%#! platex master_thesis-M2.tex
\chapter{$B?tCM7W;;$N35MW(B}\label{chap:cal_summary}

$BK\>O$G$OK\8&5f$G9T$J$C$??tCM7W;;$N35MW$K$D$$$F=R$Y$k(B. $B;YG[J}Dx<0$NF3=P$K(B
$B$D$$$F$O(B, $BIUO?(B \ref{chap:governing_equation} $B$r;2>H$5$l$?$$(B. $B$^$?(B, $B%1!<(B
$B%9$4$H$N7W;;@_Dj$N0c$$$K$D$$$F$OBh(B \ref{chap:result} $B>O$G=R$Y$k(B.

\section{$B%b%G%k$N35MW$H;YG[J}Dx<0(B}

$B?tCM7W;;$KMQ$$$?%b%G%k$O(B, Larichev and Held (1995) $B$K4p$E$/=`CO9U(B 2 $BAX%b(B
$B%G%k$G$"$k(B. $f$ $BJ?LL>e$N%V%7%M%9%/N.BN$G(B, $B1tD>J}8~$K@E?e05J?9U$r2>Dj$9(B
$B$k(B. $BN.$l$NNN0h$O(B, $B?eJ?J}8~$O(B $[0,0]\times[2\pi,2\pi]$ $B$NC;7A$G6-3&$O<~(B
$B4|E*$G$"$k$H$7(B, $B>e2<$K$OJ?$i$J8GBNJI$r2>Dj$9$k(B. $B1tD>%7%"!<$r;}$D?eJ?LLFb(B
$B$K$*$$$F0lMM$J(B $x$ $BJ}8~$NN.$l$K$h$C$F7O$r6/@)$7(B, $BD6G4@-$H%(%/%^%s%@%s%T(B
$B%s%0$K$h$C$F%(%M%k%.!<$d%(%s%9%H%m%U%#!<$r;60o$9$k(B. $BG4@-$K$D$$$F$O(B, $B>eAX(B
$B$H2<AX$G0[$J$kCM$rMQ$$$k(B. $B;YG[J}Dx<0$O(B, $B0J>e$N2>Dj$r2]$7$?(B 2 $BAX$N=`CO9U(B
$B120LJ}Dx<0(B 
\begin{subequations} %16:46$B$N<072(B
 \begin{align}
  &\DP{Q_1}{t} + J(\Psi_1, Q_1) = -\nu\bnabla^8 Q_1, \label{eq:gveq-1} \\
  &\DP{Q_2}{t} + J(\Psi_2, Q_2) = -(\nu+\Delta\nu)\bnabla^8 Q_2 -
  \kappa\bnabla^2\Psi_2 \label{eq:gveq-2}
 \end{align}
\end{subequations}
$B$G$"$k(B. $B$3$3$G(B, $B2<IU$-J8;z$N(B 1 $B$H(B 2 $B$O$=$l$>$l>eAX$H2<AX$NJ*M}NL$G$"$k$3(B
$B$H$r<($7(B, $J$ $B$O?eJ?%d%3%S%"%s$G(B, $\bnabla^2$ $B$O?eJ?%i%W%i%7%"%s$G$"$k(B.
$B$^$?(B, $\nu$ $B$OG4@-78?t(B, $\Delta\nu$ $B$O>eAX$H2<AX$NG4@-78?t$NCM$N:9(B
\footnote{Larichev and Held (1995) $B$G$O(B, $\Delta\nu=0$ $B$G$"$k$,(B, $B$3$3$G(B
$B$O$h$j0lHLE*$J(B $\Delta\nu\neq0$ $B$N>l9g$r9M$($k(B},
$\kappa$ $B$O%(%/%^%s78?t$rI=$9(B. $\Psi_\ast$ $B$ON.@~H!?t$G!$120L(B $Q_\ast$
$B$H?eJ?J}8~B.EY(B $u_\ast, v_\ast$ $B$NDj5A$O0J2<$NDL$j$G$"$k(B:
\begin{align}
 Q_1 &= \bnabla^2\Psi_1 + k_d^2\frac{\Psi_2-\Psi_1}{2}, \\
 Q_2 &= \bnabla^2\Psi_2 + k_d^2\frac{\Psi_1-\Psi_2}{2},  \\
 (u_\ast, v_\ast) &= \left(-\DP{\Psi_\ast}{y}, \DP{\Psi_\ast}{x}\right). 
\end{align}
$B$3$3$G(B, $BAX$N8|$5$O>eAX$H2<AX$GEy$7$$$H$7(B, $k_d^{-1}$ $B$OFbItJQ7AH>7B$G$"(B
$B$k(B. $B$$$^(B, $B>qMp$N%(%M%k%.!<8;$H$7$FFnKLJ}8~$K1tD>%7%"!<$r2>Dj$7$F$$$k(B. $BJ?(B
$B6QN.$NBg$-$5$r(B $U$ ($BDj?t(B)$B$H$7(B, $BN.@~H!?t$rJ?6QN.$N@.J,$HJ?6QN.$+$i$N%:%l(B
($B>qMp(B)$B$N@.J,$KJ,2r$9$k(B:
\begin{align}
 \begin{aligned}
  &\Psi_1 = -Uy + \psi_1(x,y,t), \\
  &\Psi_2 = Uy + \psi_2(x,y,t).
 \end{aligned}
\end{align}
$B$3$3$G(B, $\psi_1$ $B$H(B $\psi_2$ $B$O$=$l$>$l(B $0\leq x,y \leq 2\pi$ $B$NHO0O$G<~(B
$B4|E*$G$"$k$H$9$k(B. $B$5$i$K(B, $B=g05(B(barotripic)$B%b!<%I$H7905(B(baroclinic)$B%b!<(B
$B%I$NN.@~H!?t$r$=$l$>$l0J2<$N$h$&$KDj5A$9$k(B:
\begin{align}
 \psi = \frac{\psi_1+\psi_2}{2}, \hspace{10pt} \tau = \frac{\psi_1-\psi_2}{2}.
\end{align}
$B$3$l$i$rMQ$$$F(B, $B;YG[J}Dx<0(B (\ref{eq:gveq-1}) $B$H(B (\ref{eq:gveq-2}) $B$rJQ7A(B
$B$9$k$H0J2<$N$h$&$K$J$k(B:
\begin{screen}
 \begin{subequations} %16:45$B$N<072(B
  \begin{align}
   &\begin{aligned}
     &\DP{\bnabla^2\psi}{t}+J(\psi,\bnabla^2\psi)+J(\tau,\bnabla^2\tau)+U\DP{\bnabla^2\tau}{x}
     \\ &\quad
     =-\kappa\bnabla^2\frac{\psi-\tau}{2}-\nu\bnabla^8(\bnabla^2\psi)
     -\frac{1}{2}\Delta\nu\bnabla^8\{\bnabla^2\psi
     - (\bnabla^2-k_d^2)\tau\}, \label{eq:troeq}\\
    \end{aligned} \\
    &\begin{aligned}
      &\DP{(\bnabla^2\tau-k_d^2\tau)}{t}+J(\psi,\bnabla^2\tau-k_d^2\tau)+J(\tau,\bnabla^2\psi)+U\DP{\bnabla^2\psi}{x}+k_d^2U\DP{\psi}{x}
      \\ &\quad
      =-\kappa\bnabla^2\frac{\tau-\psi}{2}-\nu\bnabla^8(\bnabla^2\tau-k_d^2\tau)
      -\frac{1}{2}\Delta\nu\bnabla^8\{(\bnabla^2-k_d^2)\tau - \bnabla^2\psi \}. \label{eq:clieq}
     \end{aligned}
  \end{align}
 \end{subequations} 
\end{screen}

