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% $BMzNr(B 2004/11/24 $B>.9b@5;L(B $B:n@.3+;O(B
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\chapter{$B2;GH8:?j9`$K$D$$$F(B}

$BK\%b%G%k$GMQ$$$F$$$k;~4VJ}8~$NN%;62=J}K!(B($B;~4VJ,3dK!(B)$B$O(B, Klemp and
Wilhelmson (1978) $B$K$h$C$F:G=i$KDs0F$5$l$?J}K!$G$"$k(B. $B$3$NJ}K!$rMQ$$$k(B
$B$H(B, $B2;B.$*$h$S0\N.$KBP$9$k(B CFL $B>r7o$r$=$l$>$lK~$?$7$F$$$k>l9g$G$b7W;;(B
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$2\Delta t/\Delta \tau$ $B$rA}2C$5$;$F$$$/$K$D$lBg$-$/$J$k(B (Skamarock
and Klemp, 1992, $B?^(B 1 $B$r;2>H(B).  Skamarock and Klemp (1992) $B$O$3$N7W;;(B
$BIT0BDj$r2sHr$9$k$?$a(B, $B2;GH$rA*BrE*$K8:?j$5$;$k%U%#%k%?!<$H$7$F1?F0J}Dx(B
$B<0$K2;GH8:?j9`$rF3F~$9$k$3$H$rDs0F$7$?(B.

$B2;GH8:?j9`$OB.EY>l$NH/;6$KBP$9$k3H;6$H$7$F:nMQ$9$k(B.
$B$3$N$3$H$O2;GH8:?j9`$r4^$`@~7A2=$5$l$?4pACJ}Dx<0(B
\begin{eqnarray}
 \DP{u}{t} &=& - \overline{c}_{p}\overline{\theta}_{v}
                 \DP{\pi}{x} + \alpha\DP{D}{x} , \\
 \DP{w}{t} &=& - \overline{c}_{p}\overline{\theta}_{v}
                 \DP{\pi}{z} + \alpha\DP{D}{z} 
               + g\frac{\theta}{\overline{\theta}_{v}}, \\
 \DP{\pi}{t} &=& - \frac{\overline{c}^{2}}{\overline{c}_{p}
                 \overline{\rho}\overline{\theta}_{v}^{2}}
                 \left[\DP{\overline{\rho}\overline{\theta}_{v}u}{x} +
                       \DP{\overline{\rho}\overline{\theta}_{v}w}{z}
                 \right], \\
 \DP{\theta}{t} &=& -w\DP{\overline{\theta}_{v}}{z}, \\
 D &=& \DP{u}{x}+\DP{w}{z} \nonumber
\end{eqnarray}
$B$+$iH/;6J}Dx<0(B
\begin{eqnarray}
 \DP{D}{t} &=& - \overline{c}_{p}\overline{\theta}_{v}\Dlapla \pi   
               + g\DP{}{z}\left(\frac{\theta}{\overline{\theta}_{v}}\right)
             + \alpha \Dlapla D, \Deqlab{$B2;GH8:?j9`$r4^$`@~7AH/;6J}Dx<0(B}\\
 \Dlapla &=& \DP[2]{}{x} + \DP[2]{}{z} \nonumber
\end{eqnarray}
$B$r5a$a$k$3$H$GM}2r$9$k$3$H$,$G$-$k(B. 

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$B@-$,9M$($i$l$k(B. $B$7$+$7(B Skamarock and Klemp (1992) $B$O@~7A2=$5$l$?4pACJ}(B
$BDx<0$NJ,;64X78$rMQ$$$F(B, $B2;GH8:?j9`$N=ENOGH@.J,$X$N1F6A$O>.$5$$$3$H$r<((B
$B$7$F$$$k(B. $B0J2<$G$O(B Skamarock and Klemp (1992) $B$K$*$1$k5DO@$N35MW$r<($9(B. 
$B4JC1$N$?$a05NOJ}Dx<0$K8=$l$k4pK\>l$NNL$ODj?t$H$7(B, $BA4$F$NJQ?t$r(B 
$u=\hat{u}e^{i(kx+lz -\omega t)}$ $B$N$h$&$J2r$r;}$D$H2>Dj$7$FJ,;64X78$r(B
$B5a$a$k$H(B,
\begin{equation}
  \omega ^{4} + i\alpha (k^{2}+l^{2})\omega ^{3}  - 
  [\overline{c}^{2}(k^{2}+l^{2}) + N^{2}] \omega ^{2}
  - i\alpha k^{2}N^{2}\omega + \overline{c}^{2}k^{2}N^{2}=0, 
\end{equation}
$B$H$J$k(B. $B$3$3$G(B $N^{2} = \frac{g}{\overline{\theta}_{v}}\DP{
\overline{\theta}_{v}}{z}$ $B$G$"$k(B. $B=c?h$JFbIt=ENOGH$NJ,;64X78<0(B
\[
 \omega ^{2} = \frac{N^{2}k^{2}}{k^{2}+l^{2}},
\]
$B$r(B $\alpha$ $B$r4^$`9`$KBeF~$9$k$H(B $\alpha $ $B$r4^$`9`$O8_$$$KBG$A>C$7$"(B
$B$&$3$H$+$i(B, $B2;GH8:?j9`$N=ENOGH@.J,$X$N1F6A$O>.$5$$$G$"$m$&$HM=A[$5$l$k(B. 
$B<B:]$K(B, $\epsilon \equiv \alpha \sqrt{k^{2}+l^{2}}/\overline{c}$ $B$,>.(B
$B$5$$$H2>Dj$7$F(B $\omega$ $B$r(B $\epsilon$ $B$N6R$GE83+$7$F2;GH8:?j9`$N1F6A$r(B
$BI>2A$9$k$H(B, $B2;GH8:?j9`$O=ENOGH@.J,$r8:?j$5$;$kJ}8~$K$O$?$i$-(B, $B$=$N8:?j(B
$BN($OHs>o$K>.$5$$$3$H$,$o$+$k(B(Skamarock and Klemp, 1992, $B?^(B 5 $B;2>H(B).

