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,**/  .  ++  ,**/  +*  +3 !"The Kinematic Features of Volcanic Clouds: A Series of Small Eruptions
from +/ to +2, September ,**., at Asama Volcano, Japan
Akihiko TERADAῌ, Yoshiaki IDAῌῌ, Sei IIJIMAῌῌῌ, Mitsuhiro YOSHIMOTOῌῌῌῌand Taketo SHIMANOῌῌῌῌῌ
Some fundamental features of ascending volcanic clouds have been revealed using images of the clouds thatwere automatically recorded by video cameras for some eruptions at Asama volcano on +/ to +2 September, ,**..
According to the analysis of +1 volcanic clouds that are nearly isolated and of a symmetrical shape, the radius ofa cloud increases linearly with increasing height, meeting self-similarity of ascending motion nearly up to its
maximum height. If the height is measured from a suitable virtual origin, the ratio of the radius to the height canbe a constant that is identiﬁed with the entrainment constant. The entrainment constants determined in this way
have a mean value of about *.,. in good agreement with those obtained from previous laboratory experiments,
even if the values are greater than *.,/ or less than *.,* for -/ῌ of the analyzed volcanic clouds. During theascent of a cloud the height squared is nearly proportional to the time and the product of the radius and the ascentvelocity is almost constant. These empirical relations are consistent with well-known characters of a thermal thatmoves in incompressible uniform surroundings. Coupling these kinematic features of the volcanic clouds with the
Scorer’s relation and the equation of state, we evaluate the total buoyancy, the total mass, the density and the mean
temperature of the clouds that are regarded as thermals. The total buoyancy of most volcanic clouds did notchange signiﬁcantly during their ascent process. The cloud on +1 September has a relatively great density
contrast and small total buoyancy, probably reﬂecting hot ash particles in it supplied by a Strombolian eruption atthat time. The volcanic cloud discharged at ++ : /., September +/ contained ash of ,,/**῍-,1** tons or less withthe mean temperature of -+*῍-0* K or higher, and the volcanic cloud discharged at 2 : -2, September +2 contained
ash less than 2,-**῍3,+** tons with the mean temperature higher than -+* K or higher.
Key words : Asama volcano, thermal, volcanic cloud, buoyancy, entrainment#*0*῍*2+* $%&'()$*$ +* +, 2 -.
$%&/0/01!023456789:23;<=>?@
Institute of Seismology and Volcanology, Graduate
School of Science, Hokkaido University, North +*West 2, Kita-ku, Sapporo *0*῍*2+*, Japan.
#01+῍,,*+ ABCDE)FG ,+01
ABCH/0/01IJ!0234
Graduate School of Life and Science, University of
Hyogo, ,+01 Syosya, Himeji 01+῍,,*+, Japan.
#-23῍*++/ KC$LMNO PQRS ++/+῍,
TUVO P<WX
Karuizawa Weather Station, Japan Meteorological
Agency, ++/+῍, Oiwake, Karuizawa, Kitasaku, Nagano-23῍*++/, Japan.
#++-῍**-, YZ[\Z*]I +῍+῍+
YZ/07823X
Earthquake Research Institute, University of Tokyo,+῍+῍+ Yayoi, Bunkyo-ku, Tokyo ++-῍**-,, Japan.
#32*῍2/10 ^_C`a)bc*de .+Y$/0Y$fgf23=>?@
The Center of Northeast Asian Studies, Tohoku
University, .+ Kawauchi, Aoba-ku, Sendai 32*῍2/01,
Japan.
Corresponding author : Akihiko Terada
e-mail : terada@eos.hokudai.ac.jp

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Fig. /e i5 j¥ 0 XY-G C¦Z§V ,**/D
SN o62  ?@A *   5'I
q KB[tEFF

 Thermal -  \$tk/[*;<!'l4mn5 02 o6 +1 p "2  ?@A.< ¨©

* 

89bª«(¬¤k

Turner, +30.bD vw: M Fig. /ῌ

Scorer[;

8rs2 97 *.,*ῌ*.,/ Ctu Scorer, +3/1 ; Woodward, +3/3 ;q7 kE7* *.,. 

0 

/

= "T; /[0 * a;<!xy<Kz z* (Scorer, +3/1)

E7*,,.** m  @B; ,,.** m vw:
Fig. /῎  +?!y<Kz z* 2,{

7\ Fig. /e ivj;< z

PQRk=4(+3/1) 0| Thermal 02& *  \./

@A­>®¯MW
0ῌ+ 
Thermalm©°`±

u / Wk *]¢²³´¢¢²1w: (Turner,

+30.

