On Observations of Atmospheric Diffusion by Long Time Exposure Photography of Smoke Plumes

■ a 皿 ■ ■

ぶ．ｊ

On

Observations･ﾄof

Atmospheric

Diffusion

by^ Long

Time･. '.･､:-.':.l･

.'･.

     Exposure

Photography

of Siiioke

Plumes

…… ごトダ'

      レ ヘ  ー.. Ｂy……… …j.-･･.･  ･･ ・・ こ        HtsashiニＵＥＴＡ一犬ダ      ト ゛ ‘’ （Pjりｓｔｅａｌ Ｌａｂｏｒａ￡ｏり５ Ｆａｃｗlりof Litｅｒａtｕｒｅ ａｎｄ Ｓｃｉｅｎｃｅ Ｉ Ｋｏｃｈｉ Ｕｎｉｖｅｒｓiり）        ABSTRACT

 photographic technique of long time ｅχposure from ａ few to ten minutes is mentioned. In the technique, polarizing filter acts significant role for the elimination of dispersed light in the sky for both monochromatic and color films. Photographs are analysed by ａ microphotometer and eddy diffusivities are estimated on the bases of equations derived from Roberts': Inoue's and Gifford's. and they are critically commented. The order of the values of eddy diffusivity estimated for the stacks about 30∼65m high is 104∼105 cm2 Sec-1｡  I. Introduction

 In the study of atmospheric diffusion! it is of appreciable significance to know the distribution of concentration of the pollutant。and for this purpose many people and many equipments for measurement are required. To use smoke plumes as indices of atmospheric diffusion has been widely utilized by many scholars as Gifford, Inouej Saissac and Culkowski etc.・ for the sake of simplicity and of possibility of direct approach to the diffusion problem.

This method is based on the fundamental thought that the equation of diffusion can only be applied to the time-mean state or the time-mean concentration distribution of ａ plume.

Consequently,‘opacity theory' can only be applied to the long time ｅχposed photographs of plumes. In. this study) the photographic technique of time exposure from ａ few to ten minutes is mentioned, and the ways of analysis of the photographs are examined. Then the theories of Roberts; Inoue and Gifford are applied to calculate eddy diffusivity and other various parameters in atmospheric turbulence and the extent is examined in which the study of diffusion･ can be achieved by comparative】ｙ simple method of time exposure of photographs. A mi crophtometer was introduced to analyse the phtographs and much results were gained｡

 II. Photography of ａ smoke plume ( i ) Selection of ａ site

 Selection of ａ proper site to set ａ camera is important. It must be at the same height as the center line of the plume and where the axis of the camera will be perpendicular to the plume. Moreover, it is desired that the plume have a good background so as to be seen distinctly. In this study, ａ stack of 65m height of Tokyo Iron-works at Mizushima Seaside Industrial Area, Okayama Prefecture (Fig. 1), and another stack of 50 m height of the western dust burning house at Asakura in Kochi City, were selected and their smoke plumes were photographed about l kn! apart from them by cameras with telescopic lenses of focal length f =135mm or 200mm.（Figl 2づjﾌﾞｏ take ａ photograph of the smoke of the dust burning house from short distance, Shikoku Branch of Government Forest Experiment

 ろ8      高知大学学術研究報告 第16巻  自然科学 Ｉ 第５号

         -Station, situated on the hillside as high as the stack (Fig. 3), was selected. and standard lens of f=55nim was used, and above conditions were satisfied.

 When the smoke plumes of the other stacks about 30m high of the factories at Sanbashi Area in Kochi City were photographed from the summit of 120m high Godaisan hill, they were looked down upon a little obliquely. (Fig. 4 and Fig. 6)

｡ＨＥ

Ｒ≪ＶＥＲ

Photography of Smoke Plumes

(H. Ueta)

ろ9

( a ) Moment photograph (b) f= 200 mm，‘Neopan SS' （ASA 100)     F/22, Filter :

    2N.D. (8)-ﾄN. D.(4)十R2十p. L.     Exposure time : 300 sec.

Fig. 2. Photographs taken from the roof of Natural Science Department of Kochi Uni＼･ersity.     (131i００ｍon Dec. 7, 1966, Dust burning house)

Fig. 3. (a) Smoke of the dust burning      house at Asakura, photographed      from Shikoku Branch of Govern-     ment Forest Experiment Station      inKochi.

Fig. 4. (a) The view of the Industrial     Area at Sanbashi in Kochi, from     Godaisan-hill.

Fig. 3. (b) Photographic conditions of    the camera are 出ｅ same as the    above example.

    Ｅχposure time : 90 sec.     13h 30m on Oct. 19, 1966.

F!g.4. (b) the

 Photographic conditions of camera are the same as the above ｅχample.

 Ｅχposure time : 75 sec.  14h 35m on Oct. 5, 1966.

40 _{高知大学学術研究報告 第16巻  自然科学｀ Ｉ 第５号}

Fig. 5. (a) Moment photograph at      Mizushima Seaside Industrial      Area.

SANBASHl

KOCHl CITY

Fig. 5. ･(b) Photographic conditions of     the camera are the same as the     above example.      、      Exposure time : 40 sec.      15h 27m on Sep. 5、1966.

Fig. 6. The、･iew of the lりdustrial Area of     Sanbashi and Godaisan in Koclii City.

GODAISAN

THE BAY OF URADO

 As the color of the objective smoke plumes were white or greysh white･homogeneously dark backgrounds were desirable. From this point of view, the dust burning house was most suitable> having ａ background of ａ mountain range｡

 As a background) the blue sky is very good in homogeneityj but it is important to render the sky dark with filters.

(ii) Cameras, fi】tersand films used for photographing

 Nikon-F was used for long time ｅχposure, and Nikon-F or Konica for ａ moment photo-graph to measure wind velocity. The camera's relative aperture （ｏｒF-number) was 6χed at F/16 for standard lens of f = 55mmj or F/22 for telescopic lens of f= 135mm or 200mm, ａ叫1 filter factor and time of ｅχposure were changed｡

 Three kinds of filters.ａ red filter (R2) and neutral density filters (N. D. ) and ａ polarizing fi】ter(P. L. ) were used in a suitable combinationト The filter factor of R2･･ is 9.0 for panchromatic film and 5.5 for super panchromatic 削ｍ and this was used to render the blue sky darker against a white smoke. The N. D. filters with filter factor 4 and 8 were non selective for color and can weaken all colors in the light and uniformly darken ａ photograph as ａ whole without failure of color tone. The dispersed light in the sky affected time ｅχposure more than ｍｏｎ!ent photographs and the sky was tend to get ｅχcess of

of Smoke Plumes (H. Ueta)

41

exposure time, and the aim of taking good photographs was failed many times in earlier stages. As the dispersed light in the sky includes much polarized light, P. L. filter was used to eliminate this fault and a distinct image of smoke plume was obtained. Ｐ. Ｌ，

filter is also non selective for color and can weaken all color lights without ruin of color tone. This filter factor, which is changed with relation to the situations of the sun and ａ smoke and ａ camera, exists from ２ t0 4｡

 As ａ low sensitive film is advantageous for time exposure･‘Minicopy' film （ASA 32） was used in earlier stages. But owing to the narrow latitude of exposure-time, strictly appropriate exposure-time is required and sometimes one fails. On the contrary,‘Neopan SS' (ASA 100) is more sensitive, but its latitude is wider than that of‘Mini copy' film, and good negative film is gained with a little excess or short of exposure time and so failure of taking photograph is few. For the ｅｘ耳mination of change of eddy diffusivity with the change of exposure time) this film is profitable and in this study,‘Neopn ＳＳ’was mostly used. Moreover) a point which one must be careful in time-exposure is the law of reciprocity failure. This law is that as a film shows ａ character of decreasing sensitivity in exposure time longer than half a second, it is necessary to take ａ longer time than that gained by multiplying by filter factor the value indicaed in an exposure-meter for ａ camera without filter. The outline of the image of white smoke plume with the sky as a background･ is considerably indistinct in monochromatic film, and in this case or for ａ colored smoke,

color film is useful. In this study.‘Fuji' color film was used and the effect of reciprocity-failure is especially distinguished in color film and about three times of the valus calculated on the basis of the value of ｅχposure-meter, was prope･r｡

 When combination of N.D. filters and ａ p. L. filter is used) bluish color is absorbed and the 石eld of the picture has ａ tinge of ｒed･but the picture is sｕ伍cient for practical use. This nature appears both in a reversal film for slide and in a picture printed from ａ negative film. As the duration of time in which smokeぺ,vas uniformly emitted and that of constant wind velocity was comparatively short) the exposure time was decided by these elements; and the intervals from one to five minutes were many in practice. The estimation of eddy diffusivity requires mean wind velocity. For this purpose, a series･ of plume-images of moment photographs taken every two or

five'seconds. were projected by ａ projector on ａ sheet of screen-paper in successioiij and the mean wind velocity was gained by the moved distances of ａ few characteristic points in ａ smoke plume dividing by the elapsed time. And when the smoke of the dust burning house was observed on the roof of the Government Forest Exepriment Station, wind velocity was simul･ taniously measured by an anemometer and it showed ａ good identi丘cation with that gained by ａ sequence of moment 石1ms.

       Fig. 7. .Fuji color film（ASA 100）

F/22 ； Filter : 3 N.Ｄ.（8）十p. L. Exposure time : 140 sec. 11h 50m on Mar. 9. 1967.

42 高知大学学術研究報告 第16巻 ．自然科学 Ｉ 第５号        一一

 III. The theories on which ｃａ】aulation based｡

 The chief object of this paper is estimation of eddy diffusivity and examination of the other parameters which show ａ character of ａ turbulent field. The applied theories were Roberts', Inoue's and Gifford'si and some points were modified for convenience of calculation. The outlines of them are as follows:

( i ) Method derived from Roberts

 Roberts offered in his opacity theory following ｅχpression for the mean concentration in ａ smoke plume continuously emitted from ａ ｐｏｉボsource situated at the origin of the

co-ordinates χ゜コQ f一斗(1−ｃｏsθ)}      ２ ｊ

Ｐ

      ズ        Fig. 8.

 where χ ａχis directs downwindward. The co-ordinates and variables are shown in Fig. 8， and so r2 = :c2十ｙ十が，ρ2＝ヱ2十ｚ2 and Q is the strength of the point source and 尺 is eddy diffusivity assumed constant during the observing period and over the space of measurement.  The number of smoke particles ｙ contained in the line-of-sight seen from y-direction perpendicular to the plume ａχisis

Ｏ 「

y°

￨:

χdｙ°

Ｑ゛ｺﾞﾑjRｼj￣………(1)

が゜￣ﾀﾞﾄﾞ-{log-石りIUでχyＦ-logp}

Puttinｇ Ｎ＝Ｎ９７、for ２°O jmdプホ・;’ jV”｀2° iJtKux

Taking logarithm,

  log jV．゜Ｃ−￣1−ｌｏｇｘ¨‥‥‥‥‥‥‥‥ ｀゛万here Ｃ￣:＋１０ｇてj5Eｱ= const. (2) ………(3)

 Two

ways

were derived to estimate尺from

ｅχpression(2).

 The

one is the way

that an equidensity line of value N is taken as apparent outline for

the obscuration of the background.

       ｊ之

of Smoke Plumes (H. Ueta)

･(4)

( 5 )

45

KミＫａ＝=−ｊＥＪ…

where ｚ。 is the maximum half width of iV-line from the center line of the plume, ^m is the distance from the point source to the maximum half width.

 The other is that if arbitrary two equidensity lineｓＮ。 Ｎ。 constant each other (Fig. 9）･ are found. 尺iS gained by the following ｅqレC2') derived from the eq. 2）｡

    0.108z4（ｚ22−212） ……… 尺2ｖ＝ ヱ１

log Ｎx/Ｎｉ

Take Ｎ１＝Ｎ２ for simplicity and put pl=≒ρ2＝ヱ1 and

Ｋｓ＝ 0.36z4（ｚ22−ｚ12）

   ヱ1

― C2')

 Let's consider about the relation between the numbｅｔ Ｎ of smoke particles and the deflection Ｓ of the record by microphotometer. When In is the incident light into ａ negative

film and 7 is the intensity of the transparent light through the film and when Ｓ。and Ｓ are the deflections of the photometer-record corresponding t0 Io and 7， the density of the

film￡)iS shown by the following expression･      D=log V/=log Ｓ。/Ｓ     ・.

 The relation ￡)ｏ（Ｉｏｇ￡ｈａＳbeen verified in photography. Where E shows the amount of exposure. Then the mean value of photographic gamma is shown by

     −  ，￡)2−Ｄ１     １０ｇ Ｉt/1．       ＝一一一一＝一

     γ  log -E2 ―loｇ Ｅｌ   logＥｉ/Ｅ，

 In the case of ａ black smoke> E coming from ａ clear sky decreases with increase of the number of black smoke-particles Ｎ， or D=loｇＮｏ/Ｎ. Where No is the number of particles which cover the clear background. Then the above equation will be

−。log ＵｌＵ γ log ＮＪＮ．

 In general,

y is nearly 0.５ and ＮＷＮ，==(51/S2)2.

 Put ＮＷＮ，= 2/1, and ＳＩ/S2＝ソT/1.

 In the case of ａ white smoke,

the amount

of reflectedlight by

the particles of smoke

increases with N,  ａnd E

may

be assumed

to proportion to Ｎ, ａｎd

−  log Si/S2 γ゜log Ｎ．/Ｎ,

and S2/ Si =、/T/1

for Ｎ、/Ｎｏ=2/1.

 The

values oi Ｋ≪calculated from the eq. (5) using the values of ｚl and ｚ２corresponding

44 高知大学学術研究報告 第16巻  自然科学 卜 第５号

       -       Ａ    ’

Fig. 9. (a) Visible edge and two equidensity lines (Ni,

Fig. 9. (b) Microphotometric density-curve at  sectionｙi∃r for negative film of black smoke.

(２べ＝輿旦ｘおし一撃)き

Ａ Ｓ＝Ｏ N2） Ｂ

z,

Ｚλ

Fig. 9. (c) Microphotometric density-curve  for negatve film of white smoke.

(ii) Method of Inoue

 Inoue had analysed photographs of smoke, applying his theory of atmospheric. turbulence, overlapping about twenty sheets of successive moment films of smoke plums. In this study, his method of analysis was adopted for a fi】ｍof time exposure in place of the overlapping of moment filmsｱ and calculation was ｅχecuted for his so-called ‘the second region'.  The outline of the theory is as follows

>    ト     ノ

 The width of vertical ｅχpansion of ａ smoke in the second region (.t≧ｒ,。orｚ≧χ,。）is given by

……り‥‥‥‥‥‥(6)

and the relation of the width of a smoke

to the distance x. from ａ point source, makes ａ

･of Smoke Plumes･ (H. Uet八）  45

(9)

( 1 0 )

ai)

(12)

and ｒ。islife-time of ａ turbulon which

eχistsat stack-height H.

When

the lower layer

of the atmosphere is in adiabatic condition, he assumed

frictionvelocity ｙ＊tｏbe equal to

(？)みand

deduced

the next expression for eddy diffusionin this region,

K,ｏＴｌ＝ ４ ｙ２^≪,……      ２ 。

and as mean

wind

velocity-distribution is given by the relation

   ｙ＊   Ｚ ″゜アｌｏｇヱ

ｗｈｅｒｅゐiS Karman's constant and ^0 is roughness parameter. Then,

‥‥‥‥‥(71

     Ｘ,=Ｍで≫=Ｈ ＼ogテ………･･…………（8）

Diffusion angle &m is given by

tan ｅ。＝   ｙ＊２ ε一一        ｒ匍 Friction velocity  （ぶ2）1＿jｙ   ん

ｰ-＝-(万1=α･凡

u Z4 Ｚ

The

rate of dissipation of energy is

lｏｇで￣

Following linear relation had been assumed

between

theoretically derived half width of smoke (￣Z2)land the practicallyobserved mean

half width Hｚ、Between

the angle θ７formed

by two outlines of the smoke

at the apparent

point source and the angle θｇ、following relation exist.

46  高知大学学術研究報告 第16巻  自然科学 Ｉ 第５号 "←       I       ・     θ７        tan 01。＝α･tan 2 From (8), (9), U3)        応 ･(掴

     “゜(ＸＩ。ZH)｣1n(ＢｔII)………｀'…………｣………tt4)

ａｎｄαis able to be calculated.

From

(9) roughness

parameter ｚ。is gained.

     −

Between

(Z-}ii and jz]linearrelation holds and the fragment of χ-axis by the straightline

is to ｂｅら＝十χ。, and χ,。isdetermined. In practice.犬召j is used in place of (？)II.

The linear relation is shown

in Fig. 11.

      χ102

  50 (２ＨＸ)2  (剌  40 3 0 2 0 1 0 ０ _{20 ×0 40} 6 0 8 0 1 0 0 120 X(")

      Fig. 11. Relationbetween。ertical

width of smoke (2凡) and distanceCx)

      from ａ point source.(13h ００ｍ

on Dec. 7. 1966)

(iii) Method

of Gifford

 Gifford decided a visible edge of a smoke

plume

applying Roberts'‘opacity

theory' and

derived ａ simple form of diffusion-parameter by introducing Sutton's and Frenkiel's

dispersion models.

He started from

following expression which

corresponds to the eq. (1)

and which

had been assumed

by many

people

jｖ=フ誉有万Ｐｅべて贈旨｝

and gained the relation

一一一一Ｚ2

㈲

㈲

(17)

where z,. is the maximum

falf width of a plume.

Put 戸＝と夕y

and α＝ｒl子.

and

 １ 一 戸 1.0 I m oo r-０ ０ ０ ０ ． ６ ０ ． ５ ０ ． ４ ０ ． 1 0 . 2 0 ｊ ０

of Smoke Plumes (H.

Uet'a)

47

0.36 ａ

(19)

0.04 0.08 0.12 0.16 0.20 0.24 0.28

Fig

12

The curve of

＋19十゜a

(by Gifford)

      −

      戸

0.32

 The relation between ｌＩＰ ＺＶｌｄａ is shown in Fig. 12. After ｚ，ｚ。are read from the visible edge of a plumeﾀa value of ａ is decided and corresponding 1/夕is read from this graph. Then Z' is gained by the relation ７＝ε･ら2十In this paper. Zi is gained by the same way as Gifford's and then Sutton's stability parameter 7z was estimated, n is to be originally determined by the velocity profile ″゜″!(貢)ふ･but in this paper･ it was tried to estimate by following two ways｡

 ( a ) From Sutton's assumption 芦゜十Ｃｓ2° ｢￣”･

    一一

logloZ2＝ｃｏｎｓt.十(2-")logiμ‥

      −

 In the linear relation between １０９１０Ｚ２and logioa:, n is known from the straight line. Ａ few examples of (18)are plotted in Fig. 13.

 (b) n is also gained by Culkowski's equation

。，Ｔ≒＝２３

…………Q8)

gradient of the

where -'じsis total plume length and Xm is the distance from point source to the maximum plume width. Eq. (19)satisfies both the visible edge of a plume and any equidensity line.  After ，zis obtained, dispersion coefficient Ｃ・ and vertical turbulence intensity ゛2 are calculated by the following two expressions proposed by Gifford. l

48 log Z' ０     ０ ０     ０ １ ０ r ｏ 2 0 0 1 0 0 5 0 1 0 ５ 高知大学学術研究報告 第16巻  自然科学 Ｉ 第５号 ５ 1 0 2 0 5 0 1 0 0       1966 十Jan.15, IShlS" O Oct.19, I3h27" △Oct.19. I3h32"-n Nov.30, I3h42≫. ･ Dec. 7. l3h00"ヽ

Fig. 13. Examples of linear relation between log Ｚi and log

cｓ2＝2ぶ♂(普 ７び2＝な2(-;こｰ)2 log ｊ ヱ．

Ｎ

ｆ ｍａ５） ２７１

ル

ｄ

Ｎ=Ｎ i

ｏ

log Ｎ７７１＝Ｃ−

where C' = l

I  剛 一   一

where

ｃ°ｌｏｇソjｼ･u

SubstituteInoue's relation(.Z^)皿゜uぶ，１(ふ一介)1≒u。１ｊ

into above eq. (23),

and

    log

N

C'一千log

７

      Q

og l/￣万￣(Ｊ)χ,j￣￣

Photography of Smoke Plumes （Ｈ.ＵＥＴＡ） 49 log Sm 5040 ０  ０ ＣＯ CＭ 1 0 4 0 3 0 2 0 1 0 log Sm ０ ０   ０     ０ ｒ コ ４   １ り     ク ｀ ０   ０   ０   ０     ０ Ｉ   ｕ i " ^ w i c ＼ x ｙ／ 1965, Dec.3l I4h37 (0.20) Dec.30 IZhOI"*        (0.31) 1966, Sep.5 15h35≫ (0.26) 1966, Jan.5 I3h28m ＿   (0.24)    10   20 30 40 50 60 80. 1001 150 200 10g ｘ

Fig. 14. (a) Relation between deflection of peak concentration of       smoke and ｊz］. 1966, Oct. 31   l4hO3 (0.37)   I2h53・(0.27) I」、 3h42m (0.38) ￨2h50 (0.28) Dec. 7  I3h 18。（0.21） / ／ 一一一●Ｑ●一一０−。●･０･Ｑ´

oo(0七＿／11おｙｍ

  10 Fig. 14. (b) 20 30 40 50 60 80 100 150 10g ｘ I5h39" (0.20)

50  高知大学学術研究報告 第16巻  自然科学 Ｉ 第５号 -log Sm ０ ０ t n -5 ＊ ０   ０ ｆ Ｏ Ｏ J 1 0 1966, Nov. 17 I5h 11 "･     (0.25) I4h35 (0.27) Uh32・(0.35) 1 0 Fig. 14. （ｃ） 2 0 40 60 80 100 10g ｘ

Table l. Gradients of straight lines (log Sa、･ersus log x). Beyond distanceＤ、 the straight lines      havethese gradients. 1966 Oct. 31 12 12 13 14 5 0 5 3 4 2 0 3 0.28 0.27 0.38 0.37 0 0 0 4 0 n Ｃ v l C -L r t

of Smoke Plumes （Ｈ.ＵＥＴＡ） 51

15h 39m on Sep. 5， 1966 (Mizushima) 15h 28m on Sep. 5，1966 (Mizushima)

1３ｈ００ｍ on Dec. 7, 1966 (The dust burn-ing house)

1３ｈ２８ｍon Oct. 19, 1966 (The dust burn-ing hoｕsｅ）（Ａｎexample that is not Gauss-ian distribution)

    Fig.15. Records of microphotometer.

The

same

result as Roberts' eq. (3) is also derived from Inoue's relation.

From

eq. (､3）、

  log

S゛゜Ｃ″￣±log

SI°………

is derived for black smoke,

and

log Ｓ･・ル＝Ｃ″'十干 ＩＯｇ､『

C23')

(23″)

 for white smoke.

 That is to say, the relation between

log

Ｓ

and log ぶ shows ａ straight line with

gradients 一寸for

black smoke,

ｏｒ十for

white smoke

The graphs plotted by practical

data shows that this relation is considerably satisfiedbeyond some

distance from ａ stack

as. shown

in Fig.

14 and Table ｌ and most

of the gradients fallin a range of ０.2∼0.4

       ・

center in十Consequently,

the method of Roberts may

be applied beyond

the minimum

criticaldistance in ａ smoke.

 In ａ microphotometer

a light-flux of ａ small section about 0.01m

｢is perpendicularly

moved

to the plume ａχisthrough ａ negative film of 35 mm

at every constant distance and

the diagram

of ａ smoke

density is recorded

as Fig. 15. This diagram

is to be ａ density

curve with ordmate

as deflectionof photometer and abscissa as altitudeｚ in ａ smoke plume.

 From

eqs. (4) and (20),to calculate eddy diffusivity 尺and

diffusion parameter

Ｃ。it is

one of the most significant factors to determine the visible edge

that makes

a background

obscure.

In this paper･an

outline of ｇsmoke

plume was

decided by

two

ways. The

one is to draw

an outline in an･ enlarged projected image

of ａ smoke

by eye-measurement･

and the other is to decide one from ａ record of microphotometer. In

Table 6, the values

of eddy diffusivityevaluated from the outline by eye-measurement

are shown

as 尺。ぶ,and

52 _{高知大学術学研究報告 第16巻  自然科学 Ｉ 第５号.}

         -Table 2.（ａ）Ｔｈｅrelation between X and values of verticalwid由of smoke (2H-), peak   concentration (5 ).

Date

z（m）1 13.5 -27.0 -40.5 -54.0 67.5 81.0 94.5

一

一

一

一

1966  Jan. 17  14h30m 2凡(ｍ) ざ｡(Cm) 25.7 25.5 39.2 25.8 53.3 26.0 60.1 26.0 67.5 29.5  − 33.0 , 74.3   − 15 25 2凡(m) S。(Cm) 11.832.2 23.835.8 33.6 36.5 39.9 36.5 42.9 37.0 47.6 37.2  − 38.5 Jan. 20 14 02

2篤(m)

Ｓｍ(Cm)

16.1 30.0 21.5 31.0 30.9 31.0 37.6 30.0 41.6 32.5 47.0 34.0 52.334.0

x(m)

14.2 28.4 35.5 42.6 49.7 56.8 63.9 71.0 78.1 85.2

99.4

113.6 127.8 Oct. 19 10 58

2凡(ｍ)

5_(cm)

14.5 15.0  − 17.0 28.7 20.0

一

_一

34.1 21,5 37.8 23.0 42.623.0 −49.7 54.025.0 −56.8  −56.8 一一 一一 13 25

2凡(ｍ)

函｡(Cm)

14.05.6 27.0 16.0 一一 29.8 22.0 一一 38.3 25.0  −41.2 44.0 30.0 49.7 31.0 52.5 32. 0 58.2 35.0 一一 一一 13 27 2凡(m) Sm(Cm)

旧

22.6 15.0 一 一 28.816.5 一 一 30.. 2 18.0 一 一 40.5 20.0 一 一 45.8 21.0 51.8 22.0 一 一 一 一 13 30 2凡(m) S (Cm) 22.0 11.0 33.7 13.0 一一 36.9 15.0 一一 41.2 15.0 一一 46.2 17,0 54.018.0 58.2 20.0 64.6 20.0 68.9  − 74.6  − 13 32 2凡(m) Ss(Cm) 14.916.5 17.522.9 24.9 18.0 28.6 20:5 一一 34.8 21.･0 一一 39.3 24.0 一一 43.3 25.0 47.6 27.0

 −

5□

60.4 − Nov. 30  13 35 2凡(m) Sm(Cm) 26.3 22.0 36.2 24.0 44.0 24.0 46.5 27.0 49. 725.0 −53.3 一一 55.0  − 一一 一一 一一 一一 一一 14 00 2凡(ｍ) Ｓａ(Ｃｍ) 14.2  7.0 22.0  9.0 24.9  − 34.410.0  −38.0 39.8 10.0 11.045.4 51.8 11.0 一一 55.0  − 一一 一一 一一

畷ｍ）

13.5 27.0 40.5 54,0 67.5 81.0 94.5108.0 _121.5 - − 41.0 - −  − Nov. 17  15 11 2凡(m) Ss(Cm)  7.4 27.0 10.8 31.0 14.2 35.5  − 38.0 21.6 40.0 27.7 40.5 29.0  − 一一 15 31

2凡(ｍ)

5_.(cm)

6.8 21.0 11.5 33.0 14.9 35.0 17.6 39.5 22.1 40.5 一一 一一 一一 Nov. 21  14 25 2越(m) S。(Cm) 22.9 17.0 27.7 21.0 33.8 19.0 41.9 23.0 50.0 27.0 55.4 29.0 58.1 31.0

則64j

14 32 2篤(m) SS(Cm) 17.5 11.0 22.312.5 30.4 16.0 34.4 21.0 42.5 25.0 50.3 28.0 54.0 30.0 59.4 30.0 60.1 32.0 -78.3  − - −  − 14 35 2凡(m) S｡(Cm) 14.2 14.0 23.0 22.0 30.4 25.0 40.2 27.0 50.0 29.0 55.4 30.0  −66.2 −68.9 14 45 2凡(m) S｡(Cm) 17.5 27.0 20.2 31.0 25.6 33.0 29.7 37.0 43.2 38.0 50.0 40.0 一一

一

一

of Smoke Plumes (H.

Ueta)

53’ Table 2. (b)

Ｊ(ｍ)

8.5 17.0 25. 5￨ 34‘O[42.5 51.0 59.5 68.0 76.5 85.0 93.5 102.0 110.5 119.0 Dec. 7  13 00

2凡(m)

S。(Cm)

12.8 18.0 17.4 18.0 21.3 18.0 25.9 19.0 30.6 20.0 34.9 20.0 38.3 21.0 42.9 22.0 47.6 22.2 53.122.2

 −

25.5

 −60.8

一

一

 69.5 “ − 13 05

2凡(m)

Sm(Cm)

9.4 13.5 17.913.8 20.8 15. 5 25.5 16.0 18.529.8 33.2 18.0 38.7 18.0 41.2 18.0 41.7 18.5  − 20.0 47.6 21.0  − 23.0 48.523.0 一一 13 09

2凡(m)

S｡(Cm)

20.4 19.0 28.4 20.0 34.9 21.0 36.6 22.0 42.5 23.0 45.5 23.0 47.6 25.0 52.7 26.0  − 27.0 57.8 28.0  − 30.0 −63.8 一 一 −牡０ 13 15 2凡(ｍ) Ｓｓ(Ｃｍ) 13.6  8.0 16.2 10.5 24.711.5 27.6 11.5 31.5 13.0 37.0 15.0 35.7 16.0 38.7 19.0 40.0 24.0  − 26.0 36.6 30.0  − 32.0 −42.5 一一 13 16

2凡(m)

S。(c

｢)

 − 18.0 16.6 20.0 20.8 18.0 29.3 18.0 36.9 21.0 37.4 22.0 35.7 23.0 46.8 24.0  − 25.0 53.627.0 一一 −65.9 -- 63.863.8 13 18

2凡(m)

S。(cm)

11.9 24.5 17.9 27.5 22.1 30.0 28.9 31.0 34.9 33.0 37.8 34.0 38.3 35.0

 −

_36.5

42.5 37.0  − 38.0 44.6  − 一一 −51.9 一一

ﾊﾞｍ）

12.5 25.0 37.5 50.0

62.5

75.0 87.5 100 112.5 195.0 187.5  150 - −  一 一 98.7 31.0 Sep. 5  15 35 2篤(ｍ) Ｓｍ(Ｃｍ) 21. 1 21.0 29.8 23.0 35.3 25.0 39.1 24.0 44.6 22.0 50.8 22､0 52.7 22.0 55.2 27.0 62.0 27.0 一一 80.6 28.0 15 39

2凡(m)

S。(Cm)

一一 26.8 28.0 一 一 41.2 28.5 42.5 28.5 57.2 28.0 63.7 29.0 70.6 29.0 76.2 29.5 78. 1 30.0 一一 Oct. 31 12 50 2凡(ｍ) Ｓｍ(、Cm) 27.9 15.0 61.2 14.4 84.6 16.0 90.0 17.0 93.6 20.0 94.5 21.0 75.6 22.0  − 24.0  − 24.0  − 25.0 - −  一 一  − 35.0 - −  − -12 53 2Ｈｊ、m） S_ (cm) 37.8 19.0 48.6 24.0 57.6 25.0 牡1 30.0 65.7 32.0 64.8 33.0 70.2 35.0 72.0  − 一一 13 42

2凡(m)

S。(Cm)

25.2 18.0 82.4 20.0 46.0 20.5 57.0 23.0 57.6 25.0 S7. 6 28.0 62.2 29.0 60.8 33.0 58.5 33.0 14 03

2凡(ｍ)

5

(cm)

23.4 20.0 40.5 21.0 54.0 27.0 58.5 31.0 67.5 34.0 54.0 36.0 50.4 39.0  − 42.0 一一

IV. An example

of calculation of eddy difFusivities.

Date: Dec. 7, 13h 00m, 1966

Site:Ａ smoke plume of the dust burning house was measured on the roof of Kochi

 University･

Weather: fine,wind directionand velocity:ｙ， 1.65 m/sec

Stack height: H = 50m, lapse rate: -0.013 °C/m

Camera: Nikon-F f= 200mm. Film:‘Fuji Neopan SS’

（ＡＳＡバ00)F/22,

 Filter:2N. D.(8)十N.D.(4)十R2十P.L.

Exposure time: 300 sec.         ，

（i）Ｔｈｅ calculation with eq. （4）尺＝jjﾐﾄﾞｰ

  for slide-projector w=l.65 m/sec> ･≪m= 60.0m, ≪ = 9.4m      尺≪5=1.21×104（ｃｍ２/sｅｃ）

 54         高知大学学術研究報告 第16巻 丿自然科学 Ｉ 第,5号        -一一一一一一

 The calculation with eq. (5) K。＝ 0. Z()uW一之12)

 ２万1＝:12.8m, z.万=24. 7 m .^1=:85m尺jｙ＝ｺﾞﾛ慾上艇ljド2￣12‘82し＝͡3.11x10‰ｍ':/sec)

(ii) Sutton's stability parameter ，zis evalu‘ated with Culkowski's eq. 09) and in this example

 Dispersion coefficient C2，＝2jｒ♂(音)2＝2×76.5°"×(寸卜卜)2＝0193( ｢‘)

       -Turbulence intensity ７む2°“2

突)

=1.65=×(j)})2＝0086(m2/SeC2)

(iii) Estimation of ，zby the method derived from Gifford's equsatin

 Decide ａ visible edge of the smoke plume based on ‘opacity theory' and measure half widthes of the plume Zf at points ？1 （刄fｒｏｍ the stack). These values are listed in column ３ in Table ３ and ^ = 60m, Zm = 9.6m.

 The value ４＝−だtｙ at every point of Pi is listed in column ４. Measure 1かfrom the

graph of

＋10g☆=≪

in Fig 12. These values are listed in column ５

      -  -  1       - Calculate Z12 by Zi2＝マ，7心町These values are 】istedin column 5. Plot the （ZI,2亀）    ．       戸

in log-log paper and draw ａ straight line through these points. The gradient of it is read as 2-w = 1.71, and w = 0.29. Some ｅχamples are shown in Fig. 13.

       -       Table 3. An example of evaluation of Z2i.

p. _{P1 P2 P3 P4} 司(ｍ) ら(ｍ)  ＿ 応j a ES2?7i エー々   −  jり  EZ。2 -7 2   20  6.4  0.17 0.065 15.60   40  8.6  0.31 0.175 42.04   60  9.4  0.37 0.380 91.28   80  6.8  0.19 0.800 192.1

(iv)

Calculation by Inoue's method

 The

width of the smoke

plume(2H。)

gained by the record of the mi crophotometer

are

listed in Table 1. From

this Table, according to the linear relation between

(2i/x) and

X, a.］0

is decided.

of･Smoke Plumes （Ｈ.ＵＥＴＡ） 55

＝JjyﾏＬ°0.35

m/sec> ｓ〒ｊとと＝21cm/sec,

瓦＝ナV*-T,。    灸’

￢十×0.35'×571°35×104

cmVsec

にこて￣￣函￣゜

  Ｊ￣1゛ヱ

2o=7.6m 隻jL一二瓦一一= 0.656, and from １０９千＝ﾂﾞH

 94.2

二一『tan

２

 V. Results of obseryation and discussion

 The smoke plume from the stack of the dust burning house at Asakura, in Kochi City, is isolated and the condition of background is good and the best data were gained.

 The dates of measurement were Oct. 15, Dec. 30, 31, 1965; Jan. 4, 5, 1.7, 20; Oct. 19, Nov. 17, 21, 30 and Dec. 7, 1966.

 At Sanbashi Industrial Area in Kochi City, the dates of measurement were Oct. 5,. 31, 1966. As there were many stacks of factories in this area, analysis had some uncertainty) and the smoke of the nearest stack （と＝30m）ｗａｓ chief object and was able to be

practically used.

 At Mizushima, smokes were emitted from two staks iH = ()5m) neighbouring each other, but as they were observed from ａ site, where they looked like emitted ffrom one point source, the above methods were applied. The observation was executed on Sep. 5,

1966.

 The above three methods to estimates 尺, were applied to the photographs gained at these sites, and the results are shown in Table ４，5 and 6. Those photographs which had little smoke, or bad directions of smoke> or apparently had not Gaussian distribution of

smoke-concentration. were excluded.      ｜

 The values of vertical temperature gradient dTldz were gained by the temperatures measured on the roof of the building of Natural Science Department of Kochi University and on its groundｱand the difference of the heights was 15m; or the temperatures on the roof of the Forest Experiment Station and on the foot of the hill where that station stands

were measured at the same time as the photographing of smoke of the dust burning.  At Sanbashi Area, the temperatures on the summit of Godaisan and at the foot of it

were measured by an Assman-thermometer.

 At Mizushima, the temperatures were measured by aspirated thermocuople-thermometers attached to ａ baloon.

56 ･︵ＢＪｎ５(ＥＳＹ IE︶ＪｏｐａｆＯＪｄ Ｘｑ ｐｓiBｕinｓａ ｓａｎｉＢ＾Ｙ ︷Ｊ．｀Ｊｉに︸い 高知大学学術研究報告 第16巻  自然科学 Ｉ 第５号 −       − Ｓ   Ｍ Ｑ 。. I ｌ;ぶぶｊＱ ６   ci o o ｜ ｜ ｜ ｜ ｜ ｜ ｜ ’￨ ｜ ｌ ｌ ｌらに４１ １コｅ､ａ        ６６６   ６６  6 gl 旨ｌ ｌ召召に Ｃ;   ６６６ ｜ ｌ ｌ ｌ ｌ ｜ ｌ ｔ ｌ ｌ ｌ ｌ応召召【 ｌｇ吊        <=> CD CZJ   Ｃ;ｄ

 八

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色

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超

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こ い O O C ^ ' ^ ■ > ― (   I   ●   ●   ●   ●   ●O Q ヽ L O C ヽ ･ JO O O ヽ C ヽ 4 - C ヽ 4 （ ヽ a 一 一 に ･ ヽ ｏ ヽ ｎ ヽ Ｏ   ●   ●   ●   ●   ●ぐ り L O C s ] ぐ 9 t 乃 一 一 一 一 一 七 C ヽ ヽ ∽ - ^ r o o o ^ o C 3 り 旬 Ｑ Ｎ ひ t ヽ ヽ ひ   ●   蕃   ●   ●   ●   ●   ●   ●   ●   ●   ●   ●   Ｉ   ●心 C e ヽ C e ヽ - り り y − 4 C X ｺ e ヽ 心 々 ぐ ゛ つ ぐ Ｎ       一 一 e ヽ a 一 一 一 一 一 一

超

C ね ひ ド ぐ り 々 痢 L O C - ' S L O r り ｔ ∼ （ ⊃ O O C O < Z > O > C - ∼ α ⊃       y 一 司 つ 唱 吟 唱 ○   ●   ●   ●   ●   ●C ･ ヽ ﾛ ヽ ﾏ 一 ∽ ヽ g = 口 ヽ ヽ ｏ ヽ Ｏ Ｃ ヽ ヽ C ― . " - O c v j ｅ 一 一 Ｎ マ ー 4 0 N 々 N O 々 Q 句   ●   ●   ●   ●   ●   ●   ●   ●   ●   ●   ●   ●   ●   ●（ y r り L O O ^ U O ひ 苛 o ぐ り ひ u n o < i ＼ o c ヽ ヽ こ ） Ｃ ヽ （ Ｘ ） ヽ ｏ ∽ ｏ ヽ C O n ■ ■ ― * 〇 〇 〇 ヽ 7 ヽ C ヽ       一 一 一 一  /″へ_Ｊぶ  Ｗ ￨ 心 < = > C O C D O O > r o " ^ c > a 苛 々 々 e ヽ C ヽ ヽ o り 々 - ^ C O L ･ ） 々 々 心 o o o l o o o - ^ a * ぐ つ マ 々 や マ （ N N O C − 回 り m U ‘ ） ･ 々 ･ 々 − a ･ − r マ マ 々 々 々 々

則

o a c N i d C N l o a Ｃ ｇ   ●   ●   ●   ●   ●   ●− ｒ − ｒ − ｒ - ９ 々 ヽ ｑ ･ c : > C 3 o o C D U - 1 U - i L O U - 1 U O C あ ひ ひ ひ ひ C ^ C > J O J C ^ C S l ぐ Ｎ ぐ ■ N J ( Z > C 3   ●   ●   ●   ●   ●   ●   ●   ●   ●   噸   ●   ●   ●   ●< z : > < = > < = > < = > < = > ^ 二 3 V O v O ^ O v O ' ≫ O ^ O り Ｍ ⊃ 一 一 一 一 一

贈

C ） O O O O O ＼ o < ^ C O L o t o c z >   一   一 一 n O C Z 3 O < 3 > C Z > − つ ヽ Ｑ ｅ ヽ ， ･ つ ｏ ヽ こ O O O O O O O O O O O O L 乃 O O L T S O へ N ; N s O N ∽ O N O 州 ぐ ９ ∽ 一 一 ‘   一 一   一 一 一 つ 一 ヽ Ｑ ･ ヽ ･ 一 一  Ｑ  Ｅ ●← Ｈ E c ヽ ヽ o o l J ^ - c ^ r c - ヽ ○   ぐ Ｎ Ｎ ぐ ゛ ） マ マ 哨 ぶ   ･ ^ J - - ≪ : j - - - c r - ^ や 々   一 一 一 一 一 一 t乃にヽ一々ひCX） -'*"'≪< U-J 1Q O 一一一一・a -一一一一 α ⊃ - ヽ o 一 ･ n n ヽ O C ヽ C ヽ a n 乙 ｺ ヽ O C X ） U り o O 州 N 々 ﾏ 々 L n O O 州 ○ 州 ャ ー H C ^ O J C S l C N l C < 1 C V J O J ぐ Ｎ ぐ り ぐ り ぐ つ 々 句 一 一 一 一 一 一 一 一 一 一 一 一 一 一 S ra Q

 言j

−(j]￨IN 

e

茫 ra ro

九回   ６ ｅ Ｊ  Ｉ ぶ ト、   <T5 TO Ｊ    Ｉ    り Ｑ Ｑ   C i N! ；    吻吻

el じ s o L O C D O - 5 ' " a * C I N - ^   − ● - ・ 一 L n ﾏ Ｍ ⊃ ぐ り ぐ り 州 Ｎ Ｉ ㎝ ） Ｃ Ｃ Ｉ ｀ ∼ ｜   Ｉ C D ( Z J C I S < Z > < Z > C D C 3   c z > c i > c r > ｌ ｔ ｜ぷ^O 1 Ｉ Ｉ １ １  ６６

？

o ヽ L n c ヽ o o o ヽ o ヽ n   c x に っ ｎ − ｈ Ｑ ･ っ c − っ ・ Q c ヽ l 削 ﾏ ヽ ｏ 副   ｜   ●   ●   ●   ●   ●   ●   ●       ●   ●   ●c i > C 3 C 3 c : 3 c ^ c r > c z >   c z > < z > c z > ｜ ｜ ｌａ誘｜ ｜ ｜ ｜ ｜  ６６

パ

ぶ

ず つ t − 4 × L o o o ■ ･ ― 'c ヽ - - ^ O N ひ   7 − り り ｎ Ｃ い ぬ c ヽ ヽ り り o o o c ｺ ■ ･ ― i - . O [ C っ り N ひ ぐ ｀ q   ●   ●   ●   ●   ●   ●   ●       ●   ●   ●   ●   ●L 乃 ぐ ゛ ） ひ 々 X O t / り L / り   C み の り ζ ｀ ヽ - （ ね 宕 ｜ ６ ｜§ｇ呂旨ﾄﾞS I  ･尚ヽ:･゛ヽ6 j

抑

■ . - H t r- < 3 > ＼ o t r - ヽ C つ Q   O ぐ り C ゛ T C D l O       . ｜       . . c ｀ ヽ L 乃 ひ （ 刀 ﾄ ﾞ ∽ c x ⊃   ひ ひ ∽ ∽ α ⊃

い

｜フで゜？｜已｜  5Ξ;゜｀゜｀゛ コ

郷

O O O e Q O 々 々   o ･ a l ヽ C ヽ O       . ｜       . . 一 一 一 々 一 ヽ Ｑ ヽ ｏ   一 − Γ α ⊃ ｃ ヽ -･ − 回 り 一 口 -･ n や マ   − ぃ Q c り c ヽ 4 n (? ｜ ぐつ_Cり   ヽ ０ ヽ - O｜       ． ｜   ． ｌC O O ヽ   C O   ｃ ･ ） α ⊃ 一 ロ っ   ヽ ｏ   ’ 哨 ｀ 苛 々 マ   L O  /へ_対  ぶ ご × O J v o り 哨 ○ ひ 哨 L n O り 哨 吋 凶 C O C Z ) O O ひ ぱ ） ｏ （ ｙ L O O N - ^ ＼ O ^ O ^ O   ●   ●   ●   噸   Ｉ   ●   ■   ●   ●   ●   ●   ●   ●< - O Ｈ C ― L O C ― v O L O v O > - O C ヽ ヽ i n - T V - ^ ● 一 - i 一 7 一 一 i t − i ← 7 一 一 q - ¶ 一 一 4 マ ー 4 9 − ･ ← ● − 4 ← - oo −べヽ ド 6 ぐ Ｎ ｅ ヽ Ｃ り L n ∽ L 乃 o ’ 苛 ゛ - ・ ヽ ・ ｏ ヽ ・ 一 一 H O O C N J C - ∼ l ｀ 一 一   ●   ●   ●   ●   ●   ●   ●   ● − 1 ツ り 1 n l n n ヽ O C 7 ヽ C ヽ 一 一 一 一 ・ に ヽ a 一 一 t5 U - 5 C O C - ヽ N 心 N ぐ ｀ Q C O o o e x ｺ 々 （ 乃 N L O - f * " U - ^ v X 二 3 ＼ O ^ O ^ O t o - ^ L O l - O ■ ^ J ' ＼ O   ●   ●   ●   ●   ●   ●   ●   ●   ●   ●   ●   ●   ●⊂ 〉 C 3 O > c : > c Z 5 C 3 < : z > < : z > C 5 < : z > C I > c : 5 c z s 一   〇 ヽ L O   L O   ●     ●O   O C 9 や り O N （ N ひ N マ マ ヽ 4 ⊃ ﾏ ･ ｎ ｒ ヽ 々 ヽ ４ ⊃   ●   ●   争   ●   ●   ●   ●   ●Ｃ ） ｏ Ｏ Ｏ Ｏ Ｏ Ｏ Ｏ ぶ？  Ｗ O C ヽ ・ ヽ ■ 3 ' ≪ * ' - > : * ' C ― - e S ' べ ヽ o 々 ・ ヽ 1 1 n C y ヽ C C ∽ 咄 々 o o u ^ - - c r - ― < C X ） ∽ ぐ り o q c - ∼   ●   ●   ●   ●   ●   ●   ●   ●   ・   ●   ●   ●   ●l ｀ ∼ r o c z > o o ひ ∽ ∽ ひ C ― O n O O C - ∼ ド       ｱ 一 司 ・ ⊃   Ｃ ヽ ４ n   Ｃ り   ●     ●や   ｏ ヽ ヽ - O C f ヽ C O ' S j * C 3 C - ヽ l ヽ ヽ o ヽ l ヽ - 一 一 C Q 々 ヽ O C ヽ l   ●   嗇   ●   ●   ●   ●   ●   ●七 ﾏ Q L / ･ 州 り o o t ｀ ∼       一 一  ら  eﾘ_ベ  Ｊ C ヽ に ） ･ つ り C Z ) C D C O C ､ o < Z > < : Z > O < Z > < Z > に ヽ C つ n ヽ C O ヽ ･ ヽ ･ T O O C I S ヽ O n l ヽ ヽ C O I ヽ ヽ O C X ） o ヽ Q O O C ヽ a O ヽ O Q ヽ 1 Q C ヽ ャ ー H     C N l C N ] ぐ Ｑ ぐ り ぐ 7 ^ C - < 1 ぐ Ｎ く ｀ 4 ← 7 - - i 7 一 一 i Ｑ   Ｏ ヽ ロ ヽ 一 一   ヽ Ｏ O O O C ･ 3 C D C D r D C I > C 3 o o T ― ( C O e z s ' i J * c ヽ a ･ a ﾏ 州 O t ｀ ∼ O O C Z J C X ⊃ ∽ 一 一 ･ ヽ Q 一 ヽ Ｑ Ｑ ヽ ･ り C ヽ q

バ

 Ｗ

・ ４ - ‥ カ C D Ui ■ > ― 1 〇 ヽ Ｏ Ｏ ヽ ･ ｎ α ） ヽ C i r o ・ い 一 ｅ ヽ ヽ o c - ヽ ヽ Ｑ ヽ ｏ ヽ 心 乙 ぺ − 1 ･ ･ n   ●   ●   ・   ●   ●   ●   ●   ●   ・   ●   争   ●   ● ゝ一 一 一 一 一 一 一 一 一 一 一 一 一 ・つ CX3_CヽO こ ← ← ぐ り ひ N ひ り C ｀ ヽ ∽ ■ ^ a 'C O i - o u ･ ） n ヽ C ） Q ヽ e ヽ   ●   ●   ●   ●   ●   ●   争   ●一 一 一 一 C ヽ a C ヽ a 一 一

パ

 心

← ■ ･ ― I C N J 1 / り L n 吟 唱 ○ 心 l - O C ｀ ヽ C ｀ ヽ 州   ●   ●   ●   ●   ●   ●   ●   曾   ●   ●   ●   ●   ●C り C O ← ぐ N 7 一 一 i C 9 ぐ ■ ^ O ) C S l . - H ぐ N r r > r り 一 一 一 一 一 一 一 一 一 一 一 一 一 −べヽ lヽCO_Cヽa 一 ぐ ■ s j c : > v o o a や 心 N ぐ N   ●   ●   ●   ●   ■   ●   ●   ● 々 １ ａ Ｑ ヽ l n ･ カ ｔ ヽ ｏ 一 一 一 一 一       一 一

遊

O n t r - ∼ ﾏ O n N O 州 州 ぐ つ l ｀ ヽ 心 O   ●   ●   ●   ●   ・   ●   ●   ●   ●   ●   ●   ●   ●に ヽ o ヽ Q ヽ - ･ 心 ｏ ヽ １ ｎ Ｏ ヽ - ｏ ヽ ヽ ｏ ･ り o ヽ C ヽ a e ヽ C O o o o o o o o o o o o o o o o ヽ o ヽ C X D   O 一   − a ● e < i o c ⊃ ヽ 4 ⊃ C ヽ ･ J O O O C ヽ ･ as o L o ･ り   ●   ●   ●   ●   ●   ●   ●   ●l ｀ ∼ ｀ e L r つ ぐ ゛ つ N L O e 一 一 Q - C ヽ ■ a C 3 ' - H c ヽ ヽ o に ヽ 一 ・ 一 一 一  パパ  心 n O に ） 一 〇 〇 々 ｏ ヽ Ｃ ｋ ｎ ヽ ｏ ∽ ' ≪ : r - < : r - ^ ' ^ ' ^ " ^ " ^ ' ^ U - 5 ' . : S ^ や マ り ヽ 4 ⊃   々 C り   々 L n O り ｅ ヽ 心 ^ o c z > c - ∼ や 々 ･ r o ' ^ i - O − ﾛ ｰ ） n

坦

一 一 一 一 一 一 一 一 一 一 一 一 一   ●   ●   ●   ●   ●   ●   ●   ●   ●   ●   ●   ●   ●ｅ ∼ ド ド ド l ｀ ∼ t r ― c -ド ド ｌ ヽ に ｀ ヽ C ｀ ヽ ド L O   U り   ●     ●々   々 ･ つ ｎ ｎ ヽ ０ ヽ ｏ ヽ Ｃ ヽ ４ = ･ ヽ Ｏ   ●   ●   ●   ●   ●   ●   ●   ●O O O O O O C O に Ｓ に X ）

JE蒜

c i 3 c r > c ; ) < : : 5 c r > c : 3 c : > c 3 c z ) c z 3 < z > C 3 C 3 α ） N L O O O C O ∽ o o - ― < c ね C D O O L O C 3 一 一 一 一 一 一 一 e ヽ Q 一 n 一 一 ヽ C ） ｏ Ｏ ∽   Ｏ 一   C り < z > < z > c : 5 C D C 3 < : : > < 3 > C 3 C ･ ） 一 一 a ⊃ o （ ヽ Q α ⊃ ( Ｚ ) ・ y − 4 ぐ ゛ つ く ｀ Q y − i m 7 一 一 q 々 一 一 i ● 一 一 4

Ｅ

戸

Ｃ ） り L O ' ≪ : rL O " < * < C - ヽ ぐ つ L / ･ H O り N 7 一 一 - i - ― i ･ ･ ― I U O C S J C O り L O O 州 N N り ・ □ ･ o r o r o - * j ' ' ^ - ^ - ^ L r 5 u - > L O の u - > 一 一 一 一 一 一 一 一 一 一 一 一 一 こぬ ヽＳ Ｏ Ｏ −ｒ ヽＳ 一 一 o 一 々 o r ヽ 一 n o o a r り 哨 ○ 州 ぐ つ マ L Q <> a c i i r ^ n c * - i c ^ m - c ± < 一 一 一 一 一 一 一 一

IM

Q

   苫● ツ で ・ Ｑ 口   ６Ｎ    ｒむＱ    (｀Ｑ    こ   七．    こ     ｜   C   ra ヽ･=･−･・ ゝ○ ㎝ ← 1･  召 ｉ  ヤ e .ﾐ  EヽヽH_N!    Q吻 57

58 高知大学学術研究報告 第16巻  自然科学 Ｉ 第５号

Tahle _{4. (b) Values estimated by photometer (Inoue's method).}

Date

Time

 馬，

(deg)

_(ｍ)

刄

 ｒ抑 (sec)

 y*

(m/s)

  .e (c ｢/s3)  Ｚａ (ｍ) α  瓦JI (C ｢/S) μ> C/っ μ> 内 ⊂; −  1966 Jan. 17  h m_{14 30} 15 16  25 58 44 48 51.6 IS.0 53.7 34.4 50.0 35.8 0.5､8 0.40 0.56 98 32 87 17.8 U.1 17.0 ■ 0.70   0.69   0.84 5.80×104 4.00 5.59 Jan. 20 14 02 54 72.9 22.8 0.88 338 11.6 0.54 8.77 Oct. 19 10 58 13 25  27  30  32 46 54 50 56 42 104.4  95.4  90.6 104.7  82.2 33.7 30.8 29,2 33.8 26.5 0.59 0.65 0.68 0.59 0.'75 105 137 160 104 215 6.2 7.4 8.2 6.2 9.7 0.45 0.41 0.47 0.36 0.64 5.93 6.49 6.84 5.92 7.54 Nov. 17 15 11  31 35 39 119.4  36.0 23.8 19.2 0.84 1.04 294 565 4.6 7.3 0.53 0.59 8.37 10.40 A Ｓ Ａ Ｋ Ｕ Ｒ Ａ ︷︸︵○︵いヨ︶ SＡＮＢＡＳＨＩ   ︵ＫＯ︵いヨ︶ ？︷︷ＮＣ帥︸︷︸ぶμ Nov. 21 Nov. 30 Dec. ７ Oct. 5 Oct. ３ Sec. ５ 14 13 14 25 32 35 45 − 35 00 059000 31 14 12 13 14 15 15 16 18 − 35 40 41 ３ ９ ５ ･ r ｒ ^ ^ ｕ ＾ 3 5 0 2 4 2 0 3 0 4 − 0 2 ７ L O Ｃ ３ Ｏ Ｏ O n O J ｒ ｏ L o ｃ ＾ r o               ６               １ 46 42 41 36 − 64 57 − 36 37 45 37 30 46 − 42 48 41 60 42 41 − 49 43 44 40 50 − 43 46 45 48 42 44  93.3  87.0  99.9 111.9  52.5 -60.0 - 94.2 127.5 81.6 135.0 99.3 115.8 -54.0 72.0 62.1 69.6 45.9 70.2 37.8 48.6 54.0 36.6 42.0 105.0 116.1 127.5 101.1 93.6 93.6 12.4 11.6 13.3 14.9 -15.0 19.5 -57.1 77. 3 49.4 81.8 60.2 70.2 -12.6 16.7 14.4 16. 2 10.6 16. 3 -13.9 17.9 19.0 12.8 14.7 -21.8 24.2 26.5 21.0 19.5 19.5 1.60 1.72 1.50 1.34 -1.33 1.02 -0.35 0.26 0.40 0.24 0.33 0.28 -0.96 0.72 0.83 0.74 1.13 0.74 -0.86 0.67 0.63 0.94 0.82 -1.19 1.07 0.97 1. 23 1.33 1.33 2075 2562 1691 1203 1184 539 - 21  9  33  7 183  11 8 8 1 8 8 < ＞ 5 c s ｏ ｏ ｒ ｏ O 7 r o ■ ≪ ≫ ･ Ｃ Ｏ c ノ ″                 １ 331 -536 250 209 686 453 -646 471 353 717 902 902  6.2  8.8  6.8  5.3 -17.4 14.7 - 7.6  3.9  9.9  3.4  7.0  5.0 - 5.0  2.9  3.8  2.5  6.5  2.9 - 8.5  6.0  5.0  8.9  7.4 -13.0 10.9  911 13.8 15.4 15.4 0.51 0.60 0.54 0.55 -0.61 0.61 0.66 0.47 0.59 0.44 0.75 0.41 -0.58 0.37 0.52 0.30 0.68 0.47 0.70 0.63 0.55 0.90 0.61 0.65 0.53 0.50 0.58 0.72 0.69 16.06 17.24 15.00 13.40 -13.30 10.20 - 3.72  2.56  4.03  2.43  3.31  2.82 - 5.74  4.30  5.00  4.43  6.78  4.41 - 5.17  4.01  3.78  5.62  4.89 -15.36 13.78 12.48 15.88 17. 16 17.16

of Smoke Plumes （Ｈ.ＵＥＴＡ） 59

Teble 5. Values estimated by Roberts' and Gifford's methods.

Date

Time  h m Eχp time (se､c) Wind  vel (m/s)  jと1 （m）  応2 (m)  Zl (ｍ)  瓦zy (e ｢/s) jZ｀ｸﾌi （m） ろ71 (m)  Krp (c ｢/s) "o  C.2 (♂) -Ｕﾉ2 (m/s)2 ?1９ ｙ ( ﾉ っ μ ﾝ 内 C ] Z 5 y / " ^ 内 ○ ○ μ ; ご 1966 Jan. 17 14 30 15 16 15 25 34 270 360 1.5 1.5 1.5 54.0 81.0 67.5 24.3 27.7 18.9  8.1 15.2  6.8 5.25×104 3.57 3.11 54.0 81.0 67.5 14.2 15.2 12.2 2.80ב104 2. 14 1.65 0.22 0.35 0.30 0.33 0.33 0.･23 0. 16 0.08 0.07 0.29 0.24 0.17 Jan. 20 14 02 55 3.2 94.5 13.5 4.2 3.50 54.0 10.1 3.02 0.22 0.16 0.35 0.12 Oct. 19 10 58 13 25 13 27 13 30 13 32 60 180 60 90 180 3.1 3.1 3.1 3.1 3.1 49.7 56.8 71.0 78. 1 56.8 17.8 14.2 14.9 18.5 10.7 10.7  8.5 10.7 14.2  7.1 1.45 3.38 1.58 1.98 1.42 49.7 56.8 71.0 78. 1 56.8 11.4 12.6 10.3 12.8 11.4 4.05 4.33 2.31 3.25 3.54 0.44 0.28 0.46 0.33 0.56 0:58 0.31 0. 77 0.22 0.76 0.50 0.47 0.20 0.26 0.38 0.24 0.44 0.25 0.35 0.39 Nov. 30 13 35 14 00 120 240 3.5 3.1 49.7 42.4 15.4 12.3 8.1 7.0 3.39 1.76 51.5 42.4 10.6 42.4 3.84 2.81 0.54 0.77 0.71 1.53 0.52 0.53 一 一 Dec. 7 13 00 13 05 13 09 13 15 13 16 13 18 300 180 150  60  60 120 1.65 1.65 1.65 1.65 1.65 1.65 59.5 51.0 51.0 59.5 42.5 59.5 24.6 17.9 20.0 16.2 21.3 14.9 12.7 11.9 12.8  9.4  8.5  5.5 3.11 1.23 2.75 2.01 3.73 2.22 76.5 68.0 59.5 59:5 68.0 42.5 13.6 10.0 13.1 12.3 11.9 11.0 1.99 1.21 2.41 2.38 1.72 2.37 0.26 0.41 0.38 0.38 0.22 0.30 0.19 0.24 0.47 0.40 0.16 0.42 0.09 0.06 0.13 0.12 0.08 0.18 0.2（ 0.H 0.32 0.3 0.5 0.1 ͡ χ 穴 D 7 ） 工 ; ご Nov. 30 13 35 14 00 120 240 3.5 3.1 49.7 42.4 15.4 12.3 8.1 7.0 3.39 1.76 51.5 42.4 10.6 42.4 3.84 2.81 0.54 0.77 0.71 1.53 0.52 0.53 一 一 Dec. 7 13 00 13 05 13 09 13 15 13 16 13 18 300 180 150  60  60 120 1.65 1.65 1.65 1.65 1.65 1.65 59.5 51.0 51.0 59.5 42.5 59.5 24.6 17.9 20.0 16.2 21.3 14.9 12.7 11.9 12.8  9.4  8.5  5.5 3.11 1.23 2.75 2.01 3.73 2.22 76.5 68.0 59.5 59:5 68.0 42.5 13.6 10.0 13.1 12.3 11.9 11.0 1.99 1.21 2.41 2.38 1.72 2.37 0.26 0.41 0.38 0.38 0.22 0.30 0.19 0.24 0.47 0.40 0.16 0.42 0.09 0.06 0.13 0.12 0.08 0.18 0.29 0.15 0.32 0.33 0.52 0.15 C / ） S 回 回 / へ 否 ○ 舌 Oct. 5 14 35 14 49 14 55 75 180 300 4.3 4.3 4.3 108 108 90 27.0 28.8 36.0 12.6  9.0  9.0  8.17 16.09 20.89 54.0 90.0 90.0 13.5 18.0 16.2 7.25 7.74 5.27 0.82 0.30 0.30 3.29 0.31 0.25 1.16 0.74 0.60 一 一 -Oct. 31 12 53 13 02 13 42 14 03 14 04 240 190  60  60 120 2.7 2.7 2.8 2.8 2.8  90 108 90 90 72 30.6 19.8 18.0 23.4 22.5 8.1 9.0 6.3 10.8  7.2 9.40 4.20 3.96 6.03 12.72 108.0  72.0  90.0  72.0  54.0 20.3 18.9 18.9 19.8 13.5 5.15 6.67 5.55 7.62 4.73 0.35 0.76 0.86 0.56 0.82 0.36 3.54 4.19 1.66 3.29 0.26 0.49 0.35 0.62 0.49 -一 一 一 一 召 Ｎ Ｓ ; 工 ; 回 μ ﾝ Sep. 5 15 02 15 27 15 35 16 39 240  40 225 180 4.8 4.8 4.8 4.8 113  75  88  88 58.7 50.0 37.5 40.0 18.7 20.0 18.8 15.0 47.61 41.47 20.82 27.15 75.0 75.0 75.0 62.5 20.6 23.7 21.2 15.6 13.58 17.97 14.38  9.35 0.56 0.35 0.35 6.30 1.68 0.90 0.72 0.45 1.68 2.36 1.80 3.32 一 一 一 一

60      高知大学学術研究報告 第16巻  自然科学 Ｉ 第５号

 Table 6. (a) Comparison of values of eddy diffusivity（尺) and of dispersion coefficient（Ｃ）         estimated by various methods.

Date

-Time

h m

牝‰ (sec) M  vel (m/s)

INOUE ROBERTS GIFFORD

Photo

Meter Projector

Photo Meter

Projector PhotoMeter Proj.

