% $BI=Bj(B: $BCGG.29EY8:N($N7W;;(B
%
% $BMzNr(B: 2004-11-19 $B?y;39L0lO/(B


\section{$B<>=aCGG.8:N($N7W;;(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, 
%
\begin{eqnarray}
dU = \delta Q + \delta W + \delta Z ,
\Deqlab{1}
\end{eqnarray}
$B$G$"$k(B. 
%
$B$3$3$G(B $dU$ $B$OFbIt%(%M%k%.!<!$(B
 $\delta Q$ $B$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$7$F<h$j07$&$3$H$,$G$-!$(B
$B$=$NJQ2=$OCGG.E*$K$G$"$k$H$9$k$H!$(B
 \Deqref{3} $B<0$N3F9`$O0J2<$N$h$&$K=q$1$k!%(B
%
\begin{eqnarray}
dU &=& \bar{c_{v}} dT. 
 \Deqlab{2}\\
\delta Q &=& 0. 
 \Deqlab{3}\\
\delta W &=& - p dV, \nonumber \\
&=& - d(pV) + V dp,\nonumber \\
&=& - R dT + V dp, \nonumber \\
&=& - R dT + V \left( \frac{- \bar{M} p g}{R T} \right) dz, 
\; ($B"h(B $B@E?e05J?9U$N<0(B)\nonumber \\
&=&  - R dT - \bar{M} g  dz . 
 \Deqlab{4}\\
\delta Z &=& - \sum \lambda_{k} dX_{k}. 
 \Deqlab{5}
\end{eqnarray}
%
$B$3$3$G(B $\bar{c_{v}}$ $B$OBg5$$NDj@Q%b%kHfG.$NJ?6QCM!$(B
$T$ $B$O29EY(B, $p$ $B$O05NO(B, 
$V$ $B$O(B $B5$BNJ,;R$N(B 1 $B%b%kEv$?$j$NBN@Q!$(B
$R$ $B$O5$BNDj?t(B, $\bar{M}$ $B$OJ?6QJ,;RNL(B, 
$g$ $B$O=ENO2CB.EY(B, 
 $\lambda_{k}$ $B$O(B $k$ $BHVL\$N6E=L@.J,5$BN$N%b%kEv$?$j$N(B
$B6E=L$N%(%s%?%k%T!<!$(B
 $dX_{k}$ $B$O5$BN(B $k$ $B$N%b%kHf$NJQ2=$G$"$k(B. 
%
\Deqref{1} $B<0$K(B \Deqref{2} -- \Deqref{5} $B<0$rBeF~$9$k$3$H$G(B, 
%
\begin{eqnarray}
&& \bar{c_{v}}dT + R dT + \bar{M} g dz   + \sum \lambda_{k} dX_{k} = 0 ,\nonumber \\
&& \bar{c_{p}}dT + \bar{M} g dz   + \sum \lambda_{k} dX_{k} = 0 ,
\Deqlab{dQ}
\end{eqnarray}
%
$B$H$J$k!%C"$7(B $\bar{c_{p}}$ $B$OBg5$$NDj05%b%kHfG.$NJ?6QCM$G!$(B
$BM}A[5$BN$N>l9g(B $\bar{c_{p}} = \bar{c_{v}} + R$ $B$G$"$k!%(B


\subsection{$B4%AgCGG.29EY8:N((B}

\Deqref{dQ} $B<0$N@xG.$K$h$k9`$rL5;k$9$k$3$H$G4%AgCGG.29EY8:N($,(B
$B5a$^$k!%4%Ag@.J,$NHfG.$r(B $c_{p}$, $B4%Ag@.J,$NJ,;RNL$r(B $M_{d}$ $B$H$9$k$H(B, 
%
\begin{eqnarray}
 && c_{p} dT + M_{d} g dz = 0, \nonumber \\
 &&\DD{T}{z} = - \frac{ M_{d} g }{c_{p}}.
\Deqlab{dtdz-dry}
\end{eqnarray}
%
$B$^$?(B, $B29EY$N05NOHyJ,$O0J2<$N$h$&$K=q$1$k(B. 
%
\begin{eqnarray}
 &&\DD{T}{p} =  \frac{ R T }{ c_{p} p }.
\Deqlab{dtdp-dry}
\end{eqnarray}
%


