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\section{$B4pACJ}Dx<07O(B}

 $B$3$N@a$G$OM}A[5$BN$r2>Dj$7$?4%AgBg5$$KBP$9$k(B 2 $B<!85=`05=L7O$N4pACJ}Dx<0(B
 $B$rF3=P$9$k(B. $B6E7kJ*<A$r4^$^$J$$$3$H$r$N$>$-(B, $B$3$l$i$NJ}Dx<07O$O(B Klemp
 and Wilhelmson (1978) $B$HF1MM$G$"$k(B.
 
\subsection{$BJQ?t$NDj5A(B}

 $B%b%G%k$NFHN)JQ?t$O6u4V$NJQ?t(B $x, z$ $B$H;~4V$NJQ?t(B $t$ $B$G$"$k(B.
 $B%b%G%k$NM=JsJQ?t$O$3$l$i$N4X?t$H$7$FDj5A$5$l$k(B
  \begin{center}
   \begin{tabular}[tb]{lll}
    $u$ & : & $BB.EY$N(B $x$ $B@.J,(B \\
    $w$ & : & $BB.EY$N(B $z$ $B@.J,(B \\
    $\Theta$ & : & $B290L(B \\
    $\Pi$ & : & $BL5<!8505NO4X?t(B 
   \end{tabular}
  \end{center}
 $B$G$"$k(B.

 $BL5<!8505NO4X?t(B ($B%(%/%9%J!<4X?t(B) $\pi$ $B$O05NO(B $p$ $B$rMQ$$$F0J2<$N$h$&$KDj5A$5$l(B
 $B$k(B.
 \begin{equation}
  \Pi \equiv \left(\frac{p}{p_{0}}\right)^{R_{d}/c_{p}}
  \Deqlab{$B%(%/%9%J!<4X?t(B}
 \end{equation}
 $p_{0}$ $B$OCOI=LL$G$N5$05$G$"$k(B.
 $B290L(B $\Theta$ $B$O(B
 \begin{eqnarray}
  \Theta &\equiv& T \left(\frac{p_{0}}{p}\right)^{R_{d}/c_{p}}
  \nonumber \\
         &=& \frac{T}{\Pi}
  \Deqlab{$B290L(B}
 \end{eqnarray}
 $B$GM?$($i$l$k(B. 
 $B$3$3$G(B $T$ $B$O29EY(B, $c_{p}$ $B$O(B
 $BDj05HfG.(B, $R_{d}$ $B$O4%Ag6u5$$N5$BNDj?t$G$"$k(B.

%--------------------------------------------------------------------
\pagebreak

\subsection{$B4pACJ}Dx<0(B}

 $B4pACJ}Dx<0$O(B, $B4pK\>l$N@E?e05$N<0(B, $B1?F0J}Dx<0(B, $B05NOJ}Dx<0(B, $BG.NO3X$N<0$G$"$k(B. 
 $B4pK\>l$O?eJ?0lMM$J@E;_>uBV$G$"$k$H$7(B, 
 $B4pK\>l$NJQ?t$O>eIU$-%P!<(B $(\bar{~})$ $B$GI=$9(B.

 {\bf $B@E?e05$N<0(B} :
 \begin{equation}
  \DP{\overline{\Pi}}{z} = - \frac{g}{c_{p} \overline{\theta}}
 \end{equation}
 $B4pK\>l$NL)EY(B $\overline{\rho}$ $B$OM}A[5$BN$N>uBVJ}Dx<0$+$i(B
 $B0J2<$N$h$&$KM?$($i$l$k(B. 
 \begin{equation}
   \overline{\rho} = \frac{p_{0}}{R_{d}}
                    \frac{\overline{\Pi}^{c_{v}/R_{d}}}{\overline{\theta}}
 \end{equation}

 {\bf $B1?F0J}Dx<0(B} :
 \begin{eqnarray}
  \DD{u_{i}}{t} = - c_{p} \overline{\theta}_{v} \DP{\pi}{x_{i}}
   + \delta_{i3} g
       \frac{\theta}{\overline{\theta}}
       + D_{u_{i}}.
 \end{eqnarray}
 $B$3$3$G(B $i=1,3$ $B$G(B $u_{1}=u, u_{3}=w$ $B$G$"$k(B.
 $B:8JU$N;~4VHyJ,$O0J2<$N$h$&$KI=$5$l$k(B.
 \begin{eqnarray}
   \DD{}{t} = \DP{}{t} + u_{i}\DP{}{x_{i}}.
 \end{eqnarray}
 $D_{u_{i}}$ $B$O%5%V%0%j%C%I%9%1!<%k$NMpN.$KH<$&3H;69`$G$"$j(B, $B>\:Y$O(B
 \ref{$B%5%V%0%j%C%I%9%1!<%k$N3H;6(B}$B@a$G=R$Y$k(B.