> 0c

  ?v NU/b) ]¢²³´¢¢²1 k * 5I ]Kµ (.a) |0}@ 0\~< ¶/|^·\ 1G (Morton<  (.b) |AW Fig. /῍ Y/+?;<zACtt*Dn

S=

1
(/)

et al., +3/0 ; Woods, +322)  w  k7¸W_`a¹0He'2 YºThermal /G9»7a 0

8rs2 :b< Ctu Scorer, +3/1 ; Woodward, +3/3 ; Turner,

562



Fig. /. Details of ascent process of volcanic clouds shown in Fig.-. (a) ++ : /., September +/. (b) +2 : ,*,September +0. (c) +3 : +-, September +0. (d) / : ++, September +1. (e) 2 : -2, September +2. ῌ Correlation
between top heights and radii. ῍ Heights plotted versus time. Fitted curves for various “n” in the equation(/) are also indicated. Variances are shown for each ﬁtted curves. See chapter / for detail. ῎ Squaredheights from the virtual origin plotted versus time. ῏ Time-series of variation of rw, which are proportional
to the total buoyancy based on the equation (1).

0AR R.»» ,**. Q 3 ¼ +/ΐ+2  »»563

^7 Redoubt A +33* QRS

+30.b
+/ΐ+2     

ST UVn +,*** m

>

W co- k      +1

ignimbrite ash cloud  01 !V CR.

  k  / (Woods and Kienle, +33.) 7o ! (Fig. 0a)"#$%$& '  () k *+,- Fig. 0a & k./ 

0 &1 23&45/ `aXxy+ Y[UZL?
01

U   K g   Y    /  c Y j

Woods, +33-

678 6 k  *.,*

2 ?81 77 R.Ft&

9: -/& *.-* 9; +1 <=01 [O  7g *.,*ΐ*.,/2 - 7(<k >? !

 \7 k=Nx@&"-) 4+A # Morton et al.,L&]^8

(+3/0) B Woods and Kienle (+33.)

CL_(/ 7(<C"DEFGDH

DE$% k &/IJK'&(L & M)

R.$E a wA -,*** m b cc 0** m b$%*+, NO-0ῌ, U oU & `

W9b NxLd A}Eeu(vAf:/  8=

PQ -R.& (.) S (3T<7A}LBXxyL01  7/01&23U/7!V3& R.$E g()?:hU (Scorer, +3/1) 6 z WX+ 4YZ

O/-<

5[\ z* ]6 & ^7 89"_$`a

0ῌ- 

/

0ῌ-ῌ+ 

7(< "_$:O 01 8)B3! 77& /01 F+/  +2  
O6.i +0ΐ+1  &jLkl¡U ED

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a1 Bn r BCA w   CABBn&gh i j .pῌ- - k=>?@A6

-?   q6wAe§7 F &23U7/ cYjra/  ¨^W7a wUFt

Morton et al., +3/0 (0) S (-) S&l(< ;&{©  27 (,) SB (.b) S&/

OeY :ªwA -,*** m st ªwA -,*** m& { ./R.W7a '?f/wA

+
-

ῌC,F῏
rwm῍
ῐ
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(1)

u«-  +/  +1  +1 v& w
A -,*** m w¬ u/xyL 7wU(

Fig. /ῌ  ^7UBnCAD rw 0 #):h uR.&­®z¤ /7¨)

 ! Fig. /e :O rw &op6$;- a +0  +3  +. v (Fig. -c, Fig. /c) 78 (1) Sq= r k B m & 2& (.) S¯°±²D³ ./"_$NO/sop6$;7^7!VU/

9 , & 77 #J /a ra  & R.$E  -,***ΐ.,*** m ªwAstBn rs -CA ws

Fig. 0b, c

FtG /ῒ HA- cTTN, WJM u(v HMT 0 ! {´? ED¢£Sm¤

wIxJ^7yz U +0ΐ+1   +ΐ, µHAf:¶·C & { Thermal./6$    ;  7       /  c Y j Scorer,+3/1  8= rw 6$;|4& /0

1 F &op23U/7!V/
6 /01 F &
Fig. 0d

 rs  ws  (-) S&/WX

@Ae! 77@Ae& Nx@A,

Kg 7

Nx@A¸

 (ra-r) ῌ ra - `|/ Yj A}~.L M

& @Ae _  ¶·&1 /0;)aNxOPU701

 *.*/ΐ*.+/ HAFt -78 6 +0ΐcYj Woods, +322 ; Woods and Bursik ; +33+ 4++1 &}/¹Dº~u) MA

RS²(T³S´)T*µ ¶T· ¸¹Tº%»¼

564



  
!"#$ %&'() *%+,-+. /0( +1 ++1* %+,-+.+"$ +67 +0ῌ+1&23415+ 89 41:" ;<3 
 &=>9 ?@A&

+BC5 DE4F

G H/3 &I9J "KLHMNO +/ P +2 +
.&Q3 RSTU (,**/) +&V0 *W .&H/XPY1*&Z
93["O \ O] +/  ++ ^ /.
+. (Fig. -a, Fig. /a) +  4* -,*** m &J
_.+D ,,/**ῌ-,1** ton `> Y1*
 -+*ῌ-0* K `abc +2  2 ^ -2 +. (Fig. -e, Fig. /e) D 2,-**ῌ3,+** ton`> .Y1* T  -+* K `abc0ῌ-ῌ, 
Fig. 0e & rs  ws +c rs ws + , d&Q3^ef"$ (rs ws),  (1) g 9 Vh&.+i $(j !&$ +0ῌ+1 + (rs ws), & %+,-+ke93 -ῌ.ῌ+ῌ. l*mnb .op&q$r
  r+KL."op<)stu=>$ vwxyz{g+|&I9} *p~"a$ Thermal +4* i F + +ῌ. d&9 (Morton et al., +3/0)
F  rw + , d&$ (1) g  %  Fig. 2f &(rsws)+ῌ, "  .44* 

Ty!  "  $
(rsws)+ῌ, +f ke"3Yn&Z93 , Fl*&/ !^k+.4*ke"3/0(
+Vh&

G4 +.Wa*"

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(j !#r&'¡$$ .
¢ £¤A+%¥r ¦GP a§+¨©
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1

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9

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Fig. 0. Time series of parameters associated withascent processes of the volcanic clouds. (a) Expansion ratio, k (radius/height). (b) Corrected
radius rs using the equation (,) at the standard
height of -,*** m a.s.l.. (c) Corrected ascentvelocity ws using the equation (.b) at thestandard height of -,*** m a.s.l.. (d) Density
ratio, (ra-r)/ra, obtained from rs and ws using
the equation (-). (e) (rsws), that are proportional to the total buoyancy. (f) (rsws)+/, thatare proportional to the maximum cloud height.
Triangles show the observed maximum heights
of volcanic clouds, measured from the ventbottom by Seismological and Volcanological
Department, Japan Meteorological Agency (pers.
comm.).

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Scorer  !"#$  

%   &# ' 
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/. %6789:& ;+/ $ ++ ,,/**ῌ-,1** ton, '<= ;( -+*ῌ-0* K )>+*2,-**ῌ3,+** ton, 89:"&;+2 $ 2  -2 %67

 ;( -+* K )>?.1 ". '<=
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Fjkl-F mn'#op'ῌ ῑ ῐ ῍
Briggs, G. A. (+303) Plume Rise. Critical Review Series,
Rep. TID-,/*1/, At. Energy Comm. Washington, D. C.,2+ p.
Uiq[7 r[sx (+32-) 89t8u
5#v1w.l# nx oy
_`@zE ,0 B-+ 3ῌ,+.
Hill, M. J. M. (+23.) On a spherical vortex. Philos. Trans.
Roy. Soc. London., A+2/, ,+-ῌ,./.
9{ (+312) 89.SE6^
H, O v1&Plume Rise .| 89 ,+2-ῌ+31.

565

S<= (,**.) $F}89 AB[89E y~ '0 +0 z 3  ,-ῌ-+.
Morton, B. R., Taylor, G. and Turner, J. S. (+3/0) Turbulent gravitational convection from maintained and instantaneous source. Proc. Roy. Soc., Ser. a., ,-., +ῌ,-.
O+[ [ [C*7[i (,**/) R0 ^¡^ (SAR) P?
EV(89 ,**. z88A 
89 /* .*+ῌ.+*.
Saunders, P. M. (+30+) An observational study of cumulus.
J. Meteor., +2, ./+ῌ.01.
Scorer, R. S. (+3/1) Experiments of convection of isolatedmasses of buoyant ﬂuid. J. Fluid. Mech., ,, /2-ῌ/3..
Sparks, R. S. J., Moore, J. G. and Rice, C. J. (+320) The
initial giant umbrella cloud of the May +2th, +32*, explosive eruption of Mount. St. Helens. J. Volcanol. Geotherm. Res., ,2, ,/1ῌ,1..
¢[U£[  (,**-) Windows PC ¤¥¦J§¨E©89 P? 89 .2 ../ῌ./3.
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kT89:1&|V(89 ,**- z,  0 $8 5# 89 /* +2-ῌ+3..
Turner, J. S. (+30.a) The ﬂow into an expanding sphericalvortex. J. Fluid Mech., +2, +3/ῌ,*2.
Turner, J. S. (+30.b) The dynamics of spherical masses ofbuoyant ﬂuid. J. Fluid Mech., +3, .2+ῌ.3*.
Turner, J. S. (+313) Buoyancy e#ects in ﬂuids. Cambridge
University Press, pp-2..
Wilson. L., Sparks. R. S. J., Huang, T. C. and Watkins, N.
D. (+312) The control of volcanic column heights byeruption energetics and dynamics. J. Geophys. Res., 2-,+2,3ῌ+2-0.
Woods, A. W. (+322) The ﬂuid dynamics and thermodynamic of eruption columns. Bull. Volcanol. /*, +03ῌ+3-.
Woods, A. W. (+33-) Moist convection and the injection of
volcanic ash into the atmosphere. J. Geohys. Res., 32,+10,1ῌ+10-0.
Woods, A. W. and Bursik, M. I. (+33+) Particle fallout,
thermal disequilibrium and volcanic plumes. Bull.
Volcanol., /-, //3ῌ/1*.
Woods, A. W. and Kienle, J. (+33.) The dynamics andthermodynamics of volcanic clouds : theory and observation from the April +/ and April ,+ +33* eruptions ofRedoubt Volcano, Alaska. J. Volcano. Geotherm. Res.,0,, ,1-ῌ,33.
Woodward, B. (+3/3) The motion in and around isolated
thermals. Quart. J. Roy. Meteor. Soc., 2/, +..ῌ+/+.
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