\subsection{$B<>=aCGG.29EY8:N((B}

\Deqref{dQ} $B<0Cf$N(B $dX_{k}$ $B$r%b%kJ,N($HJ,05$N4X78(B
%
\begin{eqnarray}
dX_{k} &=& \Dinv{p} dp_{k} - \left( \frac{p_{k}}{p^{2}} \right) dp.
 \Deqlab{X}
\end{eqnarray}
%
$B$H%/%i%&%8%&%9!&%/%i%Z%$%m%s$N<0(B
%
\begin{eqnarray}
dp_{k} = \frac{p_{k} \lambda_{k}dT}{R T^{2}}, 
 \Deqlab{CK}
\end{eqnarray}
%
$B$rMQ$$$FJQ7A$9$k$H(B, 
%
\begin{eqnarray}
dX_{k} &=& \Dinv{p} dp_{k} - \frac{p_{k}}{p^{2}} dp, \nonumber \\
&=& \Dinv{p} \left( \frac{p_{k} \lambda_{k} dT}{R T^{2}} \right)
- \frac{p_{k}}{p^{2}} \left( - \frac{ \bar{M} p g}{R T} dz \right) , \nonumber \\ 
&=& \frac{p_{k}}{p} \frac{\lambda_{k}}{ R_{v} T^{2}} dT
+  \frac{p_{k}}{p} \frac{\bar{M} g}{ R T} dz , \nonumber \\ 
&=& \frac{ \lambda_{k} X_{k} }{ R T^{2}} dT
+  \frac{\bar{M} g X_{k}}{ R T} dz .
\Deqlab{Xk}
\end{eqnarray}
%
$B$G$"$k(B. 

\Deqref{dQ} $B<0$K(B \Deqref{Xk} $B<0$rBeF~$9$k$3$H$G<>=aCGG.29EY8:N($,5a$^$k!%(B
%
\begin{eqnarray}
 &&\bar{c_{p}} dT + \bar{M} g dz + \sum \lambda_{k} dX_{k} = 0, \nonumber \\
 &&\bar{c_{p}} dT + \bar{M} g dz + 
  \sum \lambda_{k} 
  \left(\frac{\lambda_{k} X_{k} }{ R T^{2}} dT
    +  \frac{\bar{M} g X_{k}}{ R T} dz \right)  = 0, \nonumber \\
&&\bar{c_{p}} 
\left( 1+ \frac{\sum \lambda^{2}_{k} X_{k}}{ \bar{c_{p}} R T^{2}} \right) dT 
+ \bar{M} g \left( 1 +  \frac{\sum \lambda_{k} X_{k}}{R T} \right) dz 
= 0, \nonumber \\
 &&\DD{T}{z} = - \frac{\bar{M} g}{\bar{c_{p}}} 
  \left(
 \frac{ 1 +  \frac{ \lambda_{k} X_{k}}{R T}}
{ 1 + \frac{ \lambda^{2}_{k} X_{k}}{ \bar{c_{p}} R T^{2}} }
 \right). 
\Deqlab{dtdz}
\end{eqnarray}
%
$BC"$7OB$N5,Ls$rMQ$$$F$$$k(B. \Deqref{dtdz} $B$rJQ7A$9$k$H(B, 
%
\begin{eqnarray}
 &&\DD{T}{p} =  \frac{R T}{\bar{c_{p}} p} 
  \left(
 \frac{ 1 +  \frac{ \lambda_{k} X_{k}}{R T}}
{ 1 + \frac{ \lambda^{2}_{k} X_{k}}{ \bar{c_{p}} R T^{2}} }
 \right). 
\Deqlab{dtdp}
\end{eqnarray}
%
$B$G$"$k(B. 


