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\documentclass[a4j,12pt]{jarticle}
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\usepackage{Dennou6}                      % dennou-sty-6 $B$r;HMQ(B

\Dtitle[
  {\small 2 $B<!85%V%7%M%9%/%b%G%k(B:$BFbIt=ENOGH$N7W;;(B}] % $B%X%C%@It%?%$%H%k(B, $B%b%G%kL>$HF1$8(B
{ {\large SPMODEL $B%5%s%W%k%W%m%0%i%`(B} \\  % $B$3$3$OJQ99$7$J$$(B 
  $B?eO)NN0h(B \\ 2 $B<!85%V%7%M%9%/J}Dx<0%b%G%k(B:\\           % $B%b%G%kL>(B
  $BFbIt=ENOGH$N7W;;(B \\
  {\large igwave1.f90}                   % $B%W%m%0%i%`L>(B
}
%
\Dauthor[$B>.9b(B $B@5;L(B]{$B>.9b(B $B@5;L(B}            % $BCx<T(B
\Ddate{2004 $BG/(B 6 $B7n(B 8 $BF|(B}                 % $BF|IU(B
\Dnoparindent                             % $BCJMn$N;z2<$2$r$7$J$$(B
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% $B4pK\E*$J>O@a9=@.$O0J2<$NDL$j(B. 
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%   1. $B$O$8$a$K(B 
%   2. $B;YG[J}Dx<07O(B
%   3. $BN%;62=(B
%   4. $BMxMQ%b%8%e!<%k$H$=$NB>$N@_Dj(B
%   5. $B?tCM<B83(B
%   6. $B;29MJ88%(B
%   -. $B<U<-(B
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% $BI,MW$K1~$8$F9=@.$rJQ99$9$k$3$H(B.
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\begin{document}

\maketitle                                % $B%?%$%H%k$N:n@.(B
\tableofcontents                          % $BL\<!$N:n@.(B
\pagebreak                                

%----------------------------------------------------------------------
\Dparskip
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage                                  % $B2~%Z!<%8(B
\section{$B35MW(B}

SPMODEL $B%5%s%W%k%W%m%0%i%`!X(Bigwave1.f90$B!Y$KMQ$$$i$l$F$$$k4pACJ}Dx<0$H6-3&(B
$B>r7o(B, $B$*$h$S(B, $B$3$N%W%m%0%i%`$rMQ$$$??tCM<B83$NJ}K!$K$D$$$F2r@b$9$k(B. $B4pAC(B
$BJ}Dx<0$O(B 2 $B<!85$N%V%7%M%9%/J}Dx<07O$G$"$k(B. $B7W;;$O%9%Z%/%H%kK!$rMQ$$$F9T(B
$B$$(B, $BE83+4X?t$O?eJ?J}8~$K$O%U!<%j%(5i?t(B, $B1tD>J}K!$K$O6-3&>r7o$K$"$o$;$F%U!<(B
$B%j%(@5895i?t$^$?$O%U!<%j%(M>895i?t$rMQ$$$k(B.  $BGH?t@ZCG$O;03Q@ZCG$G$"(B
$B$k(B. $B%9%Z%/%H%kJQ49$H5UJQ49$*$h$SHyJ,1i;;$K$O(B, SPMODEL $B%i%$%V%i%j(B(spml) 
$B$N(B esc\_module $B$rMQ$$$F$$$k(B. $B?tCM<B83$G$O?eJ?J}8~$KAP6K;R7?$KJB$s$@@5Ii(B
$B$N12EY6/@)$K$h$jNe5/$5$l$?FbIt=ENOGH$N7W;;$r9T$&(B.

{\bf $B%W%m%0%i%`L>(B} \\                  % $B%W%m%0%i%`L>(B
{\footnotesize
igwave1.f90
}

{\bf $B%W%m%0%i%`<hF@85(B}\\               % $B%W%m%0%i%`<hF@@h(B
{\footnotesize
http:\slash \slash www.gfd-dennou.org\slash arch\slash spmodel\slash 2d-channel-esc\slash boussinesq\slash igwave\slash SIGEN.htm
}


{\bf SPMODEL $B%5%s%W%k%W%m%0%i%`L\<!(B}\\ % $B%5%s%W%k%W%m%0%i%`L\<!(B($BJQ99$7$J$$(B)
{\footnotesize
 http:\slash \slash www.gfd-dennou.org\slash arch\slash spmodel\slash sample.htm 
}

{\bf SPMODEL $B$N;H$$J}(B}\\               % SPMODEL $B$N;H$$J}(B($BJQ99$7$J$$(B)
{\footnotesize
http:\slash \slash www.gfd-dennou.org\slash arch\slash spmodel\/
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage                                  % $B2~%Z!<%8(B
\section{$B;YG[J}Dx<07O(B}

$B$3$3$G$O;YG[J}Dx<07O$H6-3&>r7o$r5-$9(B.

\subsection{$B;YG[J}Dx<07O(B}

$B;YG[J}Dx<07O$O(B 2 $B<!85$N%V%7%M%9%/J}Dx<07O$G$"$k(B.
\begin{eqnarray}
&& \DP{u}{t}+u\DP{u}{x}+v\DP{u}{y} = -\frac{1}{\rho _{0}}\DP{p}{x} 
                                     + \nu \Dlapla u + F_{u}, \\
&& \DP{v}{t}+u\DP{v}{x}+v\DP{v}{y} = -\frac{1}{\rho _{0}}\DP{p}{y} 
                                     - \frac{\rho}{\rho _{0}}g
                                     + \nu \Dlapla v + F_{v}, \\
&& \DP{u}{x}+\DP{v}{y} = 0,\\
&& \DP{\rho}{t}+u\DP{\rho}{x}+v\DP{(\rho+\rho _{0})}{y} = \kappa \Dlapla \rho.
\end{eqnarray}
$B3F5-9f$NDj5A$O(B\Dtabref{$BJQ?t(B, $BJ*M}Dj?t$NDj5A(B}$B$KI=$9(B. 
$B0J2<$G$O4pK\>l$N29EY$HL)EY$N1tD>8{G[$O0lDj$H$9$k(B. 

$B12EY(B $\zeta$ $B$HN.@~4X?t(B $\psi$ 
\begin{eqnarray}
  &&\zeta =\DP{w}{x}-\DP{u}{y}, \\
  &&v=\DP{\psi}{x}, \quad u=-\DP{\psi}{y},
\end{eqnarray}
$B$rF3F~$7(B, $B12EY$HL)EY$NM=JsJ}Dx<0$H$7$F;YG[J}Dx<07O$rI=$9$H0J2<$N$h$&$K$J$k(B.
\begin{eqnarray}
&& \DP{\zeta }{t} + J(\psi, \zeta) + \frac{g}{\rho _{0}}\DP{\rho }{x}
   = \nu \Dlapla \zeta + F_{\zeta}, \Deqlab{$B12EYJ}Dx<0(B}\\
&& \DP{\rho}{t} + J(\psi, \rho) + \DP{\psi}{x}\DP{\rho _{0}}{y} 
   = \kappa \Dlapla \rho. \Deqlab{$BL)EY$NM=JsJ}Dx<0(B}
\end{eqnarray}
$B$3$3$G(B $J(A, B)$ $B$O%d%3%S%"%s(B
\[
  J(A,B) = \DP{A}{x}\DP{B}{y} - \DP{A}{y}\DP{B}{x}
\]
$B$G$"$j(B,
\[
  F_{\zeta} = \DP{F_{v}}{x}-\DP{F_{u}}{y}
\]
$B$G$"$k(B.

\begin{table}[h]
 \begin{center}
  \begin{tabular}{cll} \hline
   $B5-9f(B    &\qquad\qquad&  $BJQ?t(B/$BJ*M}Dj?t(B   \\ \hline 
   $x$      && $B?eJ?:BI8(B        \\
   $y$      && $B1tD>:BI8(B        \\
   $t$      && $B;~4V(B            \\ 
   $u$      && $x$ $BJ}8~B.EY(B        \\ 
   $v$      && $y$ $BJ}8~B.EY(B        \\ 
   $\rho_{0}$ && $BL)EY(B($B4pK\>l(B)  \\
   $\rho $   && $BL)EYJP:9(B        \\
   $\psi$   && $BN.@~4X?t(B        \\ 
   $\zeta$  && $B12EY(B            \\ 
   $F_{u}, F_{v}$ && $B6/@)9`(B    \\ 
   $g$      && $B=ENO2CB.EY(B      \\ 
   $\nu$    && $BF0G4@-78?t(B      \\ 
   $\kappa$ && $B3H;678?t(B      \\ \hline
 \end{tabular} 
\caption{$BJQ?t(B, $BJ*M}Dj?t$NDj5A(B}
\Dtablab{$BJQ?t(B, $BJ*M}Dj?t$NDj5A(B}
\end{center}
\end{table}


\subsection{$B6-3&>r7o(B}

$B6-3&>r7o$O?eJ?$K<~4|6-3&>r7o(B, $B1tD>J}8~$K$O(B $y=0, y_{m}$ $B$KCV$$$?9dBNJI(B
$BLL$G(B $v=0$, $B1~NO$J$7(B, $BG.%U%i%C%/%9$J$7$H$9$k(B. 
$B?eJ?J}8~$N6-3&>r7o$O7W;;NN0h$r$=$l$>$l(B $x_{m}$ $B$H$9$k$H(B
\begin{equation}
  \zeta(x+x_{m},z) = \zeta(x,z)
\end{equation}
$B$J$I$HI=$5$l$k(B. $B1tD>J}8~$N6-3&>r7o$O(B $y=0, y_{m}$ $B$K$*$$$F(B,
\begin{eqnarray}
 &&\psi = \mbox{Const.}, \\
 &&\zeta = 0, \\
 &&\DP{\rho}{y} = 0
\end{eqnarray}
$B$G$"$k(B. $B6-3&$GM?$($k(B $\psi $ $B$NCM$O4JC1$N$?$a(B $0$ $B$H$7$?(B.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage                                  % $B2~%Z!<%8(B
\section{$BN%;62=(B}
$B$3$N@a$G$OJ}Dx<07O$N6u4VN%;62=$*$h$S;HMQ$7$?;~4V@QJ,K!$K$D$$$F@bL@$7(B, $B%W%m(B
$B%0%i%`Fb$G<B:]$KMQ$$$i$l$F$$$kJ}Dx<0$r5-=R$9$k(B. $B$J$*(B, $B6/@)9`(B 
$F_{\zeta}=0$ $B$NM?$(J}$K$D$$$F$O!V(B5. $B<B83@_Dj!W$K$*$$$F<($9(B.