 {\bf $B05NOJ}Dx<0(B} :
 \begin{eqnarray}
    \DP{\pi}{t}
     + \frac{\overline{c}^{2}}{c_{p}
         \overline{\rho} \overline{\theta}^{2}}
         \DP{}{x_{j}}
	 \left(\overline{\rho} \overline{\theta}_{v} u_{j}\right)
     = 0.
 \end{eqnarray}
 $B$3$3$G(B $\overline{c}$ $B$O4pK\>l$N2;B.$G$"$j(B, $B0J2<$N$h$&$KM?$($i$l$k(B.
 \begin{equation}
  \overline{c^{2}} = \frac{c_{p} R_{d}}{c_{v}}
                  \overline{\Pi} \overline{\theta}
  .
 \end{equation}
 $B$3$3$G(B $c_{v}$ $B$ODj@QHfG.$G$"$k(B.

 {\bf $BG.NO3X$N<0(B} :
 \begin{eqnarray}
  \DD{\theta}{t} = D_{\theta}
  .
 \end{eqnarray}
 $D_{\theta}$ $B$O%5%V%0%j%C%I%9%1!<%k$NMpN.$KH<$&3H;69`$G$"$k(B.


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\pagebreak

\subsection{$B%5%V%0%j%C%I%9%1!<%k$NMpN.3H;6(B}
\label{$B%5%V%0%j%C%I%9%1!<%k$NMpN.3H;6(B}

 {\bf $B1?F0J}Dx<0Cf$N3H;69`(B} :
 \begin{eqnarray}
  D_{u_{i}} = - \DP{}{x_{j}}
       \left[
          - K_{m} \left(\DP{u_{i}}{x_{j}}
	  	        + \DP{u_{j}}{x_{i}}\right)
	  + \frac{2}{3} \delta_{ij} E
       \right].
 \end{eqnarray}
 $B$3$3$G(B $K_{m}$ $B$O1?F0NL$KBP$9$kMpN.3H;678?t$G$"$j(B,  $E$ $B$O(B
 $B%5%V%0%j%C%I%9%1!<%k$NMpN.1?F0%(%M%k%.!<(B
 \begin{eqnarray}
  E = \frac{1}{2}
      \overline{(u^{\prime \prime})^{2} 
	              + (w^{\prime \prime})^{2}}
 \end{eqnarray}
 $B$G$"$k(B.

 {\bf $BG.NO3X$N<0$N3H;69`(B} :
 \begin{eqnarray}
  D_{\theta} &=& \DP{}{x_{j}}
	            \left(K_{h}\DP{\theta}{x_{j}}\right)
  .
 \end{eqnarray}
 $B$3$3$G(B $K_{h}$ $B$O290L$KBP$9$kMpN.3H;678?t$G$"$k(B.

{\bf $BMpN.1?F0%(%M%k%.!<$N<0(B} :
 \begin{eqnarray}
  \DD{E}{t}
     &=& -\frac{g}{\overline{\theta}}
         K_{h} \DP{\theta_{e}}{z}
         + 2 K_{m} \left(\DP{u_{j}}{x_{j}}\right)^{2}
         + \frac{1}{2} \, |\varepsilon_{ijk}| K_{m}
	   \left(\DP{u_{j}}{x_{i}} + \DP{u_{i}}{x_{j}}\right)^{2}
  \nonumber \\
     & & - \frac{3}{2} \delta_{ij} E
         \left(\DP{u_{j}}{x_{j}}\right)
         + \DP{}{x_{j}} \left(K_{m} \DP{E}{x_{j}}\right)
		- \left(\frac{C_{\varepsilon}}{l}\right)
	  E^{\frac{3}{2}}.
 \end{eqnarray}
 $l$ $B$O:.9g5wN%$G$"$j(B $l = \left(\Delta x \Delta z\right)^{1/2}$ , 
 $C_{\varepsilon} = 0.2$ $B$H$9$k(B.    

 $K_{m}$, $K_{h}$ $B$O(B $E$ $B$rMQ$$$F0J2<$N$h$&$KM?$($i$l$k(B.
 \begin{eqnarray}
  K_{m} &=& C_{m} E^{\frac{1}{2}} l,\\
  K_{h} &=& 3 K_{m}.
 \end{eqnarray}
 $B$3$3$G(B $C_{\varepsilon} = C_{m}$ $B$H$9$k(B. 

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