$B@EE*0BDjEY$N7W;;(B

$B?y;39L0lO/(B($BKLBgM}!&COOG(B)

[email protected]

2005/08/21

$BL\

• 1 $B@EE*0BDjEY(B
  • 1.1 $B@EE*0BDjEY$NDj5A(B
  • 1.2 $BOG@1Bg5$$N@EE*0BDjEY$N7W;;(B
  
  
• 2 $BCGG.29EY8:N(!&@EE*0BDjEY$N6a;w7O(B
  • 2.1 $B7O$N@_Dj(B
  • 2.2 $BCGG.29EY8:N((B
  • 2.3 $B@EE*0BDjEY(B
  
  
• 3 $BLZ@1$N?e1@$rA[Dj$7$?7W;;Nc(B
  • 3.1 $BJ,;RNL$HHfG.(B
  • 3.2 $B4%AgCGG.29EY8:N((B
  • 3.3 $B<>=aCGG.29EY8:N((B
  • 3.4 $B@EE*0BDjEY(B
  • 3.5 mail protected],$r9MN8$7$?>l9g$NLZ@1Bg5$$N@EE*0BDjEY(B
  
  
• 4 $B=>Mh$NO@J8$H$NHf3S(B
  • 4.1 Achterberg and Ingersoll (1989)
  • 4.2 $BCfEg(B (1998)

1 $B@EE*0BDjEY(B

1.1 $B@EE*0BDjEY$NDj5A(B

$B5$2t$rCGG.E*$K>e>:$5$;$k2aDx$r9M$($k(B. $B5$2t$NL)EY$H<~0O$N6u5$$NL)EY:9(B $B$K$h$C$FIbNO$,@8$8(B, $B$=$NIbNO$rI|85NO$H$9$k?6F0$N?6F0?t$rIbNO?6F0?t(B $N$ $B$H8F$V(B. $BIbNO?6F0?t$N(B 2 $B>h$r@EE*0BDjEY(B $N^{2}$ $B$H8F$V(B.

$B5$2t$,>e>:$9$k$3$H$K$h$C$F(B, $BK\Mh$O5$2t$N<~0O$NBg5$$N05NO$HL)EY$b1F6A$r(B $B.$5$$$H$7$FL5;k$9$kJ}K!$r%Q!<%;%kK!$H(B $B$$$&(B. $BK\@a$G$O%Q!<%;%kK!$K$h$k@EE*0BDjEY$NDj<02=$r=R$Y$k(B.

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• $B5$2t$H<~0O$NBg5$$OM}A[5$BN$N>uBVJ}Dx<0$K=>$&(B.
• $B5$2t$rJQ0L$5$;$kA0$N9bEY(B $z = z_{0}$ $B$K$*$$$F(B, $B5$2t$H<~0O$NBg5$$NL)EY(B $\rho$ $B$OEy$7$$(B(Fig.1).
  

  $$\rho\vert _{z=z_{0}} = \rho^{*}\vert _{z=z_{0}}$$ (1)

  
  

• $B5$2t$NJ,;RNL$OJQ2=$7$J$$(B. $B$9$J$o$A(B, $B1+$H$7$F6E=LJ*$,5$2t$+$iJ,N%(B $B$9$k$3$H$O$J$$(B.
  

  $$\DD{M^{*}}{z} = 0$$ (2)

  
  
  $BC"$7(B $M^{*}$ $B$O<~0O$NBg5$$NJ,;RNL$G$"$k(B.

$B5$2t$H<~0O$NBg5$$NL)EY:9$O(B,

$$d \rho = \rho^{*} - \rho$$ (3)

$B$H=q$1$k$N$G(B, $B1?F0J}Dx<0$O(B,

$$\DD[2]{}{t} \delta z = \frac{\left(\rho - \rho^{*}\right) g}{\rho^{*}}$$ (4)

$B$H$J$k(B. $B$?$@$7(B $g$ $B$O=ENO2CB.EY$G$"$k(B. (4) $B<01&JU$N(B $\rho, \rho^{*}$ $B$r%F!<%i!e$NHy>.9`$rL5;k$9$k$H(B,

$$\frac{\left(\rho - \rho^{*}\right) g}{\rho^{*}} = \frac{g}{\rho^{*}} \left\{ \left( \rho\vert _{z=z_{0}} + \DD{\rho... ...- \left( \rho^{*}\vert _{z=z_{0}} + \DD{\rho^{*}}{z} \delta z \right) \right\},$$

$$= \frac{g}{\rho^{*}} \left( \DD{\rho}{z} \delta z - \DD{\rho^{*}}{z} \delta z \right)$$

$B$H$J$k(B. $B$?$@$7<0JQ7A$K$*$$$F(B (1) $B<0$N4X78$rMQ$$(B $B$?(B. $BM}A[5$BN$N>uBVJ}Dx<0$,@.N)$9$k$N$G(B, $B0J2<$N$h$&$KJQ7A$G$-$k(B.

$$\frac{g}{\rho^{*}} \left( \DD{\rho}{z} \delta z - \DD{\rho^{*}}{z} \delta z \right) = \frac{g T^{*}}{ M^{*} } \left\{ \DD{}{z} \left( \frac{M}{T} \right) - \DD{}{z} \left( \frac{M^{*}}{T^{*}} \right) \right\} \delta z ,$$

$$= \frac{g T^{*}}{ M^{*} } \left\{ M \DD{}{z} \left( \Dinv{T} \right... ...z} \left( \Dinv{T^{*}} \right) - \Dinv{T^{*}} \DD{M^{*}}{z} \right\} \delta z ,$$

$$= \frac{g T^{*}}{ M^{*} } \left\{ - \frac{M}{T^{2}} \DD{T}{z} + \frac{M^{*}}{{T^{*}}^{2}} \DD{T^{*}}{z} + \Dinv{T} \DD{M}{z} \right\} \delta z ,$$

$$= \left\{ \frac{g} {T } \left( - \DD{T}{z} + \frac{M}{M^{*}} \DD{T^{*}}{z} \right) + g \left( \Dinv{M} \DD{M}{z} \right) \right\} \delta z$$ (5)

$BC"$7(B $M$ $B$OBg5$$NJ,;RNL$G$"$k(B. $B$^$?<0JQ7A$K$*$$$F(B (2) $B<0$rMxMQ$7$?(B. (5) $B<0$r(B (4) $B<0$KBeF~$9$k(B $B$3$H$G(B,

$$\DD[2]{}{t} \delta z = \left\{ \frac{g} {T } \left( - \DD{T}{z} +... ...} \DD{T^{*}}{z} \right) + g \left( \Dinv{M} \DD{M}{z} \right) \right\} \delta z$$ (6)

$B$H$J$k(B. $B2r$H$7$F(B $\delta z = sin(Nt)$ $B$rMQ$$$k$3$H$G@EE*0BDjEY$O(B,

$$N^2 \equiv \frac{g}{T} \left( \DD{T}{z} - \frac{M}{M^{*}}\DD{T^{*}}{z} \right) - g \left( \Dinv{M} \DD{M}{z} \right)$$ (7)

$B$HDj5A$5$l$k(B.

$B?^(B 1: $B%Q!<%;%kK!$K$h$k@EE*0BDjEY$N8+@Q$b$j$N35MW(B. $B5$2t$N<~0O$NBg5$$N29EY(B $T$ $B$H(B $BJ,;RNL(B $M$, $B5$2t$N29EY(B $T^{*}$ $B$HJ,;RNL(B $M^{*}$ $B$H$9$k(B. $z = z_0$ $B$K$*$$$F5$2t$H<~0O$NBg5$$NL)EY$,Ey$7$/(B, $BM}A[5$BN$N>uBVJ}Dx<0(B $B$,@.N)$9$k$J$i$P(B, $M/T = M^{*}/T^{*}$ $B$H$J$k(B. $B$^$?5$2t$r>e>:!&2<9_$5$;$?:](B, $B5$2t$N29EY$OJQ2=$9$k$,(B $B5$2t$+$i6E=LJ*$,N%C&$7$J$$$H2>Dj$7$?$N$G(B, $z+dz$ $B$K$*$1$k5$2t$NJ,;RNL$O(B $M^{*}$ $B$N$^$^0];}$5$l$k(B.

1.2 $BOG@1Bg5$$N@EE*0BDjEY$N7W;;(B

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$$M = M^{*}$$ (8)

$B$,@.N)$9$k(B. $B$=$N;~(B, $B@EE*0BDjEY(B (7)$B$O(B,

$$N^2 \equiv \frac{g}{T} \left( \DD{T}{z} - \frac{M}{M^{*}}\DD{T^{*}}{z} \right) - g \left( \Dinv{M} \DD{M}{z} \right)$$ (9)

$B$HM?$($i$l$k(B.

2) $B$NBg5$$NJ?6QE*$J29EYJ,I[$O(B, $BBg5$$N<>=aCGG.29EY8:N($+$iM?$($k(B. Fig.2 $B$OCO5eBg5$$NJ?6QE*$J29EY9=B$$N7h$^$jJ}$N(B $BLO<0?^$G$"$k$,(B, $BCO5e$N$h$&$K3hH/$JBPN.$r@8$8$kBg5$$G$N29EY9=B$$O(B $B<>=aCGG.E*$J9=B$$H$J$C$F$$$k(B. $BB>$NOG@1Bg5$$K$*$$$F$b(B, $B3hH/$JBPN.3hF0$,(B $BB8:_$9$l$P(B, $B29EY9=B$$O<>=aCGG.E*$J9=B$$K$J$C$F$$$k2DG=@-$,$"$k(B.

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4) $B$N5$2t$N29EYJQ2=$OCGG.29EY8:N($K$h$C$FM?$($k(B. $B5$2tFb$G6E=L$,@8$8$k$+H]$+$G(B, $B<>=aCGG.29EY8:N($^$?$O4%AgCGG.8:N($,A*$P$l$k(B.

mail protected],$NB8:_$9$k7O$K$*$$$F(B,$BBg5$$NJ?6QE*$J29EYJ,I[$HJ,;RNLJ,I[$N(B $B6qBNE*$JDj<02=$rM?$($k$N$O:$Fq$G$"$k(B. $B$=$3$GK\@a$G$O(B 3) $B$N(B $B5$2t$N29EYJQ2=(B $\DD{T^{*}}{z}$ $B$N6qBNE*$J7A<0$rM?$($k$K$H$I$a$k(B. mail protected],$H4%[email protected],$N(B 2 mail protected],$+$i@.$kBg5$$NBg5$$NJ?6QE*$J29EYJ,I[$HJ,;RNL(B $BJ,I[$O4JC1$KM?$($k$3$H$,$G$-$k$,(B, $B$=$NDj<02=$OO$G9T$&$3$H$H$9$k(B.

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1.2.1 $B5$2tFb$G6E=L$,@8$8$J$$>l9g(B

$B5$2tFb$G6E=L$,@8$8$J$$>l9g(B, $B5$2t$N29EYJQ2=(B $dT^{*}/dz$ $B$O0J2<$N$h$&$KI=$9$3$H$,$G$-$k(B.

$$\DD{T^{*}}{z} = - \frac{M g}{c_{p}}.$$

$B>e<0$r(B (9) $B$KBeF~$9$k$3$H$G(B, $B@EE*0BDjEY$O0J2<$N$h$&$KI=8=$5$l$k(B.

$$N^{2} = \frac{g}{T} \left( \DD{T}{z} + \frac{M g}{c_{p}} \right) - g \left( \frac{1}{M} \DD{M}{z} \right) .$$ (10)

$B5$2t$OK0OB$7$F$$$k$N$G(B, $B>e>:$5$;$k$HI,$:6E=L$,@8$8$k$O$:$G$"$k(B. (10) $B$G8+@Q$b$i$l$k@EE*0BDjEY$O(B, $BK0OB$7$?5$2t$r6E=L$,@8$8$J$$$h$&2<8~$-$KJQ0L$5$;$?;~$NCM$H(B $B$_$J$9$3$H$,$G$-$k(B.

1.2.2 $B5$2tFb$G6E=L$,@8$8$k>l9g(B

$B5$2tFb$G6E=L$,@8$8$k>l9g$K$O(B, $B5$2t$NCGG.29EY8:N($O<>=aCGG.29EY8:N($KEy$7$/$J$k(B.

$$\DD{T^{*}}{z} = \DD{T}{z}$$

$B>e<0$r(B (9) $B$KBeF~$9$k$3$H$G(B, $B@EE*0BDjEY$O0J2<$N$h$&$KI=8=$5$l$k(B.

$$N^{2} = - \frac{ g}{M} \DD{M}{z}$$ (11)

$B$9$J$o$A@EE*0BDjEY$OJ,;RNL8z2L$K$h$C$F7h$^$k(B.

1.2.3 $B5$2t$NJ,;RNL$,JQ2=$7$J$$>l9g(B

$B=>Mh$N8&5f$G$O(B, mail protected],$O==J,$K>/$J$$$H2>Dj$7(B, $BBg5$$NJ?6QJ,;RNL$HJ?6QHfG.$O4%[email protected],$N$=$l$KEy$7$$$H8+$J$9(B $B$3$H$,$^$^$"$k(B. $B$=$3$G$=$N$h$&$J>l9g$K$D$$$F$b<0$r5a$a$F$*$/(B. $B$3$N>l9g(B, (9) $B<0$N(B $B1&JUBh(B 2 $B9`$NJ,;RNL8z2L$,L5;k$G$-$k$N$G(B,

$$N^{2} = \frac{g}{T} \left( \DD{T}{z} + \frac{M_{d} g}{{c_{p}}_{d}} \right)$$ (12)

$B$H=q$1$k(B. $BC"[email protected],$,==J,$K>/$J$$$N$G(B, $B5$2tFb$G6E=L$O@8$8$:(B, $B5$2t$NJ,;RNL$HHfG.$O4%[email protected],$NCM$K6a;w$7$?(B. $B$9$J$o$A@EE*0BDjEY$O<>=aCGG.8:N($H4%AgCGG.8:N($H$N:9$+$i8+@Q$b(B $B$k$3$H$,$G$-$k(B.

2 $BCGG.29EY8:N(!&@EE*0BDjEY$N6a;w7O(B

$BK\@a$G$O(B, $B@EE*[email protected],5$BN$N%b%kHf$H$N4X78$rD4$Y$k$?$a$K(B, $B4JC1$J7O$r@_Dj$7(B, $B$=$N;~$NCGG.29EY8:N($H@EE*0BDjEY$r5DO@$9$k(B.

2.1 $B7O$N@_Dj(B

$B4JC1$N$?$a$K(B, $BBg5$$O4%[email protected],[email protected],$N(B 2 mail protected],$+$i@.$k$b$N$H$9$k(B. $B4%[email protected],[email protected],$NJ,;RNL$r$=$l$>$l(B $M_{d}$ $B$H(B $M_{v}$, $B4%[email protected],[email protected],$NHfG.$r$=$l$>$l(B ${c_{p}}_{d}$ $B$H(B ${c_{p}}_{v}$, mail protected],$N%b%kHf$r(B $X$ $B$H$9$k(B. $B$=$N;~(B, $B7OA4BN$NJ,;RNL$HHfG.$O0J2<$N$h$&(B $B$K=q$1$k(B.

$$M = M_{d} (1 - X) + M_{v} X$$ (13)

$$c_{p} = {c_{p}}_{d} (1 - X) + {c_{p}}_{v} X$$ (14)

2.2 $BCGG.29EY8:N((B

Weidenschilling and Lewis (1973), Atreya and Romani (1985) $B$K=>$C$F(B $B<>=aCGG.8:N($rDj<02=$9$k(B. $BG.NO3X$NBh(B 1 $BK!B'$O(B,

$$dU = \delta Q + \delta W + \delta Z ,$$ (15)

$B$G$"$k(B. $B$3$3$G(B $dU$ $B$OFbIt%(%M%k%.! $B$O7O$K2C$($i$l$kG.NL!$(B $\delta W$ $B$O7O$K2C$($k;E;v!$(B $\delta Z$ $B$O2=3X%(%M%k%.!<$G$"$k!%(B $B9M$($F$$$k7O$K$*$$$F5$BN$OM}A[5$BN$H$7$F15) $B<0$N3F9`$O0J2<$N$h$&$K=q$1$k!%(B

$$dU = c_{v} dT.$$ (16)

$$\delta Q = 0.$$ (17)

$$\delta W = - p dV,$$

$$= - d(pV) + V dp,$$

$$= - R dT + V dp,$$

$$=$$

$$= - R dT - M g dz .$$ (18)

$$\delta Z = - \lambda dX.$$ (19)

$B$3$3$G(B $c_{v}$ $B$OBg5$$NDj@Q%b%kHfG.$NJ?6QCM!$(B $T$ $B$O29EY(B, $p$ $B$O05NO(B, $V$ $B$O(B $B5$BNJ,;R$N(B 1 $B%b%kEv$?$j$NBN@Q!$(B $R$ $B$O5$BNDj?t(B, $M$ $B$OJ?6QJ,;RNL(B, $g$ $B$O=ENO2CB.EY(B, $\lambda$ mail protected],$N%b%kEv$?$j$N(B $B6E=L$N%(%s%?%k%T! mail protected],$N%b%kHf$NJQ2=$G$"$k(B. (15) $B<0$K(B (16) - (19) $B<0$rBeF~$9$k$3$H$G(B,

$$c_{v}dT + R dT + M g dz + \lambda dX = 0 ,$$

$$c_{p}dT + M g dz + \lambda dX = 0 ,$$ (20)

$B$H$J$k!%C"$7(B $c_{p}$ $B$OBg5$$NDj05%b%kHfG.$NJ?6QCM$G!$(B $BM}A[5$BN$N>l9g(B $c_{p} = c_{v} + R$ $B$G$"$k!%(B

2.2.1 $B4%AgCGG.29EY8:N((B

(20) $B<0$N@xG.$K$h$k9`$rL5;k$9$k$3$H$G4%AgCGG.29EY8:N($,(B $B5a$^$k!%(B

$$c_{p}dT + M g dz = 0,$$

$$\DD{T}{z} = - \frac{ M g }{c_{p}},$$ (21)

$BJ?6QJ,;RNL$HJ?6QHfG.$r(B (13), (14) $B<0$rMQ$$(B $B$FI=8=$9$k$H(B, $B4%AgCGG.29EY8:N($O0J2<$N$h$&$KJQ7A$G$-$k(B.

$$\DD{T}{z} = - \frac{ M_{v} g }{ {c_{p}}_{d}} \left\{ \frac{ 1 + \... ...}{M_{d}} } { 1 + \frac{( {c_{p}}_{v} - {c_{p}}_{d} ) X}{{c_{p}}_{d}}} \right\}.$$ (22)

$B$5$i$K29EY$N05NOHyJ,$O0J2<$N$h$&$K=q$1$k(B.

$$\DD{T}{p} = \frac{ R T }{ c_{p} p },$$ (23)

$$\DD{T}{p} = \frac{ R T }{ {c_{p}}_{d} p } \left\{ \Dinv{ 1 + \frac{( {c_{p}}_{v} - {c_{p}}_{d} ) X}{{c_{p}}_{d}}} \right\}.$$ (24)

mail protected],$,>/$J$$$H$9$k6a;w<0$H(B mail protected],$,B?$$$H$9$k6a;w<0$bJ;$;$FF3=P$9$k(B. $B$=$NF3=P$O0J2<$NDL$j$G$"$k(B.

mail protected],$,>/$J$$6a;w(B

 
(22) $B<0$K$*$$$F==J,$K6E=L@[email protected],$N>/$J$$>l9g(B, $B$D$^$j(B

$$M \approx M_{d}, \;\;\; c_{p} \approx {c_{p}}_{d}, \;\;\;$$ (25)

$B$r9M$($k(B. $B$=$N>l9g$K$O(B,

$$\DD{T}{z} \approx - \frac{M_{d} g}{{c_{p}}_{d}}$$ (26)

$B$H6a;w$9$k$3$H$,$G$-$k(B.

mail protected],$,B?$$6a;w(B

 
(22) $B$K$*$$$F==J,$K6E=L@[email protected],$NB?$$>l9g(B, $B$9$J$o$A(B

$$M \approx M_{v}, \;\;\; c_{p} \approx {c_{p}}_{v},$$ (27)

$B$N>l9g$K$O(B,

$$\DD{T}{z} \approx - \frac{M_{v} g}{{c_{p}}_{v}}$$ (28)

$B$H6a;w$9$k$3$H$,$G$-$k(B.

2.2.2 $B<>=aCGG.29EY8:N((B

$dX$ $B$r%b%kJ,N($HJ,05$N4X?t$H$7$FI=$9$H0J2<$N$h$&$K$J$k(B.

$$dX = \Dinv{p} de - \left( \frac{e}{p^{2}} \right) dp.$$ (29)

$B$?$@$7(B $e$ mail protected],$NK0OB>x5$05$G$"$k(B. $B$3$N<0$K%/%i%&%8%&%9!&%/%i%Z%$(B $B%m%s$N<0(B

$$de = \frac{e \lambda dT}{R T^{2}},$$ (30)

$B$rBeF~$7$FJQ7A$9$k$H(B,

$$dX = \Dinv{p} de - \frac{e}{p^{2}} dp,$$

$$= \Dinv{p} \left( \frac{e \lambda dT}{R T^{2}} \right) - \frac{e}{p^{2}} \left( - \frac{ M p g}{R T} dz \right) ,$$

$$= \frac{e}{p} \frac{\lambda}{ R_{v} T^{2}} dT + \frac{e}{p} \frac{M g}{ R T} dz ,$$

$$= \frac{ \lambda X }{ R T^{2}} dT + \frac{M g X}{ R T} dz .$$ (31)

$B$H$J$k(B.

(20) $B<0$K(B (31) $B<0$rBeF~$9$k$3$H$G<>=aCGG.29EY8:N($,5a$^$k!%(B

$$c_{p}dT + M g dz + \lambda dX = 0 ,$$

$$c_{p} dT + M g dz + \lambda \left(\frac{\lambda X }{ R T^{2}} dT + \frac{M g X}{ R T} dz \right) = 0,$$

$$c_{p} \left( 1+ \frac{ \lambda^{2} X}{ c_{p} R T^{2}} \right) dT + M g \left( 1 + \frac{ \lambda X}{R T} \right) dz = 0,$$

$$\DD{T}{z} = - \frac{M g}{c_{p}} \left( \frac{ 1 + \frac{ \lambda X}{R T}} { 1 + \frac{ \lambda^{2} X}{ c_{p} R T^{2}} } \right).$$ (32)

$BJ?6QJ,;RNL$HJ?6QHfG.$r(B (13), (14) $B<0$rMQ$$(B $B$FI=8=$9$k$H(B, $B<>=aCGG.29EY8:N($O0J2<$N$h$&$KJQ7A$G$-$k(B.

$$\DD{T}{z} = - \frac{M_{d} g}{{c_{p}}_{d}} \left\{ \frac{ 1 + \fra... ...\frac{ \lambda X}{R T}} { 1 + \frac{ \lambda^{2} X}{ c_{p} R T^{2}} } \right) .$$ (33)

$B$5$i$K(B (32), (33) $B$rJQ7A$9$k$3$H$G(B $B29EY$N05NOHyJ,$O0J2<$N$h$&$K=q$1$k(B.

$$\DD{T}{p} = \frac{R T}{c_{p} p} \left( \frac{ 1 + \frac{ \lambda X}{R T}} { 1 + \frac{ \lambda^{2} X}{ c_{p} R T^{2}} } \right),$$ (34)

$$\DD{T}{p} = \frac{R T}{{c_{p}}_{d} p} \left\{ \Dinv{ 1 + \frac{( ... ... \frac{ \lambda X}{R T}} { 1 + \frac{ \lambda^{2} X}{ c_{p} R T^{2}} } \right).$$ (35)

$B$5$i$K=>[email protected],$,>/$J$$$H$9$k6a;w<0$r5a$a(B, mail protected],$,B?$$$H$9$k6a;w<0$bJ;$;$FF3=P$9$k(B. $B$=$NF3=P$O0J2<$N(B $BDL$j$G$"$k(B.

mail protected],$,>/$J$$6a;w(B

 
(32) $B<0$K$*$$$F==J,$K6E=L@[email protected],$N>/$J$$>l9g(B, $B$D$^$j(B

$$M \approx M_{d}, \;\;\; c_{p} \approx {c_{p}}_{d}, \;\;\; \frac{ \lambda X }{R T } \ll 1, \;\;\; \frac{ \lambda^{2} X }{ c_{p} R T^{2} } \ll 1,$$ (36)

$B$r9M$($k(B. $B$=$N>l9g$K$O(B,

$$\DD{T}{z} \approx - \frac{M_{d} g}{{c_{p}}_{d}} \left( 1 + \frac{ \lambda X}{R T} \right) \left( 1 - \frac{ \lambda^{2} X}{ {c_{p}}_{d} R T^{2}} \right) ,$$

$$\approx - \frac{M_{d} g}{{c_{p}}_{d}} \left\{ 1 - \frac{\lambda X}{ {c_{p}}_{d} T} \left( \frac{ \lambda}{ R T} - \frac{{c_{p}}_{d}}{R} \right) \right\},$$ (37)

$B$H6a;w$9$k$3$H$,$G$-$k(B. $BC"$7(B $X$ $B$K4X$9$k(B 2 $B/NL$O==J,$K>.$5$$$b$N$H$7$FL5;k$7$?(B.

mail protected],$,B?$$6a;w(B

 
(32) $B$K$*$$$F==J,$K6E=L@[email protected],$NB?$$>l9g(B, $B$9$J$o$A(B

$$M \approx M_{v}, \;\;\; c_{p} \approx {c_{p}}_{v}, \;\;\; \frac{ \lambda X }{R T } \gg 1, \;\;\; \frac{ \lambda^{2} X }{ c_{p} R T^{2} } \gg 1,$$ (38)

$B$N>l9g$K$O(B,

$$\DD{T}{z} \approx - \frac{M_{v} g}{{c_{p}}_{v}} \frac{\frac{ \lambda X}{R T}} {\frac{ \lambda^{2} X}{ {c_{p}}_{v} R T^{2}} } ,$$

$$= - \frac{M_{v} g T}{\lambda}$$ (39)

$B$H6a;w$9$k$3$H$,$G$-$k(B.