\section{TO03 $B$N%b%G%k$H$N0c$$(B}

TO03 $B$G;H$o$l$?%b%G%k$O(B, $\beta$ $BLL>e$N=`CO9U(B 2 $BAX?eO)%b%G%k$G(B, $B@ZCGGH(B
$B?t$N6a$/$G(B subgrid $B%9%1!<%k$N8=>]$K$h$kG4@-;60o5!9=$rF~$l$?%b%G%k$G$"$k(B. 
$B?eO)%b%G%k$G(B $\beta$ $B8z2L$H(B subgrid $B%9%1!<%k$N;60o5!9=$r4^$`E@$K$*$$$F(B,
$BK\8&5f$GMQ$$$?%b%G%k$H0[$J$k(B. $B$7$+$7(B, TO03 $B$G=R$Y$i$l$F$$$k9bGH?tB&$G$N(B
$k^{-5/3}$ $B$N%9%Z%/%H%k$N7A@.$O(B, $B!V1#$l$?%(%M%k%.!<%+%9%1!<%I!W$K$h$k47(B
$B@-NN0h%9%Z%/%H%k$H$7$F@bL@$5$l$F$$$k(B. $B$=$3$G(B, $BNN0h$N4v2?3X$d;60o5!9=$K$O(B
$B0MB8$7$J$$$@$m$&$H9M$($i$l$k(B. $B$^$?(B, $\beta$ $B8z2L$ODcGH?tB&$G8z2LE*$KF/$/(B
$B$N$G(B, $B$$$^LdBj$K$7$F$$$k9bGH?tNN0h$G$O8z$+$J$$$G$"$m$&$H?dB,$G$-$k(B. $B$h$C(B
$B$F(B, $BH`$i$NDs>'$9$k%a%+%K%:%`$NIaJW@-$rA0@a$G=R$Y$?%b%G%k$G8&5f$9$k$3$H$O(B
$BBEEv$G$"$k$H9M$($i$l$k(B. 