$B2;GH8:?j9`$N78?t(B $\alpha$ $B$NCM$r7h$a$k$K$"$?$j(B, $B9MN8$7$J$1$l$P$J$i$J$$(B
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$B$J$i$J$$$h$&$9$k$3$H$G$"$k(B. $BA0<T$O(B\Deqref{$B2;GH8:?j9`$r4^$`@~7AH/;6J}Dx(B
$B<0(B}$B$K<($7$?$h$&$K(B, $B2;GH8:?j9`$,H/;6J}Dx<0$N3H;69`$H$J$k$3$H$+$iMW@A$5(B
$B$l$k(B.  $B2;GH8:?j9`$N;~4V@QJ,$OA0?J:9J,$rMQ$$$F9T$o$l$k$N$G(B
(\Deqref{uwpi:u_sabun}, \Deqref{uwpi:w_sabun}$B$r;2>H(B), $B7W;;IT0BDj$r5/$3(B
$B$5$J$$$?$a$K$O3H;69`$rA0?J:9J,$G;~4V@QJ,$9$k>l9g$N0BDj@->r7o(B
\begin{equation}
 \frac{\alpha \Delta \tau}{\mbox{Min}(\Delta x^{2}, \Delta z^{2})} \leq \frac{1}{2}
 \Deqlab{$B2;GH8:?j9`78?t$N>r7o(B1}
\end{equation}
$B$rK~$?$5$J$1$l$P$J$i$J$$(B. $B8e<T$OA0CJMn$G>R2p$7$?(B Skamarock and Klemp
(1992) $B$N5DO@$GMQ$$$?(B $\epsilon$ $B$,>.$5$$$H$$$&2>Dj$+$iMW@A$5$l$k(B
\footnote{$B$3$N>r7o$K4X$9$k5DO@$O(B Skamarock and Klemp (1992) $B$G$O$J$5$l$F(B
$B$$$J$$(B}. $\epsilon$ $B$N:GBgCM$O(B
\begin{eqnarray*}
  \mbox{Max}(\epsilon) 
    &=& \frac{2\alpha}{\mbox{Min}(\Delta x, \Delta z)\overline{c}} \nonumber \\
    &=& \frac{2\alpha \Delta \tau}{\mbox{Min}(\Delta x^{2}, \Delta z^{2})}
        \left/
        \frac{\overline{c}\Delta \tau}{\mbox{Min}(\Delta x, \Delta z)}
        \right.
\end{eqnarray*}
$B$HM?$($i$l$k$N$G(B, $\mbox{Max}(\epsilon) \leq 1$ $B$H$9$k$?$a$K$O(B
\begin{equation}
    \frac{\alpha \Delta \tau}{\mbox{Min}(\Delta x^{2}, \Delta z^{2})}
    \leq \frac{1}{2}
        \frac{\overline{c}\Delta \tau}{\mbox{Min}(\Delta x, \Delta z)}
  \Deqlab{$B2;GH8:?j9`78?t$N>r7o(B2}
\end{equation}
$B$G$J$1$l$P$J$i$J$$(B.\Deqref{$B2;GH8:?j9`78?t$N>r7o(B2}$B1&JU$K8=$l$k2;B.$KBP(B
$B$9$k%/!<%i%s?t$O(B 1 $B$h$j>.$5$$CM$H$9$k$N$G(B, \Deqref{$B2;GH8:?j9`78?t$N>r(B
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$B$k$3$H$K$J$k(B.