2.3 $B@EE*0BDjEY(B

$B@EE*0BDjEY$N<0(B (10) $B$K(B (13) $B<0(B $B$rBeF~$9$k$3$H$GF@$i$l$?<0(B,

$$N^{2} = \frac{g}{T} \left( \DD{T}{z} + \frac{M g}{c_{p}} \right) - \frac{ g (M_{v} - M_{d})}{M} \DD{X}{z},$$

$B$K%/%i%&%8%&%9!&%/%i%Z%$%m%s$N<0(B (31) $B$r(B

$$\DD{X}{z} = \frac{ \lambda X }{ R T^{2}} \DD{T}{z} + \frac{M g X}{ R T}$$

$B$N$h$&$KJQ7A$7$FBeF~$9$k$H(B,

$$N^{2} = \frac{g}{T} \left( \DD{T}{z} + \frac{M g}{c_{p}} \right) - \frac{... ...{M} \left( \frac{ \lambda X }{ R T^{2}} \DD{T}{z} + \frac{M g X}{ R T} \right),$$

$$= \frac{g}{T} \left[ \frac{M g}{c_{p}} + \DD{T}{z} \left\{ 1 - \fra... ... T} \right\} \right] - \frac{g}{T} \frac{ (M_{v} - M_{d})}{M} \frac{M g X}{ R }$$ (40)

$B$H$J$k(B. $BJ?6QJ,;RNL$HJ?6QHfG.$r(B (13), (14) $B<0$rMQ$$(B $B$FI=8=$9$k$H(B, $B@EE*0BDjEY$O0J2<$N$h$&$KJQ7A$G$-$k(B.

$$N^{2} = \frac{g}{T} \left[ \frac{M_{d} g}{{c_{p}}_{d}} \left\{ \frac{ 1 +... ...}} {M_{d} \left\{ 1 + \frac{(M_{v} - M_{d})X}{M_{d}} \right\}} \right\} \right]$$

$$- \frac{g}{T} \frac{ (M_{v} - M_{d}) g X}{ R }.$$ (41)

mail protected],$,>/$J$$$H$9$k6a;w<0$H(B mail protected],$,B?$$$H$9$k6a;w<0$bJ;$;$FF3=P$9$k(B. $B$=$NF3=P$O0J2<$NDL$j$G$"$k(B.

mail protected],$,>/$J$$6a;w(B

 
(40) $B<0$K(B (26), (36), (37) $B<0$r(B $BBeF~$9$k(B. $B$=$N7k2L(B, mail protected],$,>/$J$$>l9g$N@EE*0BDjEY$N6a;w<0$,F@$i$l$k(B.

$$N^{2} \approx \frac{g}{T} \left[ \frac{M_{d} g}{{c_{p}}_{d}} - \frac{M_{d} g}{{... ...\{ 1 - \frac{ (M_{v} - M_{d})}{M_{d}} \frac{ \lambda X }{ R T} \right\} \right]$$

$$- \frac{g}{T} \frac{ (M_{v} - M_{d})}{M_{d}} \frac{M_{d} g X}{ R }$$

$$\approx \frac{M_{d} g^{2}}{{c_{p}}_{d} T} \left\{ \frac{\lambda X}{{c_{p}... ...g^{2}}{{c_{p}}_{d} T} \frac{ (M_{v} - M_{d})}{M_{d}} \frac{ {c_{p}}_{d} X}{ R }$$

$$= \frac{M_{d} g^{2}}{{c_{p}}_{d} T} \left( \frac{ \lambda}{ R T} - ... ...{M_{d}} \left( 1 - \frac{\lambda^{2} X}{{c_{p}}_{d} R T^{2}} \right) \right\} X$$

$$\approx \frac{M_{d} g^{2}}{{c_{p}}_{d} T} \left( \frac{ \lambda}{ R T} - ... ...left( \frac{\lambda}{{c_{p}}_{d} T} + \frac{ (M_{v} - M_{d})}{M_{d}} \right) X.$$ (42)

mail protected],$,B?$$6a;w(B

 
(40) $B<0$K(B (28), (38), (39) $B<0$rBeF~$9$k(B. $B$=$N7k2L(B, mail protected],$,B?$$>l9g$N@EE*0BDjEY$N6a;w<0$,F@$i$l$k(B.

$$N^{2} \approx \frac{g}{T} \left[ \frac{M_{v} g}{{c_{p}}_{v}} - \frac{M_{v} g T}... ...}{ R T} \right\} - \frac{ (M_{v} - M_{v})}{M_{v}} \frac{M_{v} g X}{ R } \right]$$

$$= \frac{g}{T} \left[ \frac{M_{v} g}{{c_{p}}_{v}} \left( 1 - \frac{{... ...lambda X }{ R T} - \frac{ (M_{v} - M_{d})}{M_{v}} \frac{M_{v} g X}{ R } \right]$$

$$= \frac{M_{v} g^{2}}{{c_{p}}_{v} T} \left( 1 - \frac{{c_{p}}_{v} T}{\lambda} \right)$$ (43)

3 $BLZ@1$N?e1@$rA[Dj$7$?7W;;Nc(B

$BK\@a$G$O(B, $BLZ@1$N?e1@$rA[Dj$7$?7W;;Nc$r<($9(B. $BBg5$$N4%[email protected],$H$7$F?eAG$H%X%j%&%`$N:.9gBg5$(B(H/He = 0.095), $B<>[email protected],$H$7$F?e$rA[Dj$9$k(B. $B$=$7$F29EY(B, $BAjJQ2=$N%(%s%?%k%T!<$r8GDj$7(B, $B?e$N%b%kHf$rJQ2=$5$;$?>l9g$NCGG.29EY8:N($H@EE*0BDjEY$N(B $BJQ2=$rD4$Y$k(B.

$B7W;;$GMQ$$$kJ*M}NL$K$D$$$F9M;!$9$k(B. $B29EY$r8GDj$7$?>l9g(B, $BAjJQ2=$N%(%s%?%k%T!<$O%/%i%&%8%&%9(B-$B%/%i%Z%$%m%s$N<0$H(B $BK0OB>x5$05$N<0$+$iF@$i$l$k(B. $B?e$NK0OB>x5$05$N<0$H$7$F(B Antoine $B$N<0$r(B $BMxMQ$9$k>l9g(B, $B$=$NCM$O0J2<$N$h$&$KM?$($i$l$k(B($B2=3XJXMw(B $B2~D{Bh;MHG(B).

$$\ln{e} = A - \frac{B}{C + T},$$

$$$B$?$@$7(B A = 7.9186968d0$$

$$B = 1636.909d0$$

$$C = 224.92d0$$

$B$?$@$7>e5-$N(B $e$ $B$NC10L$O(B mmHg $B$G$"$j(B, $T$ $B$NC10L$O(B $^{\circ}$C $B$J$N$G(B, SI $BC10L7O$KJQ49$9$k$H(B,

$$\ln{e} = \left( A - \frac{B}{C + T - 273.15 } \right) \ln{10} + \ln{133.322}$$ (44)

(44) $B<0$r(B (30) $B<0$KBeF~$9$k$H(B, $BAjJQ2=$N%(%s%?%k%T!<$O0J2<$N$h$&$KI=8=$5$l$k(B.

$$\lambda = R T^{2} \DD{\ln{e}}{T}$$

$$= R T^{2} \frac{B * \ln{10}}{ ( C + T - 273.15 )^2 }$$ (45)

$B0J>e$N5DO@$rF'$^$($?>e$G7W;;$KMxMQ$9$kJ*M}NL$H%Q%i%a%?$r$^$H$a$k$H(B $B0J2<$N$h$&$K$J$k(B.

$BDj?t0lMw(B

 

	$B4%[email protected],(B	$B<>[email protected],(B($B?e(B)
$BJ,;RNL(B (kg/mol)	$18 \times 10^{-3}$	$2.323 \times 10^{-3}$
$BHfG.(B (J/K mol)	33.5	27.66
$B=ENO2CB.EY(B (m/s$^2$)	23.2
$B5$BNDj?t(B	8.314

$B

 

	$B29EY(B	$BAjJQ2=$N%(%s%?%k%T!<(B
	(K)	(J/K mol)
$B%1!<%9(B 1	200	54417
$B%1!<%9(B 2	300	44492
$B%1!<%9(B 3	400	40518
$B%1!<%9(B 4	500	38384

$B=>Mh$N8&5f$G$O(B, $BLZ@1Bg5$$K4^$^$l$k?e$N%b%kHf$O==J,>.$5$$$b$N$H$7$F(B $BCGG.29EY8:N($*$h$S@EE*0BDjEY$r6a;w$7$?<0$,$7$P$7$PMQ$$$i$l$F$-$?(B. $B$^$:$OLZ@1Bg5$$K$*$1$k%b%kHf$r==J,>.$5$$$H$9$k6a;w$N>r7o$r5a$a$k(B. $B$D$$$G==J,Bg$-$$$H$9$k6a;w$N>r7o$b5a$a$k$3$H$H$9$k(B ¹.

mail protected],$N>/$J$$6a;[email protected])$9$k>r7o(B $\Deqref{lapserate:Cond_LapseRate_low}$ $B<0$O0J2<$N$h$&$K=q$1$k(B.