\section{$B?tCM7W;;$N@_Dj(B}

$B6u4V:9J,$O%9%Z%/%H%kK!(B, $B;~4V:9J,$O(B 4 $B<!$N%k%s%2%/%C%?K!$rMQ$$$?(B.
$B=i4|CM$O(B, $B=g05%b!<%I$H7905%b!<%I$N%(%M%k%.!<%9%Z%/%H%k$rA4GH?t$G0lDjCM$H(B
$B$7$?(B :  $E_{\psi}(k,t=0)=E_{\tau}(k,t=0)=6.0\times10^{-8}$.
$BDc2rA|EY$N7W;;$GE}7WE*Dj>o>uBV$KC#$7$?$H;W$o$l$k;~9o$G7W(B
$B;;$r;_$a(B, $B$=$N:G8e$N;~9o$N=g05%b!<%I$H7905%b!<%I$N12EY$r=i4|CM$H$7$F$h$j(B
$B9b2rA|EY$N7W;;$r9T$&J}K!$r:N$C$?(B($B$3$N$h$&$JJ}K!$O(B, $B$7$P$7$P!V%9%T%s%"%C%W!W(B
$B$H8F$P$l$k(B). $B$^$:(B, $B2rA|EY(B $256^2$ $B$N7W;;$+$i;O$a(B, $B%9(B
$B%T%s%"%C%W$r9T$J$C$F(B $512^2$, $1024^2$ $B$N7W;;$r9T$C$?(B. $k_d$ $B$h$j$b9b(B
$BGH?tB&$N%a%+%K%:%`$r>\$7$/2r@O$9$k$?$a$K(B, Larichev and Held (1995) $B$G$O(B
$k_d = 50$ $B$KBP$7$F(B, $BK\8&5f$G$O(B $k_d=10$$B$H$7$?(B. $BJ?6QN.$N6/$5(B $U$, $B%(%/%^(B
$B%s%@%s%T%s%0$N78?t(B $\kappa$$B$O(B Larichev and Held (1995) $B$NCM$r;29M$K(B, $U
= 2.5\times10^{-2}$, $\kappa=4.0\times10^{-2}$ $B$H$7$?(B\footnote{ %
$B7O$X$N%(%M%k%.!<CmF~$O(B $U \, k_d^2$ $B$KHfNc$9$k$N$G(B, $U \, k_d^2$ $B$,(B
Larichev and Held (1995) $B$HF1$8$K$J$k$h$&$K@_Dj$7$F$$$k(B. $B$^$?(B, $B%(%M%k%.!<(B
$B$N;60o$O<g$K%(%/%^%s%@%s%T%s%0$K$h$C$F5/$3$k$N$G(B, $\kappa$ $B$NCM$O(B
Larichev and Held (1995) $B$HF1$8CM$K@_Dj$7$F$$$k(B.
}. $BG4@-78?t(B $\nu$ $B$N(B
$BCM$O2rA|EY$K$h$C$F(B 
\begin{itemize}
 \item $256^2$ $B$N$H$-(B : $\nu=1.350\times10^{-14}$ 
 \item $512^2$ $B$N$H$-(B : $\nu=5.280\times10^{-17}$
 \item $1024^2$ $B$N$H$-(B : $\nu=2.017\times10^{-19}$
\end{itemize}
$B$H$7$?(B. $BG4@-78?t$r$3$N$h$&$KJQ$($F$$$k$N$O(B, $B@ZCGGH?t$K$*$1$kG4@-$N%?%$%`(B
$B%9%1!<%k$rF1$8$K@_Dj$7(B, $B9b2rA|EY$N7W;;$G$O$h$j%l%$%N%k%:?t$N9b$$>uBV$r<B(B
$B8=$9$k$?$a$G$"$k(B.


%%% Local Variables:
%%% mode: yatex
%%% TeX-master: "platex master_thesis-M2"
%%% End: