) for the dissipation of ener87i assuming that D
of the flow o d .,?' (37)
and let us substitute the value value A? from (37) for (35). Then
ZT_
(39)
On the other hand, the average quadratic movement of a particle in ir-
regular movement 'X_ D~.u? (40)
Inasmuch as the average quadratic movement of a particle in both cases
will be the some, then it is evident from (39) and (40) that
?y ^- ? ?ti=. (41)
Inasmuch as Dch is determined only by the viscosity of the medium, we may
assume 3L
by (?)
;sl?nrw b. in the dimonsionleas constant.
Henoo, we ob'.sin the equation p3
Dy= d? ~~ ~
(43)
identical with equation (34) obtained earlier, where A3 - b.
However, according to the theory of Obukhov, equation (43) my be true
only i n t h e case A 7 A,?
The cubical relation of the constant of speed of coagulation to the
coefficient of diffusion, whlnh we found experimentally permits in our opinion
the extension of the equations obt3inod in the theory of locally isotropic
tmbulenvse of Kolmogorov-Obukbov to scales lase than Ap? assuming that in these
-sealer there actually exist pulsations of random dimensions produced by e.
turbulent flow.
Ontie may a1eo estimate the part of the energg,present in the pulsations
producing the coagulation of particles, using the valuos of the doofficionts
of diffusion of the flow and particles.
In conclusion let us examine constant A. It must charwrterise the scale
of the phevomans observed.
AotD.Lly, the speed of ooagulrition is determined by the number of collisions
of particles located at minute 1istances from one unothor. For those distaucoe
the coefficient of turbulent diffusion oill be considerably less than the ooef-
ficient of turbulent diffusion DP , calculated for the diffusion of the amolm
aloud as a whole.
Dsnotiag by D the coefficient of turbulent diffusion for scales of the
order of disb+noc~e7batween particles, we may assumes
A t " (44)
For determination of A and n in the case of turbulent coagulation me
may also assume! 54 ", ~? ,d ;lid pv ti~ 4 w~ ?
(45)
From eque ion (35) i; in obvious that
4&&. -F2)~3 - (46)
-12-
movement of particles
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Substituting equations (45) and (46) in (44 ,
9 ), we obtain
(47)
Magnitude A is determined from the averain distance between particles,
In our experiments the avc-age distance between two particles was equivalent
to 'A =L3?lQ acrr,.
For " determining the magntude 1 we use tau equation of laykhtman (10) it,r the
length."
Because we are examining the case of adla~cttio distribution of temperatitros,
the vertical component of t'Ue "mixing longth" ,
`i =X2. (ltla)
At a height of 1 meter .0, -.X,/= 0.39 meter.
It was, indicated abive that the average height at which isotavpio turb;lonce
is resohed in equiva 2.en+? to 13 meters. Therefoin, we wiy assunc
. ,' ='I~, 2 A_, - x, /3 a al?S2,,. 48)
Magnitude tefor eight of 1 meter may be eRtcrminecl in the same pay as ,he
average value of the aoafficiont of diffusion.
Aooording to (-4),
Substituting the found values ,A and. for (35), is find that .Q
Comparing she value A (A 0.25.10"'5) tbtainad !Tara the experiment with the
calculated ve'ae, we find that these magnittdas are of the aims order.
Thos *A sxpression for the constant o.' speed of ttxbulant coagulation as-
anmss the :o1lnatng final forms p
vrr r ji 9 .) i.'=.
(50)
Tli equation found relating the conata. of speed of coagulation of pertiolar,
in a +wbulent aedtum to the ooeffioient of iurbulent dift eion may be used to ex=
plat: oertaiu ooagoiation processes which We place in ol:uds and in the floooula?
tt:`of on1?oida?, particles in moving fluids.
Iu oonlusion I must express my gretit/.ie to M. K. Baraaoyev for a number of
ve;amtbie suggestions.
B ThLIOCaki-AY
1,,
s.
3.
4.
5.
6.
7.
8.
9.
Taylor, 0? t;., Phil. Trans. Roy. Sac (a), 215, 1, 1915.
Richardso8, L. F., t.seichsr Drediotion, Cambridge, 1922.
Sohaidt, A., Da. tkeoenaustauach in frei.r Lnft and verwandte srE:yei y,
Hauburg, 1925.
Roberts, 0. B. T., Pros. P.oy. Soo.. ~A), 1%, 640, 1923.
Richardson, L. F., Froc. Hoy. Soo. (A), 11o, 7r9, 1926.
8iOtan, 0., P: . Bay. Soc. (A), 135, 14:, 1932.
14ylchtsan, D. L., Isv. AN SSSIt, Der. geogr. i gnof. , Vol VIII, No 1, 944,
t's-eroeakig Ye. R., 7ebesbinskaye, Ta. L., Tekhr-13M i voorusheniye, No 7,
1940.
Brent, 1. D., FJsioheehe a i dinamtcheghe n matecrologiya, Gidromotiado
1938. t
STAT
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fo~
10. i 9., 1yu11er, 0., 8b. Eoagu2at~s ko12 id vr, star. 7,40
Md. 61-74, OJU 1936.
11.. 1gdtw3 and Paterson, 4m, OBI, 1934.
1?w K4*.;und
., s L,, LLvs Plpdk. Ztoa., 31930.
aM it, to., lfaklimM w .prp1oeb and, OOIZ, 1946.
34. , A. X., a" AX 88 t, Vol XU, No 4, 2299 1941.
15. ObofficAr9 A.: 8., Isv. AN 8301 wr. POP* i Wt., )b 4/6, 1941.
16. Takla, IL P., Do 1. AN S=p Vol LI, 1b 2, 89, 1946.
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