こぬ）

K。H 瓦ｙ

Krp

瓦刄ぷ C｡2（m"） C21 1966  Jan. 17 亘乙＝∠0.007  ∂Z（゜c/m）    ① 14 30 15 16  25  34 270 360 1.5 1.5 1.5 5.80×104 4.00 5.59 3.82×104 4.40 4.00 5.25×104 ､3.57 3.11 2.80〉く104 2.14 1.65 2.89〉く104 2.30 1.78 0.33 0.33 0.23 0.31 0.40 0.47  -0. 13 Jan. 20 14 02 55 3.2 8.77 7.34 3.50 3.02 4.23

0.16

0.36 Oct. 19 浴−0.027   ① 10 58 13 25  27  30  32 60 180  60  90 180 3.1 3.1 3.1 3.1 3.1 5.93 6.49 6.84 5.92 7.54  7.21  8.43  7.04 10.30  − 1.45 3.38 1.58 1.98 1.42 4.05 4.33 2.31 3.25 3.54 1.81 3.43 1.55 3.59 2.70 0.58 0.31 0. 77 0. 22 0.76 0.19 0.49 0.11 0. 74  −  Nov. 17 登。-0.02 15 11  31 180 300 5.0 5.0 8.37 10.40 一 一 0.97 1.04 3.10 7.23‘ 1.05 1.40 0.49 0.25 一 一 Nov. 21 §万一 0.013 14 25  32  35  45 180 180 130 180 7.5 7.5 7.5 7.5 16.06 17.24 15.00 13.40 一 一 一 一 0.20 0.24 3.58 5.05 3.71 3.65 3.62 4.65 3.08 1.75 4.20 1.55 0.10 0.10 0.18 0.48 一 一 一 一

 Nov. 30

{ﾄo。

13 35 14 00 120 240 3.5 3.1 13.30 10.20 一 一 3.39 1.76 3.82 2.81 4.00 2.33 0.71 1.53 一 一  Ｄec. 1 葺。-0.013 13 00  05  09  15  16  18 300 180 150  60  60 120 1.7 1.7 1.7 1.7 1.7 1.7 3.72 2.56 4. 03 2.43 3.31 2.82 4.47 4.28 4.69 4.61 3.54 4.54 3.11 1.23 2.75 2.01 3.73 2.22 1.99 1.21 2.41 2.38 1.72 2.37 1.21 2.41 2.84 1. 19 1.22 0.72 0.19 0.24 0.47 0.41 0.16 0.42 0.41 0.69 0.59 0.19 0.27 0.17

of Smoke Plumes （Ｈ.ＵＥＴＡ） 61 Table 6.(b)

Date

Time  h m 臨。 (sec) Wind  vel (m/s)

INOUE ROBERTS GIFFORD

Photo

Meter Projector

Photo Meter

Projector Photo  Meter Proi.

だ仏）

瓦Jr

瓦zv

瓦。？ _瓦刄ぶ C2s( ｢゛)

C≒

1966  Oct. 5 亘ﾆこ＝−0.020  ∂Z （゜c/m）    ①    C/）    y    Z    改j    y    （/っ    μ; 14 35  40  41  43  49  、55 75 60 90 90 180 300 4.3 4.3 4.3 4.3 4.3 4.3 5.74×104 4.30 5.00 4.43 6.78 4.41 5.16×104 4.81 4.30 4.96 5.57 5. 21 8.17×104 8.02 3.04 6.49 16.09 20.89  7. 25×104   − 13.95 15L 66  1.14  6.27 7.46×104 5.45 5.84 5.50 4.44 4.26 3.29  − 1.91 1.95 0.31 0.25 2.79 0.97 0.64 2.98 1.42 1.39  Oct. 31 葺石0.017    C/)    y    Z    りづ    μｯ    C/つ    ]] 12 53 13 02 13 42 14 03 14 04 240 190  60  60 120 2.7 2.7 2.8 2.8 2.8 5.17 4.01 3.78 5.62 4.89 3.49 4.90 3,20 3.21 3.77 9.40 4.20 3.96 6.03 ， 12.72 5.15 6.67 5.55 7.62 4.73 4.00 4.76 4.37 6.72 5.16   0.36   3.54   4.20   1.66 ニ 3.29 0.77 1.36 2.90 0.73 1.53 Sep. 5 Sタ -0.014    0    ぶ    応   べ二;    C/）    ｺ;    Ｋ    μ> 15 02  27  35  39  50 16 28  39 240  40 225 300  92 300 180 4.8 4.8 4.8 4.8 4.8 4.8 4.8 15.36 13.78 12.48 16.98 15.88 17. 16 17. 16 14.75 15.48 15.18 15.95 17.50 13.61 16.54 47.61 41.47 20.82 15.12 31.29 20.42 27.15 13.58 17.97 14.38 8.5  −  − 9.35 4.50 6.00 3.30 4.20 3.50 3.51 1.88 1.68 0.90 0.72 0.22  −  − 0.45 0.10 0.13 0.39 0.78 0.36 0.15 0.08

 (i) In ｃａ】culationof eddy diffusivity尺by eq. 圃after reading of ｚｓ and ら。尺,l。 by microphtometer shows considerably good agreement with尺ns by eye-measurement. Uncertainty sometimes appears to determine ^m in this method. -Km,! and the other turbulent parameters by Inoue's method. are almost controlled by χｌひand some uncertainty remains in decision of χla .In this methodi the values gained by mi crophotometer were close to those by eye-measurement ’ｏｆimage with ａ projector. Among eddy diffusivities gained by the above mentioned three ｍｅthodS，尺2ｖ by eq. （5〉is thought to be the most reliable in the point of possibility of precise reading got from ａ record of ａ microphtometer. The order of the values was almost 104 cm2 sec"^ The values of 尺ａt Mizushima are large and it may be owing to the highest stack among the above three sites and to strong wind･ It is also seen that the value of eddy di斤usivity is tend to increase with wind velocity

62  高知大学学術研究報告 第16巻  自然科学

．Ｉ 第５号

- (ii) The rate of dissipation of turbulent energy Ｅ increases with wind velocity.

 (iii) Sutton's stability parameter 7z was estimated by the above mentioned two ways. The values n. ｅｖａ】t!ated by Gifford's method scattered little and many reasonable values close to 0, 25 were gained) and nc by Culkowski's equation scattered and had often larger values. The reason why is thought to be that the values of jz],71and 苓 have uncertainty and logarithm of 亀/ヱ771much affects･71 in eq. ㈲. Though ng is more reliable than 馬，it is deduced        lafter all that 7z is the best which is calculated by Sutton's

equation of wind profile ic = uJ貢)焉

 (iv) Inoue had assumed that square of friction velocity       -Ｖ＊2 is equal to intensity of turbulence zv- 姐 adiabatic condition. In this study, many were near to adiabatic condition and the values of ｙ。２ calculated by Inoue's equation ｙ＊＝feH/Ｔ＾  ｓhows very good agreement with thosｅｏｆ石2＝が(ｚ。/ヱ。)2 by Gifford's equation) in spite of their quite different methods. (Table i, 5, 7,)  VI. Conclusion

 Many

observed data of long

time exposed

photographs

are anaylsed in this paper, and the chief points of

contri-bution are as fo1!ows :

Table. 7

1966

Time   h m y＊2 -tむ2 Jan. 17 14 30 15 16 15 25 0.34 0.16 0.31 0.16 0.08 0.07 Jan. 20 14 02 0.77 0.35 Oct. 19 10 58 13 25 13 27 13 30 13 32 0.35 0.42 0.46 0.35 0.56 0.50 0.47 0.20 0.26 0.38 Nov. 30 13 35 14 00 1.77 1.04 0.52 0.53 ＤｔＣ、 1 Oct. ５ Oct. 31 Sep. 5 059568 000111 333333111111 14 14 14 35 49 55 nｃ＾ m -1^ uｎ０００ ｎ／″344 1111 27590233 55561111 9 6 3 2 8 ︷ 6 0 0 1 1 0 1   I 一 一 Ｉ 一 一 0 0 0 0 0 0   幽 1 1 0 1 0 0000 1101 y o -^ < = : > １ ７ ６   1 1 1 1 0 0 x O Ｃ y ^ Ｃ ＾ O n 2 4 6 4 0 0 0 0 8602 ＼o n ｏｏ CO 1213

 ( i ) Polarizing filter is indispensable in addition to neutral density filters in taking photograph of long time一exposure.

 (ii) It is possible to measure precise concentration of photographic smoke by micro-photometer.

 (iii) In Inoue's method, eddy diffusivity K and the other diffusion parameter are controlled by ｡λふ> into which personal error is apt to enter. In calculation of 尺。by modified Roberts' equation adapting the data gained by ａ microphtometer･personal error is nearly impossib】ｅ to enter･and the resu］ts are reliable･

 Sutton's stability parameter 7z much affects the calculation of dispersion parameter Ｃ。 by Gifford's method and uncertainty remains in 7z.

 Defletion of peak concentration ざｓ of ａ center 】ine of a plume and distance X from ａ point source, considerably satisfy the relation ｌｏ尽ぶ。＝ど十干log jz］for white smoke; beyond some distance from ａ stack. From this point of view, it is deduced that Inoue's and Roberts' equations are correct.

       Acknowledgments

 The author wishes to express his hearty thanks to Dr. K. Takasu and Dr. T. Seo, the Ohara Institute for Agricultural Biology, Okayama University, who gave him ａ chance

-6ろ

of observation at Mizushima,

and to the Director-General,

Shikoku

Branch

of Government

Forest Experiment

Station at Ｋｏｃｈｉ･

for allowing him

to use the facilitiesof the station

for observation. Thanks

are due to Mr.

N.

Yamaguchi,

Lecturer of Kochi University, for

reading the manuscript

and offering many

valuable suggestions･ and to Miss Ｍ. Tokuhiro･

N.

Tamai,

T. Kawakami

and Ｕ. Kato.

the students of Kochi University. for their kind

co-operations in the observations and calculation.

       References

Gifford, F., 1959 : Smoke plumes as quantitative air pollution indices, Int. J. Air PoU., 2, 42. Inoue, E., 1960 : Form of smoke from ａ stack, Meteorological Note of Japan, Vol. 11, No. 5.

Saissac, J. , 1957 : Sur la diffusion turbulente des particules, 75 th Anniv. Vol., Japan Met. Soc. Culkowski, M. Time exposure photography of smoke plumes.

Roberts, O. F. T., 1923 : The theoretical scattering of smoke in ａ turbulent atmosphere, Proc. Roy｡  Soc, A, 104, 640.

Sutton, O. G., 1953 : Micrometeorology, McGraw-Hill, New York.