$M \approx M_{d}$ mail protected])>r7o(B

$$\frac{(M_{v} - M_{d}) X}{M_{d}} = \frac{(18.0 - 2.323) \times 10^{-3}}{ 2.323 \times 10^{-3} },$$

$$= 6.7486 X \ll 1.$$

$$X \ll 1.5 \times 10^{-1}.$$ (46)

$c_{p} \approx {c_{p}}_{d}$ mail protected])>r7o(B

$$\frac{( {c_{p}}_{v} - {c_{p}}_{d} ) X}{ {c_{p}}_{d}} = \frac{23.5 - 27.66}{27.66}X,$$

$$= 0.21 X \ll 1.$$

$$X \ll 4.76.$$ (47)

$\frac{ \lambda X}{R T} \ll 1$ mail protected])>r7o(B

$$\frac{ \lambda X}{R T} = \frac{44492}{8.31 \times 300} X$$

$$= 17.8 X \ll 1.$$

$$X \ll 5.6 \times 10^{-2}.$$ (48)

$\frac{ \lambda^{2} X}{ c_{p} R T^{2} } \ll 1$ mail protected])>r7o(B

$$\frac{ \lambda^{2} X}{ c_{p} R T^{2} } = \frac{(44492)^{2}}{30 \times 8.31 \times (300)^{2}} X$$

$$= 88 X \ll 1.$$

$$X \ll 1.1 \times 10^{-2}.$$ (49)

$B0J>e$h$j(B, (36) $B<[email protected])>r7o$rA4$FK~$?$9(B $B%b%kHf$NHO0O$O(B $X \ll 1.1 \times 10^{-2}$ $B$G$"$k(B.

mail protected],$NB?$$6a;[email protected])$9$k>r7o(B $\Deqref{lapserate:Cond_LapseRate_high}$ $B<0$O0J2<$N$h$&$K=q$1$k(B.

$M \approx M_{v}$ mail protected])>r7o(B

$$X \approx 1.$$ (50)

$c_{p} \approx {c_{p}}_{v}$ mail protected])>r7o(B

$$X \approx 1.$$ (51)

$\frac{ \lambda X}{R T} \gg 1$ mail protected])>r7o(B

$$\frac{ \lambda X}{R T} = \frac{44492}{8.31 \times 300} X$$

$$= 17.8 X \gg 1.$$

$$X \gg 5.6 \times 10^{-2}.$$ (52)

$\frac{ \lambda^{2} X}{ c_{p} R T^{2} } \gg 1$ mail protected])>r7o(B

$$\frac{ \lambda^{2} X}{ c_{p} R T^{2} } = \frac{(44492)^{2}}{30 \times 8.31 \times (300)^{2}} X$$

$$= 88 X \gg 1.$$

$$X \gg 1.1 \times 10^{-2}.$$ (53)

$B%b%kHf$NHO0O$O(B $X \le 1$ $B$J$N$G(B, (50)-(53) $B$,(B mail protected])$9$k%b%kHf$NHO0O$O(B $X = 1$ $B$N$4$/6aK5$N$_$G$"$k(B. $B$7$+$7LZ@1Bg5$$K$*[email protected],$N%b%kHf$,(B 1 $B$H$J$k>u67$O(B $B$^$:9M$($i$l$J$$$N$G(B, mail protected],$NB?$$6a;w$,@.N)$9$k$3$H$OL5$$(B.

$B0J2<$G$OLZ@1Bg5$>r7o$G$N4%AgCGG.29EY8:N((B, $B<>=aCGG.29EY8:N((B, $B@EE*0BDjEY$K$D$$$F(B, $B

3.1 $BJ,;RNL$HHfG.(B

Fig.3, Fig.4 $B$KJ,;RNL$HHfG.$r(B $B%b%kHf$N4X?t$H$7$F%W%m%C%H$9$k(B. $B%b%kHf$O(B 1 $B3dDxEY$7$+CM$,JQ2=$7$J$$$,(B, $BJ,;RNL$O7e$GCM$,JQ2=$9$k(B.

$B?^(B 3: $BJ,;RNL(B

$B?^(B 4: $BHfG.(B

3.2 $B4%AgCGG.29EY8:N((B

Fig.5 $B$G4%AgCGG.29EY8:N($r%b%kHf$N4X?t$H$7$F(B $B%W%m%C%H$9$k(B. $B%b%kHf$,(B 0.1 $B$rD6$($?$"$?$j$+$i5^7c$KCM$,Bg$-$/$J$k(B. $B4%AgCGG.29EY8:N($O6E7k29EY$K0MB8$7$J$$$N$G(B, $B$I$N

$B?^(B 5: $B4%AgCGG.29EY8:N((B. $B%b%kHf$,(B 0.1 $B$rD6$($?$"$?$j$+$i5^7c$KCM$,Bg$-(B $B$/$J$k(B. $B@V@~(B; $B6a;w$J$7(B((22) $B<0(B)$B$rMQ$$$?>l9g(B. $BNP@~(B: mail protected],$N>/$J$$6a;w(B((26) $B<0(B) $B$rMQ$$$?>l9g(B. $B@D@~(B: mail protected],$NB?$$6a;w(B((28) $B<0(B) $B$rMQ$$$?>l9g(B.

3.3 $B<>=aCGG.29EY8:N((B

Fig.6 $B$K$*$$$F(B, case2 ($T = 300$ K)$B$G$N(B $B<>=aCGG.29EY8:N($r%b%kHf$N4X?t$H$7$F%W%m%C%H$9$k(B. mail protected],$N%b%kHf$rA}2C$5$;$k$H(B $BAjJQ2=$KH<$&G.$N2rJ|$K$h$C$F<>=aCGG.29EY8:N($O$7$@$$$K>.$5$/$J$k(B. $B$7$+$7%b%kHf$,(B 0.1 $B$rD6$($?$"$?$j$+$iJ,;RNLJQ2=$N8z2L(B ($M$ $B$,(B $M_{d} = 2.323 \times 10^{-3}$ $B$+$i(B $M_{d} = 18 \times 10^{-3}$ $B$^$GJQ2=(B)$B$N$?$a$KCM$,A}2C$KE>$8$k(B.

$BAjJQ2=$KH<$&G.$N2rJ|$N8z2L$r8+$k$?$a$K(B, (33)$B<0$N1&JU$N(B $(1 + \lambda X/ RT)/ (1 + {\lambda }^{2}X / c_{p} R T^{2})$ $B$r%W%m%C%H$9(B $B$k(B(Fig.7 $B;2>H(B). $B%b%kHf$rA}$d$7$F$$$/$HCM$,>.$5$/$J$C$F$$$/$,(B, $B%b%kHf$,(B 0.1 $B$rD6$($k$"$?$j$+$i$O:GBgCM$KA26a$9$k$h$&$K$J$k(B.

(50)-(53) $B$G(B $B<($7$?$h$&$K(B, $BLZ@1Bg5$$K$*[email protected],$,B?$$$H$9$k>r7o(B (38) $B$O8= $1.0 \times 10^{-1} \le X \le 1$ $BDxEY$N>[email protected])$9$k(B $B6a;w<0$r:n$l$J$$$o$1$G$O$J$$(B. $B$=$N>l9g$O(B (53) $B$N(B mail protected])$9$k$3$H$r9M$((B,

$$\DD{T}{z} \approx - \frac{M_{d} g R T^{2} }{\lambda^{2}} \left\{ ... ...\frac{ \lambda }{R T} + \frac{(M_{v} - M_{d}) \lambda X }{M_{d} R T} \right\} ,$$ (54)

$B$H$9$l$P$h$$(B. (54) $B$r(B Fig.8$B$K<($9(B.

Fig.9 $B$K$O(B, case1-case4 $B$N>l9g$H$7$F(B, $B29EY(B $T$ $B$rJQ2=$5$;$?>l9g$N<>=aCGG.29EY8:N($r<($9(B.

$B?^(B 6: $T = 300$ K $B$G$N<>=aCGG.29EY8:N((B. mail protected],$N%b%kHf$rA}2C$5$;$k$H(B $BAjJQ2=$KH<$&G.$N2rJ|$K$h$C$F<>=aCGG.29EY8:N($O$7$@$$$K>.$5$/$J$k(B. $B$7$+$7%b%kHf$,(B 0.1 $B$rD6$($?$"$?$j$+$iJ,;RNLJQ2=$N8z2L(B ($M$ $B$,(B $M_{d} = 2.323 \times 10^{-3}$ $B$+$i(B $M_{d} = 18 \times 10^{-3}$ $B$^$GJQ2=(B)$B$K$h$C$F(B, $BCM$,Bg$-$/$J$k(B. $B@V@~(B; $B6a;w$J$7(B((33) $B<0(B)$B$rMQ$$$?>l9g(B. $BNP@~(B: mail protected],$N>/$J$$6a;w(B((37) $B<0(B) $B$rMQ$$$?>l9g(B. $B@D@~(B: mail protected],$NB?$$6a;w(B((39) $B<0(B) $B$rMQ$$$?>l9g(B.