\Deqref{dtdz} $B$K$*$$$F==J,$K6E=L@-@.J,$N>/$J$$>l9g(B, $B$D$^$j(B
%
\begin{eqnarray}
\frac{ \lambda^{2}_{k} X_{k} }{ \bar{c_{p}} R T^{2} } \ll 1 
  \Deqlab{approx_low}
\end{eqnarray}
%
$B$N>l9g$K$O(B, 
%
\begin{eqnarray}
\DD{T}{z} 
 &\approx& - \frac{\bar{M} g}{\bar{c_{p}}} 
  \left( 1 +  \frac{ \lambda_{k} X_{k}}{R T} \right)
  \left( 1 - \frac{ \lambda^{2}_{k} X_{k}}{ \bar{c_{p}} R
   T^{2}} \right) ,
  \nonumber \\
 &\approx& - \frac{\bar{M} g}{\bar{c_{p}}} 
  \left\{  1 -  \frac{\lambda_{k} X_{k}}{\bar{c_{p}} T} 
   \left( \frac{ \lambda_{k}}{ R T} 
    - \frac{\bar{c_{p}}}{R} \right) \right\}. 
\Deqlab{dtdz_low}
\end{eqnarray}
%
$B$H6a;w$G$-$k(B.  $B?e$N6E=L$N>l9g$NBeI=E*$JCM$rBeF~$9$k$H(B$ \lambda_{k} /
\bar{c_{p}} T > 1$ $B$G$"$k(B. $B$=$N$?$a(B$ \lambda^{2}_{k} X_{k}/ \bar{c_{p}}
R T^{2} \ll 1 $ $B$J$i$PI,$:(B $\lambda_{k} X_{k} / R T \ll 1$ $B$G$"$k(B.
\Deqref{dtdz_low} $B<0$NF3=P$K$*$$$F(B, $B$3$l$i(B 2 $B<!$NHy>.NL$N@Q$O==J,$K>.$5(B
$B$$$b$N$H$_$J$7L5;k$7$?(B.


\Deqref{dtdz} $B$K$*$$$F==J,$K6E=L@-@.J,$NB?$$>l9g(B, $B$9$J$o$A(B 
%
\begin{eqnarray}
 \frac{\lambda_{k} X_{k} }{R T }\gg 1 
\Deqlab{approx_high}
\end{eqnarray}
%
$B$N>l9g$K$O(B, 
%
\begin{eqnarray}
\DD{T}{z} 
 &\approx& - \frac{\bar{M} g}{\bar{c_{p}}} 
  \frac{\frac{ \lambda_{k} X_{k}}{R T}}
  {\frac{ \lambda^{2}_{k} X_{k}}{ \bar{c_{p}} R
   T^{2}} } ,
  \nonumber \\
 &\approx& 
  - \frac{\bar{M} g}{\bar{c_{p}}} \frac{\bar{c_{p}} T}{\lambda_{k}}
\Deqlab{dtdz_high}
\end{eqnarray}
%
$B$H6a;w$G$-$k(B. $B?e$N6E=L$N>l9g$NBeI=E*$JCM$rBeF~$9$k$H(B$ \lambda_{k} /
\bar{c_{p}} T > 1$ $B$G$"$k(B. $B$=$N$?$a(B $\lambda_{k} X_{k} / R T \gg 1$ 
$B$J$i$PI,$:(B $\lambda^{2}_{k} X_{k}/ \bar{c_{p}}
R T^{2} \gg 1 $ $B$G$"$k(B. 


\begin{screen}
\begin{description}
\item[$B<>=aCGG.29EY8:N((B]
\begin{eqnarray}
\DD{T}{z} &=& - \frac{\bar{M} g}{\bar{c_{p}}} 
  \left(
 \frac{ 1 +  \frac{ \lambda_{k} X_{k}}{R T}}
{ 1 + \frac{ \lambda^{2}_{k} X_{k}}{ \bar{c_{p}} R T^{2}} }
 \right). 
\nonumber 
\end{eqnarray}

\item[$B2D6E=L@.J,$NB8:_NL$,>.$5$$>l9g(B]
\begin{eqnarray}
\DD{T}{z} 
 &\approx& - \frac{\bar{M} g}{\bar{c_{p}}} 
  \left\{  1 -  \frac{\lambda_{k} X_{k}}{\bar{c_{p}} T} 
   \left( \frac{ \lambda_{k}}{ R T} 
    - \frac{\bar{c_{p}}}{R} \right) \right\}. 
\nonumber 
\end{eqnarray}

\item[$B2D6E=L@.J,$NB8:_NL$,Bg$-$$>l9g(B]
\begin{eqnarray}
\DD{T}{z} 
 &\approx& 
  - \frac{\bar{M} g}{\bar{c_{p}}} \frac{\bar{c_{p}} T}{\lambda_{k}}. 
\nonumber 
\end{eqnarray}
\end{description}
\end{screen}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{$B2>29EY8:N($N7W;;(B}