\subsection{$B6u4VN%;62=(B}
$B;YG[J}Dx<0(B\Deqref{$B12EYJ}Dx<0(B}, \Deqref{$BL)EY$NM=JsJ}Dx<0(B}$B$G(B, $B6/@)9`(B 
$F_{\zeta}=0$ $B$H$7$?>l9g$NN%;6I=8=$O0J2<$N$h$&$K$J$k(B.
\begin{eqnarray}
&& \DP{\zeta _{i,j}}{t} + 
   \DP{\psi_{i,j}}{x}\DP{\zeta _{i,j}}{y} - 
   \DP{\psi_{i,j}}{y}\DP{\zeta _{i,j}}{x}  
   + \frac{g}{\rho _{0}}\DP{\rho _{i,j}}{x}
   = \nu \Dlapla \zeta_{i,j} , \Deqlab{$BN%;62=$5$l$?12EYJ}Dx<0(B}\\
&& \DP{\rho_{i,j}}{t} + 
   \DP{\psi_{i,j}}{x}\DP{\rho _{i,j}}{y} - 
   \DP{\psi_{i,j}}{y}\DP{\rho _{i,j}}{x}  
   + \DP{\psi _{i,j}}{y}\DP{\rho _{0}}{y}
   = \kappa \Dlapla \rho_{i,j}. \Deqlab{$BN%;62=$5$l$?L)EY$NM=JsJ}Dx<0(B}
\end{eqnarray}
$B$3$3$GE:;z(B $i,j$ $B$O3J;RE@(B $(x_{i}, y_{j})$ $B>e$NCM$G$"$k$3$H$rI=$9(B.


\subsection{$B6u4VJ}8~$N%9%Z%/%H%kI=8=(B}
$B6u4VN%;62=$7$?;YG[J}Dx<0(B\Deqref{$BN%;62=$5$l$?12EYJ}Dx<0(B}, \Deqref{$BN%;6(B
  $B2=$5$l$?L)EY$NM=JsJ}Dx<0(B}$B$r%9%Z%/%H%kK!$rMQ$$$FI=8=$9$k(B.  $B%9%Z%/%H%k(B
$BE83+$O?eJ?J}8~$K%U!<%j%(5i?t(B, $B1tD>J}K!$K$O6-3&>r7o$K$"$o$;$F%U!<%j%(@5(B
$B895i?t$^$?$O%U!<%j%(M>895i?t$rMQ$$$F9T$&(B. $BHs@~7A9`$r07$&>l9g$O(B, $B@h$K3J(B
$B;RE@>e$G$NHs@~7A9`$NCM$r7W;;$7(B, $B$=$NCM$N%9%Z%/%H%k$r5a$a$kJ}K!(B($BJQ49K!(B)
$B$rMQ$$$k(B. $BIbNO9`$K$D$$$F$bF1MM$K07$&(B. $B0J2<$G$O(B $k,l$  $B$r$=$l$>$l(B$x,z$ 
$BJ}8~GH?t(B, $K,L$ $B$r@ZCGGH?t(B, $I,J$ $B$r3J;RE@?t$H$9$k(B.

$\zeta_{i,j}, \psi _{i,j}, \rho _{i,j}$ $B$O%9%Z%/%H%k5UJQ49$K$h$C$F0J2<(B
$B$N$h$&$KE83+$5$l$k(B.
\begin{eqnarray}
  \zeta_{i,j} &=& \sum _{k=-K}^{K}\sum _{l=0}^{L}
                 \exp\left(\frac{2\pi i k x_{i}}{x_{m}}\right)
                 \sin\left(\frac{\pi l y_{j}}{y_{m}}\right)\hat \zeta_{k,l}, \\
  \psi_{i,j} &=& \sum _{k=-K}^{K}\sum _{l=0}^{L}
                \exp\left(\frac{2\pi i k x_{i}}{x_{m}}\right)
                \sin\left(\frac{\pi l y_{j}}{y_{m}}\right)\hat \psi_{k,l}, \\
  \rho_{i,j} &=& \sum _{k=-K}^{K}\sum _{l=0}^{L}
                 \exp\left(\frac{2\pi i k x_{i}}{x_{m}}\right)
                 \cos\left(\frac{\pi l y_{j}}{y_{m}}\right)\hat \rho_{k,l}.
\end{eqnarray}
$B%9%Z%/%H%k78?t(B $\hat \zeta_{i,j}, \hat \psi _{i,j}, \hat \rho _{i,j}$ $B$O(B
$B%9%Z%/%H%kJQ49$K$h$C$F0J2<$N$h$&$KM?$($i$l$k(B.
\begin{eqnarray}
 \hat \zeta_{k,l} &=& \frac{1}{I}\frac{1}{J}
      \sum _{i=0}^{I-1}\sum _{j=0}^{J-1}
      \exp\left(-\frac{2\pi i k x_{i}}{x_{m}}\right)
      \sin\left(\frac{\pi l y_{j}}{y_{m}}\right)\zeta_{i,j}, \\
 \hat \psi_{k,l} &=& \frac{1}{I}\frac{1}{J}
      \sum _{i=0}^{I-1}\sum _{j=0}^{J-1}
      \exp\left(-\frac{2\pi i k x_{i}}{x_{m}}\right)
      \sin\left(\frac{\pi l y_{j}}{y_{m}}\right)\psi_{i,j}, \\
 \hat \rho_{k,l} &=& \frac{1}{I}\frac{1}{J}
      \sum _{i=0}^{I-1}\sum _{j=0}^{J-1}
      \exp\left(-\frac{2\pi i k x_{i}}{x_{m}}\right)
      \cos\left(\frac{\pi l y_{j}}{y_{m}}\right)\rho_{i,j}.
\end{eqnarray}

$B0J>e$rMQ$$$k$H;YG[J}Dx<0(B\Deqref{$BN%;62=$5$l$?12EYJ}Dx<0(B}, \Deqref{$BN%;6(B
$B2=$5$l$?L)EY$NM=JsJ}Dx<0(B}$B$N%9%Z%/%H%kI=8=$O0J2<$N$h$&$K$J$k(B.
\begin{eqnarray}
 \DP{\hat \zeta _{k,l}(t)}{t} &=& -
      \frac{1}{I}\frac{1}{J} \sum _{i=0}^{I-1}\sum _{j=0}^{J-1}
        \exp\left(-\frac{2\pi i k x_{i}}{x_{m}}\right)
        \sin\left(\frac{\pi l y_{j}}{y_{m}}\right)
        \left(\DP{\psi}{x}\right)_{i,j}
        \left(\DP{\zeta}{y}\right)_{i,j}  \nonumber \\
&&  + \frac{1}{I}\frac{1}{J} \sum _{i=0}^{I-1}\sum _{j=0}^{J-1}
        \exp\left(-\frac{2\pi i k x_{i}}{x_{m}}\right)
        \sin\left(\frac{\pi l y_{j}}{y_{m}}\right)
        \left(\DP{\psi}{y}\right)_{i,j}
        \left(\DP{\zeta}{x}\right)_{i,j}  \nonumber \\
&& - \frac{1}{I}\frac{1}{J} \sum _{i=0}^{I-1}\sum _{j=0}^{J-1}
        \exp\left(-\frac{2\pi i k x_{i}}{x_{m}}\right)
        \sin\left(\frac{\pi l y_{j}}{y_{m}}\right)
        \frac{g}{\rho _{0}}\left(\DP{\rho}{x}\right)_{i,j} \nonumber \\
&& - \nu \left[
     \left(\frac{2\pi k}{x_{m}}\right)^{2}+
     \left(\frac{\pi l}{y_{m}}\right)^{2}\right]\hat \zeta _{k,l},
     \Deqlab{$B12EYJ}Dx<0$N%9%Z%/%H%kI=8=(B}\\
 \DP{\hat \rho _{k,l}(t)}{t} &=& -
      \frac{1}{I}\frac{1}{J} \sum _{i=0}^{I-1}\sum _{j=0}^{J-1}
        \exp\left(-\frac{2\pi i k x_{i}}{x_{m}}\right)
        \cos\left(\frac{\pi l y_{j}}{y_{m}}\right)
        \left(\DP{\psi}{x}\right)_{i,j}
        \left(\DP{\rho}{y}\right)_{i,j}  \nonumber \\
&&  + \frac{1}{I}\frac{1}{J} \sum _{i=0}^{I-1}\sum _{j=0}^{J-1}
        \exp\left(-\frac{2\pi i k x_{i}}{x_{m}}\right)
        \cos\left(\frac{\pi l y_{j}}{y_{m}}\right)
        \left(\DP{\psi}{y}\right)_{i,j}
        \left(\DP{\rho}{x}\right)_{i,j}  \nonumber \\
&& - \frac{\pi l}{y_{m}}\DP{\rho _{0}}{y}\hat \psi _{k,l} 
   - \kappa \left[
     \left(\frac{2\pi k}{x_{m}}\right)^{2}+
     \left(\frac{\pi l}{y_{m}}\right)^{2}\right]\hat \rho _{k,l}.
     \Deqlab{$BL)EY$NM=JsJ}Dx<0$N%9%Z%/%H%kI=8=(B}
\end{eqnarray}
$B$3$3$G(B
\begin{eqnarray}
 \left(\DP{\zeta}{x}\right)_{i,j} &=& \sum _{k=-K}^{K}\sum _{l=0}^{L}
                            \exp\left(\frac{2\pi i k }{x_{m}}\right)
                            \sin\left(\frac{\pi l }{y_{m}}\right)
                            \frac{2\pi i k}{x_{m}}\hat \zeta _{k,l}, \\
 \left(\DP{\zeta}{y}\right)_{i,j} &=& \sum _{k=-K}^{K}\sum _{l=0}^{L}
                            \exp\left(\frac{2\pi i k }{x_{m}}\right)
                            \cos\left(\frac{\pi l }{y_{m}}\right)
                            \frac{\pi l}{y_{m}}\hat \zeta _{k,l}, \\
 \left(\DP{\psi}{x}\right)_{i,j} &=&  \sum _{k=-K}^{K}\sum _{l=0}^{L}
                            \exp\left(\frac{2\pi i k }{x_{m}}\right)
                            \sin\left(\frac{\pi l }{y_{m}}\right)
                            \frac{2\pi i k}{x_{m}}\hat \psi _{k,l}, \\
 \left(\DP{\psi}{y}\right)_{i,j} &=& \sum _{k=-K}^{K}\sum _{l=0}^{L}
                            \exp\left(\frac{2\pi i k }{x_{m}}\right)
                            \cos\left(\frac{\pi l }{y_{m}}\right)
                            \frac{\pi l}{y_{m}}\hat \psi _{k,l}, \\
 \left(\DP{\rho}{x}\right)_{i,j} &=& \sum _{k=-K}^{K}\sum _{l=0}^{L}
                            \exp\left(\frac{2\pi i k }{x_{m}}\right)
                            \cos\left(\frac{\pi l }{y_{m}}\right)
                            \frac{2\pi i k}{x_{m}}\hat \rho _{k,l}, \\
 \left(\DP{\rho}{y}\right)_{i,j} &=& - \sum _{k=-K}^{K}\sum _{l=0}^{L}
                            \exp\left(\frac{2\pi i k }{x_{m}}\right)
                            \sin\left(\frac{\pi l }{y_{m}}\right)
                            \frac{\pi l}{y_{m}}\hat \rho _{k,l}
\end{eqnarray}
$B$G$"$k(B.