$B?^(B 7: $(1 + \lambda X/ RT)/ (1 + {\lambda }^{2}X / c_{p} R T^{2})$ $B$N(B $B%W%m%C%H(B. $B@V@~(B; $B6a;w$J$7$N>l9g(B. $BNP@~(B: mail protected],$N>/$J$$>r7o(B((36) $B<0(B) $B$,@.N)$9$k>l9g(B. $B@D@~(B: mail protected],$NB?$$>r7o(B((38) $B<0(B) $B$,@.N)$9$k>l9g(B.

$B?^(B: $T = 300$ K $B$G$N<>=aCGG.29EY8:N((B. $B@V@~(B, $BNP@~(B, $B@D@~$O(B Fig.6 $B$KF1$8(B. $B;g@~(B: (54) $B<0$rMQ$$$?>l9g(B.

$B?^(B 9: $B29EY(B $T$ $B$rJQ2=$5$;$?>l9g$N<>=aCGG.29EY8:N((B. $BNP@~$O(B case1 ($T=200$K), $B@V@~$O(B case2 ($T = 300$K), $B@D@~$O(B case3 ($T=400$K), $B;g@~$O(B case4 ($T=500$K).

3.4 $B@EE*0BDjEY(B

Fig.10 $B$K$*$$$F(B, case2($T = 300$K)$B$G$N@EE*0BDjEY$r(B $B%W%m%C%H$9$k(B. mail protected],$N%b%kHf$rA}2C$5$;$k$H(B, $B4%AgCGG.29EY8:N($O$[$\0lDj$K$b4X$o$i$:<>=aCGG.29EY8:N($O(B $B4K$d$+$K8:>/$9$k$N$G(B, $B@EE*0BDjEY$NCM$O$f$C$/$j$HA}2C$9$k(B. $B$7$+$7%b%kHf$,(B 0.1 $B$rD6$($?$"$?$j$+$iJ,;RNLJQ2=$N8z2L(B ($M$ $B$,(B $M_{d} = 2.323 \times 10^{-3}$ $B$+$i(B $M_{d} = 18 \times 10^{-3}$ $B$^$GJQ2=(B)$B$K$h$C$F(B, $B$=$NCM$,5^7c$KA}2C$9$k(B.

Fig.11 $B$K$O(B, case1-case4 $B$N>l9g$H$7$F(B, $B29EY(B $T$ $B$rJQ2=$5$;$?>l9g$N@EE*0BDjEY$r<($9(B.

$B?^(B 10: $T = 300$ K $B$G$N@EE*0BDjEY(B. mail protected],$N%b%kHf$rA}2C$5$;$k$H(B, $B4%AgCGG.29EY8:N($O$[$\0lDj$K$b4X$o$i$:<>=aCGG.29EY8:N($O(B $B4K$d$+$K8:>/$9$k$N$G(B, $B@EE*0BDjEY$NCM$O$f$C$/$j$HA}2C$9$k(B. $B$7$+$7%b%kHf$,(B 0.1 $B$rD6$($?$"$?$j$+$iJ,;RNLJQ2=$N8z2L(B ($M$ $B$,(B $M_{d} = 2.323 \times 10^{-3}$ $B$+$i(B $M_{d} = 18 \times 10^{-3}$ $B$^$GJQ2=(B)$B$K$h$C$F(B, $B$=$NCM$,5^7c$KA}2C$9$k(B. $B@V@~(B; $B6a;w$J$7(B((40) $B<0(B)$B$rMQ$$$?>l9g(B. $BNP@~(B: mail protected],$N>/$J$$6a;w(B((42) $B<0(B) $B$rMQ$$$?>l9g(B. $B@D@~(B: mail protected],$NB?$$6a;w(B((43) $B<0(B) $B$rMQ$$$?>l9g(B. $B;g@~(B: $BJ,;RNL$NA}2C$9$k8z2L$rD4$Y$k$?$a$K(B, $B6a;w$J$7$N<0(B (40) $B$K$*$$$F(B, $BJ,;RNL$HHfG.$rDj?t$H8+$J$7$?>l9g(B.

$B?^(B 11: $B29EY(B $T$ $B$rJQ2=$5$;$?>l9g$N@EE*0BDjEY(B. $B@EE*0BDjEY$O29EY$N5U?t$K(B $BHfNc$9$k$N$G(B, $B29EY$,9b$/$J$k$[$I@EE*0BDjEY$NCM$O>.$5$/$J$k(B. $BNP@~$O(B case1 ($T=200$K), $B@V@~$O(B case2 ($T = 300$K), $B@D@~$O(B case3 ($T=400$K), $B;g@~$O(B case4 ($T=500$K).

3.5 mail protected],$r9MN8$7$?>l9g$NLZ@1Bg5$$N@EE*0BDjEY(B

Table 1 $B$K<($5$l$?2=3XA[E*$JLZ@1Bg5$$N@EE*0BDjEY(B $B$r7W;;$7(B, $B?e1@212 $B$K<($9(B. $B4%[email protected],$G$"$k(B H $B$H(B He $B$NB8:_EY$OB@M[7O85AGB8:_EY(B (Anders and Grevesse, 1989) $B$KEy$7$$$H$7(B, mail protected],$G$"$k(B C, N, O, S $B$NB8:_EY$OB@M[7O85AGB8:_EY$N(B 1, 5, 10, 30, 50 $BG\$H$7$F7W;;$9$k(B. Fig.12 $B$+$i(B, 1) $B@EE*0BDjEY$O?e$NB8:_EY$KHfNc$7$J$$$3$H(B, 2) $B@EE*0BDjEY$,A}2C$7$J$$M}M3$O@EE*0BDjEY$O29EY$N5U?t$KHfNc$9$k$?$a$G$"(B $B$k$3$H$,<($5$l$k(B.

Fig.13 $B$O(B, Achterberg and Ingersoll (1989) $B$N;XE&$7$?(B $B@EE*0BDjEY$H?e$N%b%kHf$NHfNc4X78(B((42) $B<0(B)$B$H(B, $B2f!9$N7W;;$GF@$i$l$?@EE*0BDjEY$N:GBgCM(B, $B$5$i$K(B (40) $B<0$r%W%m%C%H$7$?$b$N$G$"$k(B. (42), (40) $B<0$rMQ$$$k:][email protected],$O(B $B?e$N$_9MN8$7$?(B. Fig.13 $B$+$iL@$i$+$J$h$&$K(B, Achterberg and Ingersoll (1989) $B$N;XE&$7$?HfNc4X78$O(B, $B?e$NB8:_EY$r(B $BB@M[7O85AGB8:_EY$N?tG\0J>eA}2C$5$;$?>[email protected])$7$J$$(B.

Fig.14 $B$OLZ@[email protected],$NB8:_EY$r(B, $BB@M[7O85AGB8:_EY$N(B 1, 5, 10 $BG\$7$?;~$N@EE*0BDjEY$r<($9(B. $BLZ@1$G$O(B H$_2$O(s), NH$_4$SH(s), NH$_3$(s) $B$,6E=L$7(B, $BB@M[7O85AGB8:_EY$N(B 5 $BG\(B, 10 $BG\$H$7$?>l9g$K$O(B NH$_3$-H$_2$S-H$_2$O(liq) $B$b6E=L$9$k(B. $B@EE*0BDjEY$O$=$l$>[email protected],$N6E7k9bEY$KBP1~$7$?%T!<%/$r;}$D(B. $BLZ@1Bg5$$K$*$$$F:[email protected]$O(B H$_2$O $B$K$h$C$F7A@.$5$l$k(B.

$BI=(B 1: $B%b%G%[email protected],(B. (g) $B$O5$Aj(B, (l) $B$O1UAj(B, (s) $B$O8GAj$rI=$9(B.

gas (g)	liquid (l)	solid (s)
H$_2$, He, H$_2$O,	H$_2$O, NH$_3$,	H$_2$O, NH$_3$, H$_2$S,
CH$_4$, NH$_3$, H$_2$S	H$_2$S, CH$_4$,	CH$_4$, NH$_4$SH

spc

$B?^(B 12: $BLZ@1Bg5$$KB@M[AH@.$N(B 1, 5, 10, 30, 50 $BG\$N?e$,B8:_$9$k$H>l9g$K(B, $B?e1@2.$5$/$J$k(B. $B@10u$O?e1@240) $B<0$h$j5a$a$?(B $B@EE*0BDjEY(B. $BNP@~$O(B $T = 271.9$ K, $B@V@~$O(B $T = 304.5$ K, $B@D@~$O(B $T = 324.5$ K, $B;g@~$O(B $T = 376.6$ K, $BMu?'@~$O(B $T = 422.6$ K $B$G$"$k(B. $B$?$@$7(B (40) $B<0$rMxMQ$9$k:][email protected],$O?e$N$_$H$7$?(B.

$B?^(B 13: $B@EE*0BDjEY$N:GBgCM$H(B Acterberg and Ingersoll (1989) $B$N;XE&$7$?(B $B@EE*0BDjEY$N6a;w<0(B. Achterberg and Ingersoll (1989) $B$N;XE&$7$?HfNc4X78$O(B, $B?e$NB8:_EY$r(B $BB@M[7O85AGB8:_EY$N?tG\0J>eA}2C$5$;$?>[email protected])$7$J$$(B. $B@10u$O?e1@242) $B$h$j5a$a$?@EE*0BDjEY(B. $B@V@~$O(B (40) $B<0$h$j5a$a$?(B $B@EE*0BDjEY(B($T = 271.9K$). $B$?$@$7(B (42), (40) $B<0$r(B $BMxMQ$9$k:][email protected],$O?e$N$_$H$7$?(B.

$B?^(B 14: $BLZ@1$G$N@EE*0BDjEY(B. $B@EE*0BDjEY$N%T!<%/$O6E=L$K5/0x$7(B, $B2<$+$i=g$K(B, H$_2$O $B?eMO1U(B(5 $\times$ solar, 10 $\times$ solar $B$N$_(B), $BI9(B, $BN22=%"%s%b%K%&%`(B, $B%"%s%b%K%"I9$K5/0x$9$k(B. $B@V@~(B: 1 $\times$ solar, $BNP@~(B: 5 $\times$ solar, $B@D@~(B: 10 $\times$ solar. H$_2$O mail protected]$,:G$bBg$-$$(B.

4 $B=>Mh$NO@J8$H$NHf3S(B

$B=>Mh$NO@J8$G$O(B, $B$=$b$=$b5$2t$K4^$^[email protected],$O>/$J$$$H2>Dj$7(B, $B5$2t$K$O4%[email protected],$7$+4^$^$l$J$$$,(B, $B<~0O$NBg5$$K$O4%[email protected],[email protected],$,(B $BB8:_$9$k$h$&$J7O$r9M$($F$-$?(B. $BK\@a$G$O=>Mh$NO@J8$K=>$C$F(B,

• $BBg5$$O4%[email protected],[email protected],$N(B 2 mail protected],$+$i@.$k$b$N$H$9$k(B.
• $BBg5$Cf$K4^$^[email protected],$O>/$J$$(B
• $BBg5$$NJ,;RNL$OK0OBBg5$$N$=$l$G$O$J$/(B, $B<>EY(B $r$ $B$N;~$NCM$H$9$k(B. $M = (1 - rX^{sat}) M_{d} + rX^{sat} M_{v}$.
• $BBg5$$N29EY8:N((B $dT(z)/dz$ $B$r(B, $BK0OBBg5$$G$N<>=aCGG.29EY8:N($H$9$k(B.
• $B5$2t$NJ,;RNL$r4%[email protected],$NJ,;RNL$H$9$k(B. $M = M_{d}$.
• $B5$2t$N29EY8:N((B $dT^{*}(z)/dz$ $B$r4%Ag5$2t$NCGG.29EY8:N($H$9$k(B. $dT^{*}/dz = - M_{d} g/ {c_{p}}_{d}$.

$B$H2>Dj$7$?>l9g$K$D$$$F@EE*0BDjEY$NDj<02=$r9T$$(B, $B=>Mh$NO@J8Cf$N<0$NF3=P$r(B $B9T$&(B.

$B5$2t$HBg5$$NJ,;RNL$,0[$J$k$?$a(B, $M = M^{*}$ $B$r2>Dj$7$F$$$J$$(B (7) $B<0$+$i9M;!$r;O$a$kI,MW$,$"$k(B. $M^{*} = M_{d}$ $B$r(B (7) $B<0$KBeF~$9$k$H(B,

$$N^{2} = \frac{g}{T} \left( \DD{T}{z} + \frac{M g}{{c_{p}}_{d}} \right) - g \left( \Dinv{M} \DD{M}{z} \right).$$ (55)

$B$H$J$k(B. $B$3$N<0$r(B (10) $B<0$HHf3S$9$k$H(B, $B5$2t$NJ,;RNL$NItJ,$@$10[$J$C$F$$$k(B. $B$5$i$KBg5$$NJ,;RNL(B $M = (1 - rX^{sat}) M_{d} + rX^{sat} M_{v}$ $B$rBeF~$9$k$H(B,

$$N^{2} = \frac{g}{T} \left( \DD{T}{z} + \frac{M g}{{c_{p}}_{d}} \right) - g \left( \frac{r (M_{v} - M_{d})}{M} \DD{X^{sat}}{z} \right)$$ (56)

$B$H$J$k(B. $B$^$?(B, (55) $B<0$r2>29EY(B $T_{v} = M_{d} T/ M$ $B$rMQ$$$FI=8=$9$k$H(B,

$$N^{2} = \frac{g}{T_{v}} \left( \DD{T_{v}}{z} + \frac{M_{d} g}{{c_{p}}_{d}} \right)$$ (57)

$B$H$J$k(B.

4.1 Achterberg and Ingersoll (1989)

Achterberg and Ingersoll (1989) $B$O@EE*0BDjEY(B, $B2>29EY(B, $B<>=a5².

$$N^{2} = \frac{g}{T_{v}} \left( \DD{T_{v}}{z} + \frac{g}{{c_{p}^{\dagger}}_{d}} \right),$$ (58)

$$T_{v} = \frac{T }{1 + (\varepsilon - 1) e /p },$$ (59)

$$\DD{T}{z} = - \frac{g}{c_{p}^{\dagger}} \left( \frac{ 1 + \frac{\... ...mbda^{\dagger}}^{2} \varepsilon q}{R^{\dagger} c_{p}^{\dagger} T^{2}} } \right)$$ (60)

$B$?$@$7E:;z(B $\dagger$ $B$NIU$$$?NL$OC10L $R^{\dagger} = R/M$ $B$OBg5$$NC10L $c_{p}^{\dagger} = c_{p}/M$ $B$OBg(B $B5$$NC10L ${c_{p}^{\dagger}}_{d}=c_{p}/M_{d}$ $B$OC10L $\lambda^{\dagger}=\lambda/M_{v}$ $B$OC10L $\varepsilon = M_{v}/M_{d}$ mail protected],$NJ,;RNL$H4%Ag(B mail protected],$NJ,;RNL$H$NHf(B, $e$ mail protected],$NK0OB>x5$05(B, $q$ mail protected],$N:.9g(B $BHf$G$"$k(B.

$B0J2<$G$O(B, $BA0@a$G5a$a$?@EE*0BDjEY(B, $B2>29(B $BEY(B, $B<>=aCGG.8:N($,(B, $B$=$l$>$l(B (58) - (60) $B<0$G(B $BI=8=$G$-$k$3$H$r<($9(B. $B$?$@$7H`$i$N7W;;$G$O(B $r = 1$ $B$r2>Dj$7$F$$$k(B.

$B=i$a$K@EE*0BDjEY$N<0(B (58) $B$O(B, () $B<0Cf$NC10L%b%kEv$?$j(B $B$NNL$rC10L

$$N^{2} = \frac{g}{T_{v}} \left( \DD{T_{v}}{z} + \frac{M_{d} g}{{c_{p}}_{d}} \right)$$

$$= \frac{g}{T_{v}} \left( \DD{T_{v}}{z} + \frac{g}{{c_{p}^{\dagger}}_{d}} \right)$$

$B29EY$N<0(B (59) $B$O(B, $B2>29EY$NDj5A<0$rJQ7A$9$k$3$H$GF3$+$l$k(B.

$$T_{v} = T \frac{M_{d}}{M} ,$$

$$= T \frac{M_{d}}{M_d (1 - X) + M_{v} X} ,$$

$$= T \frac{M_{d}}{M_d (p - e)/p + M_{v} e/p } ,$$

$$= T \frac{M_{d} p}{M_d p + (M_{v} - M_{d}) e } ,$$

$$= T \frac{1}{1 + (M_{v} - M_{d})/M_{d} e/p } ,$$

$$= \frac{T}{1 + (\varepsilon - 1) e/p }.$$

$B:G8e$K(B (32) $B$K2D6E=LJ*/$J$$$H$$$&>r7o$rM?$($k$3$H$G(B (60) $B$,F@$i$l$k$3$H$r<($9(B. mail protected],$,>/$J$$>l9g(B,

$$q = \frac{M_{v} X}{M_{d} (1 - X) + M_{v} X} \approx \frac{M_{v}}{M_{d}} X.$$ (61)

$$M \approx M_{d}$$ (62)

$B$H$J$k$N$G(B, $B$3$N4X78$rMQ$$$F(B (32) $B<0$rJQ7A$7(B, $B$^$?(B (32) $B<0Cf$NC10L%b%kEv$?$j$NNL$rC10L

$$\DD{T}{z} = - \frac{M g}{c_{p}} \left( \frac{ 1 + \frac{ \lambda X}{R T}} { 1 + \frac{ \lambda^{2} X}{ c_{p} R T^{2}} } \right),$$

$$= - \frac{M g}{( M c_{p}^{\dagger} ) } \left( { 1 + \frac{ (M_{v} \... ...M_{d} / M_{v})} { (M_{d} c_{p}^{\dagger}) (M_{d} R^{\dagger}) T^{2}} } \right),$$

$$= - \frac{g}{c_{p}^{\dagger}} \left( \frac{ 1 + \frac{\lambda^{\dag... ...da^{\dagger}}^{2} \varepsilon q}{R^{\dagger} c_{p}^{\dagger} T^{2}} } \right) .$$

4.2 $BCfEg(B (1998)

$BCfEg(B (1998) $B$O<>=aCGG.29EY8:N($H@EE*0BDjEY$r0J2<$N$h$&$KM?$($?(B. $B$?$@$7J*M}NL$r<($9J8;z$rJQ$($F$"$k(B.

$$\DD{T}{z} = - \frac{g}{{c_{p}^{\dagger}}_{d}} \left( \frac{ 1 + \frac{\lambda... ...lambda^{\dagger}}^{2} q}{R_{v}^{\dagger} {c_{p}^{\dagger}}_{d} T^{2}} } \right)$$ (63)

$$= - \frac{g}{{c_{p}^{\dagger}}_{d}} \left\{ 1 - \left( \frac{\lambd... ...\right) \frac{\lambda^{\dagger} q^{\dagger}}{{c_{p}^{\dagger}}_{d} T} \right\}.$$ (64)

$$N^{2} = \frac{g}{T} \left( \DD{T}{z} + \frac{g}{{c_{p}^{\dagger}}_{d}} \right) + g \left(\frac{M_{d}}{M_{v}} - 1 \right) \DP{ (rq)}{z},$$ (65)

$$\approx \frac{g^{2}}{{c_{p}^{\dagger}}_{d} T} \left( \frac{\lambda^{\dagg... ...r}}{{c_{p}^{\dagger}}_{d} T} + \left(1 - \frac{M_{d}}{M_{v}} \right) \right\} q$$ (66)

$B$?$@$7E:;z(B $\dagger$ $B$NIU$$$?NL$OC10L $R_{d}^{\dagger} = R/M_{d}$ $B$O4%[email protected],$NC10L $R_{v}^{\dagger} = R/M_{v}$ mail protected],(B $B$NC10L ${c_{p}^{\dagger}}_{d}=c_{p}/M_{d}$ $B$OC10L $\lambda^{\dagger}=\lambda/M_{v}$ $B$OC10L $B$O>e>:[email protected],$N:.9gHf$G$"$j(B, $B5$2t$N<~0O$NBg(B $B5$$N:.9gHf$r<>EY(B $r$ $B$rMQ$$$F(B $r q$ $B$H$7$?(B.

$B0J2<$G$O(B, $BA0@a$G5a$a$?<>=aCGG.29EY8:N($H@EE*0BDjEY$,(B, $B$=$l$>$l(B (63), (65) $B<0$GI=8=$5$l$k$3$H$r<($9(B. $B$^$?(B () $B$H(B (65) $B<0$rJQ7A$9$k$3$H$G(B (64) $B$H(B (66) $B<0$,$=$l$>$lF3$+$l$k$3$H$r<($9(B.

(63) $B<0$O(B (60) $B<0$K$*$$$F(B, $M \approx M_{d}, R^{\dagger}_{v} = R^{\dagger} / \varepsilon$ $B$H$9$k$3$H$GD>$A$K5a$^(B $B$k(B. mail protected],$N>/$J$$$H$9$k>r7o$,@.N)$9$k>l9g$K$O(B $1 \gg \frac{{\lambda^{\dagger}}^{2} q}{R_{v}^{\dagger} {c_{p}^{\dagger}}_{d} T^{2}}$ $B$H$J$k$N$G(B, (64) $B<0$O0J2<$N$h$&$KF3=P$5$l$k(B.

$$\DD{T}{z} = - \frac{g}{{c_{p}^{\dagger}}_{d}} \left( \frac{ 1 + \frac{\lambda... ...mbda^{\dagger}}^{2} q}{R_{v}^{\dagger} {c_{p}^{\dagger}}_{d} T^{2}} } \right) ,$$

$$\approx - \frac{g}{{c_{p}^{\dagger}}_{d}} \left( 1 + \frac{\lambda^{\dagg... ...\lambda^{\dagger}}^{2} q}{R_{v}^{\dagger} {c_{p}^{\dagger}}_{d} T^{2}} \right),$$

$$= - \frac{g}{{c_{p}^{\dagger}}_{d}} \left\{ 1 - \left( \frac{\lambd... ...\right) \frac{\lambda^{\dagger} q^{\dagger}}{{c_{p}^{\dagger}}_{d} T} \right\}.$$

$B$?$@$7(B $q$ $B$N(B 2 $Br7o$N>l9g(B, $B$3$N6a;w$,@.N)$9$k>r7o$O$*$*$h$=(B $q \ll 2.0 \times 10^{-2}$ $B$G$"$k(B.

$B@EE*0BDjEY$N<0(B (65) $B$O(B, $B@EE*0BDjEY$N<0(B (55) $B$K$*$$$F(B, $BC10L%b%kEv$?$j$N(B $BNL$rC10L/$J$$>r7o2<$G$N%b%kHf$H:.9gHf$N4X78<0(B (61) $B$*$h$SJ,;RNL$N4X78(B (62) $B$rMQ$$$k$3$H$G5a$^$k(B.

$$N^{2} = \frac{g}{T} \left( \Gamma_{m} + \frac{M g}{{c_{p}^{\dagger}}_{d} M} \right) - g \left( \frac{r (M_{v} - M_{d})}{M} \DD{X}{z} \right)$$

$$= \frac{g}{T} \left( \Gamma_{m} + \frac{ g}{{c_{p}^{\dagger}}_{d}} ... ... g \left( \frac{r (M_{v} - M_{d})}{M_{d}} \frac{M_{d}}{M_{v}} \DD{q}{z} \right)$$

$$= \frac{g}{T} \left( \Gamma_{m} + \frac{ g}{{c_{p}^{\dagger}}_{d}} \right) + g \left( \frac{M_{d}}{M_{v}} - 1 \right) \DD{(r q)}{z}$$

$B$?$@$7(B $dT/dz = \Gamma_{m}$ $B$H$7$?(B. $B$5$i$K(B (65) $B<0$NJQ7A$r(B $B9T$&(B. (31) $B<0$r(B $dq/dz$ $B$N<0$K=q$-49$($k$H(B,

$$\DD{ ( r q )}{z} = \left( \frac{ \lambda^{\dagger} M_{v} }{ R^{\dagger}_{d} M_{d} T^{2}} \DD{T}{z} + \frac{M g }{ R^{\dagger}_{d} M T} \right) (r q) ,$$

$$= \left( - \frac{ \lambda^{\dagger} }{ R^{\dagger}_{v} T^{2}} \frac{g}{{c_{p}^{\dagger}}_{d}} + \frac{g }{ R^{\dagger}_{d} T} \right) (r q) ,$$

$$= \frac{g}{{c_{p}^{\dagger}}_{d} T} \left( \frac{ {c_{p}^{\dagger}}... ...\dagger}_{d} } - \frac{ \lambda^{\dagger} }{ R^{\dagger}_{v} T} \right) (r q) .$$ (67)

$B$H$J$k(B. $B$?$@$7(B $q$ $B$O>.$5$$$N$G(B, $dT/dz \approx - g /{c_{p}^{\dagger}}_{d}$ $B$H$7$?(B. (67) $B<0$H(B (64) $B<0$r(B (65) $B<0$K(B $BBeF~$9$k$3$H$G(B, (66) $B<0$,F@$i$l$k(B.

$$N^{2} = \frac{g}{T} \left( \Gamma_{m} + \frac{ g}{{c_{p}^{\dagger}}_{d}} \right) + g \left( \frac{M_{d}}{M_{v}} - 1 \right) \DD{(r q)}{z}$$

$$= \frac{g}{T} \left[ \frac{g}{{c_{p}^{\dagger}}_{d}} \left\{ \left(... ...{d} } - \frac{ \lambda^{\dagger} }{ R^{\dagger}_{v} T} \right) (r q) \right\} ,$$

$$= \frac{g^{2}}{{c_{p}^{\dagger}}_{d} T} \left( \frac{\lambda^{\dagg... ...{c_{p}^{\dagger}}_{d} T} + r \left( 1 - \frac{M_{d}}{M_{v}} \right) \right\} q.$$

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