$BCGG.29EY8:N($+$i2>29EY8:N($r7W;;$9$k(B. 
%
\begin{eqnarray}
 \DD{T_{v}}{z} 
  &=& \DD{}{z}\left( \frac{M_{d}}{\bar{M}} T \right)
  \nonumber \\
 &=& \frac{M_{d}}{\bar{M}} \DD{T}{z} - \frac{M_{d} T}{\bar{M}^{2}}
  \DD{\bar{M}}{z}
  \Deqlab{vdtdz_org}
   \\
 &=& \frac{M_{d}}{\bar{M}} \DD{T}{z} - \frac{M_{d} T}{\bar{M}^{2}} 
  \DD{}{z}(M_{d}(1 - X) + M_{v} X)
  \nonumber \\
 &=& \frac{M_{d}}{\bar{M}} \DD{T}{z} - \frac{M_{d} T}{\bar{M}^{2}} 
  \DD{}{z}\left\{ (M_{v} - M_{d}) X \right\}
  \nonumber \\
 &=& \frac{M_{d}}{\bar{M}} \DD{T}{z} 
  - \frac{M_{d} (M_{v} - M_{d}) T}{\bar{M}^{2}} 
    \DD{X}{z}
  \nonumber 
\end{eqnarray} 
%
$B$?$@$7(B, $M_{d}$ $B$O4%Ag5$2t$NJ,;RNL(B, $M_{v}$ $B$O6E=L@.J,$NJ,;RNL(B, $T_{v} =
M_{d} T / \bar{M}$ $B$O2>29EY$G$"$k(B. $B$3$3$G%/%i%&%8%&%9!&%/%i%Z%$%m%s$N<0(B
(\Deqref{Xk} $B<0(B)$B$rBeF~$9$k$H(B, 
%
\begin{eqnarray}
 \DD{T_{v}}{z} 
  &=& \frac{M_{d}}{\bar{M}} \DD{T}{z} 
  - \frac{M_{d} (M_{v} - M_{d}) T}{\bar{M}^{2}} 
\left\{
  \frac{ \lambda_{k} X_{k} }{ R T^{2}} \DD{T}{z}
  +  \frac{\bar{M} g X_{k}}{ R T} 
\right\} 
\nonumber \\
  &=& \frac{M_{d}}{\bar{M}} \DD{T}{z} 
  - \frac{M_{d} (M_{v} - M_{d}) }{\bar{M}^{2}} 
    \frac{ \lambda_{k} X_{k} }{ R T } \DD{T}{z}
  - \frac{M_{d} (M_{v} - M_{d}) }{\bar{M}} 
    \frac{ g X_{k}}{ R} 
\nonumber \\
  &=& \frac{M_{d}}{\bar{M}}
   \left(  
    1 - \frac{(M_{v} - M_{d}) }{\bar{M}} 
    \frac{ \lambda_{k} X_{k} }{ R T } 
   \right) \DD{T}{z}
  - \frac{M_{d} (M_{v} - M_{d}) }{\bar{M}} 
    \frac{ g X_{k}}{ R} 
\Deqlab{vdtdz}
\end{eqnarray}


$B2D6E=L@.J,$NB8:_NL$,>.$5$$>l9g$K$O(B, \Deqref{vdtdz} $B<0$K(B \Deqref{dtdz_low} 
$B<0$rBeF~$9$k$H(B, 
%
\begin{eqnarray}
\DD{T_{v}}{z}
  \approx 
  - \frac{ M_{d} (M_{v} - M_{d}) }{\bar{M}} 
    \frac{ g X_{k} }{ R} 
  - 
  \frac{M_{d} g}{\bar{c_{p}}}
  \left(
   1 
   + \frac{ \lambda_{k} X_{k}}{R T}
   - \frac{ \lambda^{2}_{k} X_{k}}{ \bar{c_{p}} R T^{2}} 
   - \frac{ M_{v} - M_{d} }{\bar{M}}  \frac{ \lambda_{k} X_{k}}{R T}
  \right)
\Deqlab{vdtdz_low}
\end{eqnarray}
%
$B$H$J$k(B. 