\subsection{$B;~4V@QJ,(B}
$B$3$3$G$O;~4V@QJ,K!$K$D$$$F5-=R$7(B, $B%W%m%0%i%`Fb$G<B:]$KMQ$$$i$l$F$$$kJ}(B
$BDx<0$r5-=R$9$k(B. $B0J2<$G$O(B $\Delta t$ $B$r;~4V3J;R4V3V(B, $B;~9o(B $\tau \Delta t$ 
$B$K$*$1$k(B $\hat \zeta_{k,l}$ $B$NCM$r(B $\hat \zeta_{k,l}^{\tau}$ $BEy$HI=$9(B.

$B;~4VJ}8~$NN%;62=$O(B Euler $B%9%-!<%`$rMQ$$$F9T$&(B. $B;~6u4VJ}8~$KN%;62=$5$l(B
$B$?J}Dx<0$O0J2<$N$h$&$KI=$5$l$k(B.
\begin{eqnarray}
 &&\hat \zeta _{k,l}^{\tau +1} = \hat \zeta _{k,l}^{\tau} + \Delta t \hat F_{k,l}^{\tau},  \\
 &&\hat \rho _{k,l}^{\tau +1} = \hat \rho _{k,l}^{\tau} + \Delta t \hat G_{k,l}^{\tau}, 
\end{eqnarray}
\begin{eqnarray}
\hat F_{k,l}^{\tau} &=& 
  -  \frac{1}{I}\frac{1}{J} \sum _{i=0}^{I-1}\sum _{j=0}^{J-1}
        \exp\left(-\frac{2\pi i k x_{i}}{x_{m}}\right)
        \sin\left(\frac{\pi l y_{j}}{y_{m}}\right)
        \left(\DP{\psi}{x}\right)_{i,j}^{\tau}
        \left(\DP{\zeta}{y}\right)_{i,j}^{\tau}  \nonumber \\
&&  + \frac{1}{I}\frac{1}{J} \sum _{i=0}^{I-1}\sum _{j=0}^{J-1}
        \exp\left(-\frac{2\pi i k x_{i}}{x_{m}}\right)
        \sin\left(\frac{\pi l y_{j}}{y_{m}}\right)
        \left(\DP{\psi}{y}\right)_{i,j}^{\tau}
        \left(\DP{\zeta}{x}\right)_{i,j}^{\tau}  \nonumber \\
&& - \frac{1}{I}\frac{1}{J} \sum _{i=0}^{I-1}\sum _{j=0}^{J-1}
        \exp\left(-\frac{2\pi i k x_{i}}{x_{m}}\right)
        \sin\left(\frac{\pi l y_{j}}{y_{m}}\right)
        \frac{g}{\rho _{0}}\left(\DP{\rho}{x}\right)_{i,j}^{\tau} \nonumber \\
&& - \nu \left[
     \left(\frac{2\pi k}{x_{m}}\right)^{2}+
     \left(\frac{\pi l}{y_{m}}\right)^{2}\right]\hat \zeta _{k,l}^{\tau}, 
   \Deqlab{$B12EY$NA}J,(B}
   \\
\hat G_{i,j}^{\tau} &=& - 
      \frac{1}{I}\frac{1}{J} \sum _{i=0}^{I-1}\sum _{j=0}^{J-1}
        \exp\left(-\frac{2\pi i k x_{i}}{x_{m}}\right)
        \cos\left(\frac{\pi l y_{j}}{y_{m}}\right)
        \left(\DP{\psi}{x}\right)_{i,j}^{\tau}
        \left(\DP{\rho}{y}\right)_{i,j}^{\tau}  \nonumber \\
&&  + \frac{1}{I}\frac{1}{J} \sum _{i=0}^{I-1}\sum _{j=0}^{J-1}
        \exp\left(-\frac{2\pi i k x_{i}}{x_{m}}\right)
        \cos\left(\frac{\pi l y_{j}}{y_{m}}\right)
        \left(\DP{\psi}{y}\right)_{i,j}^{\tau}
        \left(\DP{\rho}{x}\right)_{i,j}^{\tau}  \nonumber \\
&& - \frac{\pi l}{y_{m}}\DP{\rho _{0}}{y}\hat \psi _{k,l}^{\tau} 
   - \kappa \left[
     \left(\frac{2\pi k}{x_{m}}\right)^{2}+
     \left(\frac{\pi l}{y_{m}}\right)^{2}\right]\hat \rho _{k,l}^{\tau}.
\end{eqnarray}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage                                  % $B2~%Z!<%8(B
\section{$B;HMQ%b%8%e!<%k$H$=$NB>$N@_Dj(B}

$B%9%Z%/%H%kJQ49$H5UJQ49(B, $BHyJ,1i;;$O(B SPMODEL $B%i%$%V%i%j(B (spml) $B$N(B
esc\_module $B$K4^$^$l$k4X?t$rMQ$$$F9T$&(B. $B%U!<%j%(@589$*$h$SM>89JQ49(B, $B$=(B
$B$l$i$N5UJQ49$N:]$N?tCM@QJ,$OBf7A8x<0$rMQ$$$F9T$&(B. spml $B$,2<0L$G;HMQ$9(B
$B$k(B ISPACK $B$N;EMM$+$i(B, $B3J;RE@?t(B $I,J$ $B$O6v?t$G(B, $B$+$D(B 
$I/2, J/2=2^{a}3^{b}5^{c}$ ($a, b, c$  $B$O(B 0 $B$^$?$O@0?t(B) $B$G$J$1$l$P$J$i$J(B
$B$$(B. $BHs@~7A9`$N7W;;$K$h$C$F@8$8$k%(%j%"%8%s%0$rKI$0$?$a(B, $B3J;RE@?t(B $I,J$ 
$B$H@ZCGGH?t(B $K,L$ $B$O(B  $I>3K,J>3K/2$ $B$rK~$?$9$h$&$KM?$($k(B.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage                                  % $B2~%Z!<%8(B
\section{$B?tCM<B83(B}

$B?tCM<B83$G$O?eJ?J}8~$KAP6K;R7?$KJB$s$@@5Ii$N12EY6/@)$K$h$jNe5/$5$l$?FbIt(B
$B=ENOGH$N7W;;$r9T$&(B. $B12EY6/@)$O0J2<$N$h$&$KM?$($k(B.

\begin{equation}
 F_{\zeta} = \DP{F_{v}}{x}
           = \DP{}{x}\left[A_{0}\exp 
                     \left(-\frac{(x-x_{0})^{2}+(y-y_{0})^{2}}{\sigma^{2}}
                     \right)
             \sin \omega t \right]
\end{equation}

$B$3$N$H$-6/@)9`(B $F_{\zeta}$ $B$O?eJ?J}8~$K%U!<%j%(E83+(B, $B1tD>J}8~$K%U!<%j%((B
$B@589E83+$5$l$k(B. \Deqref{$B12EY$NA}J,(B}$B$N1&JU$K$O(B
\[
  \frac{1}{I}\frac{1}{J} \sum _{i=0}^{I-1}\sum _{j=0}^{J-1}
        \exp\left(-\frac{2\pi i k x_{i}}{x_{m}}\right)
        \sin\left(\frac{\pi l y_{j}}{y_{m}}\right)
        F_{\zeta, i,j}^{\tau}
\]
$B$,DI2C$5$l$k(B. $B%Q%i%a!<%?$O(B\Dtabref{$B;HMQ$7$?%Q%i%a!<%?$NCM(B}$B$K$^$H$a$?CM$r(B
$BMQ$$$k(B.

$B3J;RE@?t(B $I, J$ $B$H@ZCGGH?t(B $K, L$ $B$O$=$l$>$l(B $I=128, J=64, K=L=42$ $B$H(B
$B$9$k(B. $B;~4V3J;R4V3V(B $\Delta t$ $B$O(B $0.1$ sec, $B7W;;%9%F%C%W?t$O(B 
4,000  $B%9%F%C%W$G$"$k(B.

%\Dfigref{$BL)EYJ,I[$N;~4VJQ2=(B}$B$K7W;;$5$l$?L)EYJ,I[$N;~4VJQ2=$r<($7$?(B. $B<<(B
%$BFb<B83$H$NBPHf$,$7$d$9$$$h$&$K(B $0\leq x\leq 60$ cm $B$^$G$NHO0O$r<($7$F$"(B
%$B$k(B.

\begin{table}[h]
 \begin{center}
  \begin{tabular}{cll} \hline
   $B%Q%i%a!<%?(B    &\qquad\qquad&  $B?tCM(B   \\ \hline 
   $\rho_{0}$    && 1.0 kgm${}^{-3}$  \\
   $\DP{\rho _{0}}{y}$ && $-1.0$ kgm${}^{-2}$ \\
   $g$           && 9.8 msec${}^{-2}$   \\ 
   $\nu$         && 10${}^{-5}$ m${}^{2}$sec${}^{-1}$  \\ 
   $\kappa$      && 10${}^{-9}$ m${}^{2}$sec${}^{-1}$  \\ 
   $x_{m}$       && 2.0 m       \\ 
   $y_{m}$       && 1.0 m       \\ 
   $A_{0}$       && 1.0$\times 10^{-5}$ kgm${}^{-3}$ \\ 
   $x_{0}$       && $x_{m}/2$  \\ 
   $y_{0}$       && $y_{m}/2$  \\  
   $\sigma$      && 2.0$\times 10^{-2}$ m \\ \hline
 \end{tabular} 
\caption{$B;HMQ$7$?%Q%i%a!<%?$NCM(B}
\Dtablab{$B;HMQ$7$?%Q%i%a!<%?$NCM(B}
\end{center}
\end{table}

$B12EY6/@)$N?6F0?t(B $\omega$ $B$O(B, $B%V%i%s%H(B--$B%P%$%5%i?6F0?t(B
\[
  N \equiv \sqrt{\left|\frac{g}{\rho _{0}}\DP{\rho _{0}}{y}\right|}
\]
$B$KBP$9$kHf$H$7$FM?$($k(B(\Dtabref{$B12EY6/@)$N?6F0?t(B}).
 
\begin{table}[h]
 \begin{center}
  \begin{tabular}{cll} \hline
   $B<B83HV9f(B &\qquad\qquad&  $\omega $ $B$NCM(B  \\ \hline 
   case 1   &&  $0.3 N$ \\   
   case 2   &&  $0.6 N$ \\   
   case 3   &&  $0.9 N$ \\  
   case 4   &&  $1.2 N$ \\  \hline
 \end{tabular} 
\caption{$B12EY6/@)$N?6F0?t(B}
\Dtablab{$B12EY6/@)$N?6F0?t(B}
\end{center}
\end{table}

$B$=$l$>$l$N(B $\omega $ $B$rM?$($?>l9g$N(B $t=400$ sec $B$K$*$1$kL)EYJP:9$NJ,I[$r(B
\Dfigref{case 1 $B$NL)EYJP:9J,I[(B}$\sim$\Dfigref{case 4 $B$NL)EYJP:9J,I[(B}$B$K<((B
$B$9(B. $BFbIt=ENOGH$NEAGE$K$H$b$J$$(B, $BL)EYJP:9$NJ,I[$O!_0u>u$N%Q%?!<%s$r<($9(B
(\Dfigref{case 1 $B$NL)EYJP:9J,I[(B}). $B6/@)$N?6F0?t$r%V%i%s%H(B--$B%P%$%5%i?6F0(B
$B?t$K6a$E$1$k$K$D$l$F(B, $B!_0u$N%Q%?!<%s$OJD$8$F$$$/(B(\Dfigref{case 2 $B$NL)EY(B
$BJP:9J,I[(B}, \Dfigref{case 3 $B$NL)EYJP:9J,I[(B}). $B6/@)$N?6F0?t$,%V%i%s%H(B--$B%P(B
$B%$%5%i?6F0?t$r1[$($k$HGH$,H/@8$7$J$/$J$k(B(\Dfigref{case 4 $B$NL)EYJP:9J,I[(B}).

\begin{figure}[p]
\begin{center}
\Depsf[15cm][]{./figs/igwave1-omega0.3.ps}
\vspace*{-1.0cm}
\caption{$t=400$ sec $B$K$*$1$kL)EYJP:9$NJ,I[(B. case 1 $B$N(B $\omega = 0.3 N$ $B$N>l9g(B.}
\Dfiglab{case 1 $B$NL)EYJP:9J,I[(B}

\Depsf[15cm][]{./figs/igwave1-omega0.6.ps}
\vspace*{-1.0cm}
\caption{$t=400$ sec $B$K$*$1$kL)EYJP:9$NJ,I[(B. case 2 $B$N(B $\omega = 0.6 N$ $B$N>l9g(B.}
\Dfiglab{case 2 $B$NL)EYJP:9J,I[(B}
\end{center}
\end{figure}

\begin{figure}[p]
\begin{center}
\Depsf[15cm][]{./figs/igwave1-omega0.9.ps}
\vspace*{-1.0cm}
\caption{$t=400$ sec $B$K$*$1$kL)EYJP:9$NJ,I[(B. case 3 $B$N(B $\omega = 0.9 N$ $B$N>l9g(B.}
\Dfiglab{case 3 $B$NL)EYJP:9J,I[(B}

\Depsf[15cm][]{./figs/igwave1-omega1.2.ps}
\vspace*{-1.0cm}
\caption{$t=400$ sec $B$K$*$1$kL)EYJP:9$NJ,I[(B. case 4 $B$N(B $\omega = 1.2 N$ $B$N>l9g(B.}
\Dfiglab{case 4 $B$NL)EYJP:9J,I[(B}
\end{center}
\end{figure}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage                                  % $B2~%Z!<%8(B
\newpage
\section{$B;29MJ88%(B}
\begin{description}
 \item GFD-online ($B<r0f(B $BIR(B, $BHS_7(B $B8y(B, $B9S4,(B $B1Q<#(B), 1997:
       $B<B83<<$NCf$N6u$H3$(B, $BFbIt=ENOGH(B, 
       http:\slash \slash www.gfd-dennou.org\slash arch\slash gfd-exp\slash gfd\_exp\slash exp\_j\slash doc\slash iw\slash guide01.htm.	     

 \item $BLZB<N5<#(B, 1983: 
       $BCO5eN.BNNO3XF~Lg(B, $B5$>]3X$N%W%m%`%J!<%I(B 13, $BEl5~F2=PHG(B, pp.247. 

 \item Mowbray, D. E., Rarity, B. S. H., 1967: 
       A theoretical and experimental investigation of the phase
       configuration ofinternal waves of small amplitude in a density
       stratified liquid. 
       {\it J. Fluid Mech.}, {\bf 28}, 1--16.

 \item $BC]9-??0l(B, $B@P2,7=0l(B, $B?9@nLwBg(B, $B>.9b@5;L(B, $B@PEO@5<y(B, $BNS>M2p(B, SPMODEL $B3+H/%0%k!<%W(B, 2004: 
       $B3,AXE*CO5eN.BNNO3X%9%Z%/%H%k%b%G%k=8(B (SPMODEL),
       http:\slash \slash www.gfd-dennou.org\slash arch\slash spmodel\slash ,
       $BCO5eN.BNEEG>6f3ZIt(B. 
\end{description}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage                                  % $B2~%Z!<%8(B
\section*{$B<U<-(B}                           % $B<U<-(B. $B$3$N$^$^MxMQ$9$k(B.
\markright{$B<U<-(B}                          % $B%X%C%@$KI=<((B
\addcontentsline{toc}{section}{$B<U<-(B}      % $BL\<!$KI=<((B

$BK\;q8;$O(B, $BCO5eN.BNEEG>6f3ZIt$N%$%s%?!<%M%C%H>e$G$N3X=QCN<1$N=8@Q$H3hMQ(B
$B$N<B83$N0l4D$H$7$F(B
\begin{center}
 http:\slash \slash www.gfd-dennou.org\slash arch\slash spmodel\slash 
\end{center}
$B$K$*$$$F8x3+$5$l$F$$$k$b$N$G$"$k(B 
(\copyright $BCO5eN.BNEEG>6f3ZIt%9%Z%/%H%k%b%G%k%W%m%8%'%/%H(B 
spmodel@gfd-dennou.org 2002. ). 
$BK\;q8;$O(B, $BCx:n<T$N=t8"Mx$KDq?($7$J$$(B($BLBOG$r$+$1$J$$(B)$B8B$j$K$*$$$F<+M3$K(B
$BMxMQ$7$F$$$?$@$$$F9=$o$J$$(B. $B$J$*(B, $BMxMQ$9$k:]$K$O:#0lEY<+$iFbMF$r3N$+$a(B
$B$k$3$H$r$*4j$$$9$k(B($BL5J]>ZL5@UG$86B'(B).

$BK\;q8;$K4^$^$l$k85;q8;Ds6!<T(B($B?^Ey$NHG85Ey$r4^$`(B)$B$+$i$O(B,  $BD>@\E*$J7A$G(B
$B$N(B WEB $B>e$G$NCx:n8"$^$?$O;HMQ5vBz$rF@$F$$$J$$>l9g$,$"$k$,(B,  $B>!<j$J$,$i(B, 
$B!VL$Mh$N650i!W$N$?$a$N<B83$H$$$&3X=QL\E*$G$"$k$3$H$r$4M}2r$$$?$@$1$k$b(B
$B$N$H?.$8(B,  $B3X=QI8=`$N0zMQ<j=g$r<i$k$3$H$G=t<jB3$-$rN,$5$;$F$$$?$@$$$F(B
$B$$$k(B.  $BK\;q8;$NMxMQ<T$K$O(B, $B$3$NE@$rM}2r$N>e(B,  $BCm0U$7$F07$C$F$$$?$@$1$k(B
$B$h$&$*4j$$$9$k(B.  $BK|0l(B, $BITET9g$N$"$k>l9g$K$O(B
\begin{center}
 spmodel@gfd-dennou.org
\end{center}
$B$^$GO"Mm$7$F$$$?$@$1$l$P9,$$$G$"$k(B. 


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\end{document}