$B2D6E=L@.J,$NB8:_NL$,Bg$-$$>l9g$K$O(B, \Deqref{vdtdz} $B<0$K(B
 \Deqref{dtdz_high} $B<0$rBeF~$9$k$H(B, 
%
\begin{eqnarray}
\DD{T_{v}}{z} 
&\approx& 
   - \frac{M_{d}}{\bar{M}}
       \left( \frac{ \bar{M} g}{\bar{c_{p}}} 
             \frac{\bar{c_{p}} T}{\lambda_{k}} \right)
    - \frac{M_{d} T}{\bar{M}^{2}} \DD{\bar{M}}{z}
\nonumber \\
&\approx& - \frac{ M_{d} g}{\bar{c_{p}}} 
             \frac{\bar{c_{p}} T}{\lambda_{k}} 
    - \frac{M_{d} T}{\bar{M}^{2}} \DD{\bar{M}}{z}
\Deqlab{vdtdz_high}
\end{eqnarray}
%
$B$H$J$k(B. $BCGG.8:N((B \Deqref{dtdz} $B<0$K$h$C$F7h$a$?29EY(B, $B05NO(B, $BAH@.$rMxMQ$7$F(B
$B2D6E=L@.J,$NB8:_NL$,Bg$-$$>l9g$N29EY8:N($r(B \Deqref{dtdz_high} $B<0$+$i5a$a(B
$B$k$H(B, $B%/%i%&%8%&%9!&%/%i%Z%$%m%s$N<0$,I,$:$7$bK~$?$5$l$J$$(B. $B$3$N$?$a(B, 
\Deqref{vdtdz_org} $B<0$+$i2>29EY8:N($rI>2A$9$k$3$H$H$7$?(B. 



\begin{screen}
\begin{description}
\item[$B2>29EY8:N((B]
\begin{eqnarray}
\DD{T_{v}}{z}
  = 
  &-& \frac{ M_{d} (M_{v} - M_{d}) }{\bar{M}} 
    \frac{ g X_{k} }{ R} 
\nonumber \\
  &-& 
  \frac{M_{d} g}{\bar{c_{p}}}
   \left(  
    1 - \frac{ M_{v} - M_{d} }{\bar{M}} 
    \frac{ \lambda_{k} X_{k} }{ R T } 
   \right) 
 \frac{ 1 +  \frac{ \lambda_{k} X_{k}}{R T}}
{ 1 + \frac{ \lambda^{2}_{k} X_{k}}{ \bar{c_{p}} R T^{2}} }
\nonumber 
\end{eqnarray}

\item[$B2D6E=L@.J,$NB8:_NL$,>.$5$$>l9g(B]
\begin{eqnarray}
\DD{T_{v}}{z}
  \approx &-& \frac{ M_{d} (M_{v} - M_{d}) }{\bar{M}} 
    \frac{ g X_{k} }{ R} 
\nonumber \\
  &-& 
  \frac{M_{d} g}{\bar{c_{p}}}
  \left(
   1 
   + \frac{ \lambda_{k} X_{k}}{R T}
   - \frac{ \lambda^{2}_{k} X_{k}}{ \bar{c_{p}} R T^{2}} 
   - \frac{ M_{v} - M_{d} }{\bar{M}}  \frac{ \lambda_{k} X_{k}}{R T}
  \right)
\nonumber 
\end{eqnarray}

\item[$B2D6E=L@.J,$NB8:_NL$,Bg$-$$>l9g(B]
\begin{eqnarray}
\DD{T_{v}}{z} 
&\approx& 
   -  \frac{ M_{d} g}{\bar{c_{p}}} 
             \frac{\bar{c_{p}} T}{\lambda_{k}} 
    - \frac{M_{d} T}{\bar{M}^{2}} \DD{\bar{M}}{z}
\nonumber 
\end{eqnarray}
\end{description}
\end{screen}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{$B@EE*0BDjEY$N7W;;(B}

$B@EE*0BDjEY(B $N^{2}$ $B$r<>=aCGG.8:N($H4%AgCGG.8:N($N:9$+$iI>2A$9$k$H(B, 
%
\begin{eqnarray}
 N^{2} = 
  \frac{g}{T_{v}} \left( \DD{T_{v}}{z} + \frac{M_d g}{c_{p}} \right)
\Deqlab{vstab}
\end{eqnarray}
%
$B$G$"$k(B. $B$3$3$G(B ${c_{p}}$ $B$O4%Ag5$2t$NHfG.$G$"$k(B. 


$B2D6E=L@.J,$NB8:_NL$,>.$5$$>l9g(B, \Deqref{vstab} $B<0$K(B \Deqref{vdtdz_low} 
$B<0$rBeF~$9$k$H(B, 
%
\begin{eqnarray}
N^{2} &=& 
 \frac{\bar{M} g}{M_{d} T}
 \left( \DD{T_{v}}{z} + \frac{M_d g}{c_{p}} \right)
\nonumber \\
&=&
 \frac{\bar{M} g}{M_{d} T}
\left\{
  - \frac{ M_{d} (M_{v} - M_{d}) }{\bar{M}} 
    \frac{ g X_{k} }{ R} 
  - 
  \frac{M_{d} g}{ c_{p} }
  \left(
    \frac{ \lambda_{k} X_{k}}{R T}
   - \frac{ \lambda^{2}_{k} X_{k}}{ c_{p} R T^{2}} 
   - \frac{ M_{v} - M_{d} }{\bar{M}}  \frac{ \lambda_{k} X_{k}}{R T}
  \right)
\right\}
\nonumber \\
&=&
 \frac{\bar{M} g^{2}}{ c_{p} T}
\left\{
 - \frac{ M_{v} - M_{d} }{\bar{M}} 
    \frac{ c_{p} }{ R} 
  -  \frac{ \lambda_{k}}{R T}
   + \frac{ \lambda^{2}_{k}}{ c_{p} R T^{2}} 
   + \frac{ M_{v} - M_{d} }{\bar{M}}  \frac{ \lambda_{k}}{R T}
\right\} X_{k} 
\nonumber \\
&=&
 \frac{\bar{M} g^{2}}{ c_{p} T}
\left\{
 \frac{ M_{v} - M_{d} }{\bar{M}} 
 \left( 
  \frac{ \lambda_{k}}{R T} - \frac{ c_{p} }{ R} 
 \right)
   + \frac{ \lambda_{k}}{ c_{p} T}
   \left(
     \frac{ \lambda_{k} }{ R T } 
    - \frac{ c_{p} }{ R }
   \right)
\right\} X_{k} 
\nonumber \\
&=&
 \frac{M_{d}  g^{2}}{ c_{p} T}
 \left( 
  \frac{ \lambda_{k}}{R T} - \frac{ c_{p} }{ R} 
 \right)
 \left(
  \frac{ \lambda_{k}}{ c_{p} T}
  + \frac{ M_{v} - M_{d} }{M_{d}} 
 \right)
 X_{k} 
\Deqlab{vstab_low}
\end{eqnarray}
%
$B$H$J$k(B. $BC"$76E=LJ*$NNL$,>/$J$$$H$7$F(B
$\bar{c_{p}} = c_{p}$, $\bar{M} = M_{d}$ $B$H$_$J$7$F$$$k(B. 

$B2D6E=L@.J,$NB8:_NL$,Bg$-$$>l9g(B, \Deqref{vstab} $B<0$K(B \Deqref{vdtdz_high}
$B<0$rBeF~$9$k$3$H$G(B, 
%
\begin{eqnarray}
 N^{2} = 
  \frac{g}{T_{v}} 
  \left( 
    - \frac{ M_{d} g}{\bar{c_{p}}} 
      \frac{\bar{c_{p}} T}{\lambda_{k}} 
    - \frac{M_{d} T}{\bar{M}^{2}} \DD{\bar{M}}{z}
   + \frac{M_d g}{c_{p}} 
  \right)
\Deqlab{vstab}
\end{eqnarray}
%
$B$G$"$k(B. 


\begin{screen}
\begin{description}
\item[$B@EE*0BDjEY(B]
\begin{eqnarray}
 N^{2} = 
  \frac{g}{T_{v}} \left( \DD{T_{v}}{z} + \frac{M_d g}{c_{p}} \right)
\nonumber 
\end{eqnarray}

\item[$B2D6E=L@.J,$NB8:_NL$,>.$5$$>l9g(B]
\begin{eqnarray}
N^{2} \approx
 \frac{M_{d}  g^{2}}{ c_{p} T}
 \left( 
  \frac{ \lambda_{k}}{R T} - \frac{ c_{p} }{ R} 
 \right)
 \left(
  \frac{ \lambda_{k}}{ c_{p} T}
  + \frac{ M_{v} - M_{d} }{M_{d}} 
 \right)
 X_{k} 
\nonumber 
\end{eqnarray}

\item[$B2D6E=L@.J,$NB8:_NL$,Bg$-$$>l9g(B]
\begin{eqnarray}
 N^{2} \approx
  \frac{g}{T_{v}} 
  \left( 
    - \frac{ M_{d} g}{\bar{c_{p}}} 
      \frac{\bar{c_{p}} T}{\lambda_{k}} 
    - \frac{M_{d} T}{\bar{M}^{2}} \DD{\bar{M}}{z}
   + \frac{M_d g}{c_{p}} 
  \right)
\nonumber
\end{eqnarray}
\end{description}
\end{screen}

