%
% Chapter 3   Scale Analysis
%             3-5 TROPICS
%
% 2002/11/13  ���� ����   ����
% 2002/11/14  ���� ����   ����
% 2003/01/23  ���� ����   ���ߥʡ���ν���
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%   Subtitle, Date, Filename Setting     %%%%%%%%
\markboth{4-5 Ǯ��}{4-5 Ǯ��}
%\markright{3-5 Ǯ��}
%\Ddate{2003/01/23}
%\Dfile{hw-03-05.tex}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%   Set Counter (chapter, section etc. ) %%%%%%%%
\setcounter{chapter}{4}
\setcounter{section}{4}
\setcounter{footnote}{0}
\setcounter{equation}{77}
%\setcounter{page}{1}
%\setcounter{figure}{0}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%        Counter Output Format           %%%%%%%%
\def\thesection{\arabic{chapter}-\arabic{section}}
\def\thesubsection{\arabic{chapter}-\arabic{section}-\arabic{subsection}}
\def\theequation{\arabic{chapter}-\arabic{equation}}
\def\thepage{\arabic{page}}
\def\thefigure{\arabic{chapter}-\arabic{figure}}
\def\thetable{\arabic{chapter}-\arabic{table}}
%\def\thefootnote{\arabic{footnote})}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%              Text Start                %%%%%%%%

\section{Ǯ��}

\begin{itembox}[l]{����}
 \Dparskip \vspace{-6mm}
 ���ѵ��Ϥ�Ǯ�ӤΥ�������󥰤�Ԥ�.

 Ǯ�ӤǤ�����٤����, �����ӡ���$R_O$��10�ܤ��礭���Υ�����������.
 (�դ˸����Ф���ʳ��Υ��������Ʊ���Ǥ���).
 ���η��, ��������󥰤�Ԥ�������٤ȤϤޤ��ۤʤä�����, ȯ����������
 ��������.

 ������, �����Ǥ�Ǯ�Ӥǵ����뱿ư�����Ƥϰ���ʤ�. 
\end{itembox}

����٤ˤ��������ѵ��Ϥξ���Υ�������ǤϤ��줾��ѥ�᡼����
$R_O \sim 0.1, L/a \sim 0.1 , \varepsilon \sim 1$��Ŭ�����ͤǤ���.
������Ф�, Ǯ�Ӥξ���Ǥ�
%
\begin{eqnarray}
 R_O \sim 1, \quad
  L/a \sim 0.1, \quad
  \varepsilon \sim 10^{-2} \quad
  \beta L/f \sim 1
\end{eqnarray}
%
�Ȥʤ�
\footnote{
 �����ӡ�����$R_O = V/fL$�Ǥ���. ����٤����Ǯ�Ӥ�����
 ���ꥪ��ѥ�᡼��������������$R_O$������٤�10�ܤˤʤ�.
}.
$\varepsilon$��$R_i = 100$
\footnote{
 (4-51)����.
}
�ʤΤ�(4-49)����������.
�����$f$����ƻ($f=0$)�����Υ$L$�ˤ�������$f$�ޤ��Ѳ�����Τ�
$\beta \sim f/L$�Ǥ���.
����������Ϥ���ݤ�ʣ���ιब�Х�󥹤��뤿��ˤ�, 
����������(4-43)�Ǥ�$R_1 \leq R_O \sim 1$�Ǥʤ��Фʤ餺,
����Ǯ�ϳ���1ˡ§(4-46)�Ǥ�$R_1 \leq R_O \varepsilon \sim \varepsilon$
�Ǥʤ���Фʤ�ʤ�.
����������������ˤ�
%
\begin{eqnarray}
 R_1 = \varepsilon
\end{eqnarray}
%
�Ǥ���ɬ�פ�����.
(4-43)�ˤ����ƥ���������$V^2/10L^2$�ʲ��ι�����, �ʲ��Τ褦�˴�ñ�ˤʤ�.
%
\begin{eqnarray}
 \DP{\zeta}{t} + \Dvect{V}_{\Psi} \cdot \nabla (\zeta + f) = 0.
\end{eqnarray}
%
ȯ���μ��ϰʲ��Τ褦�ˤʤ�.
%
\begin{eqnarray}
 \Ddiv (\Dvect{V}_{\Psi} \cdot \nabla \Dvect{V}_{\Psi})
  + \Dlapla \phi' - f \zeta
  - \Dvect{k} \times \nabla f \cdot \Dvect{V}_{\Psi} = 0.
\end{eqnarray}
%
����������(4-81)��{\bfseries �Х��������}({\itshape balance equation})
�ȸƤФ��.
���μ��Ϥ��Ф��Хץ�ߥƥ��֥�ǥ�ν���ͤ�����˻Ȥ���.
ȯ��$D$��(4-80)�ˤϸ���ʤ��Τ�Ǯ�ϳ���1ˡ§�Ϥ����������Υ��åȤˤ�
ɬ�פʤ�
\footnote{
 ���������٥���������ϤǤϱ��٤μ���ȯ��$D$�����줿����,
 �ʤ�餫����ˡ�Ǥ����õ��ɬ�פ����ä�.
 �õ�뤿���(4-45)���Ѥ���$D$��$e^{-Z} \dot{Z}$�ι���Ѵ���,
 �����Ǯ�ϳ���1ˡ§���Ѥ��ƾõ��.
 �����ȯ��$D$������ʤ������Ǯ�ϳ���1ˡ§���Ѥ����Ȥ����������򤱤�Τ�
 ɬ��̵��.
}.
������, Ǯ�ӤǶ�����Ǯ�����������, (4-46)�β�Ǯ�ι�Υ��������$fV^2$���
�礭���ʤ�.
���ξ��ˤϱ�ľ��ư���������(4-79)
\footnote{
 ����$R_1$�ϱ��٤��Ф���ȯ�����礭������ʤΤ�, (4-79)��
 ��ȯ����������󥰡פȤ����褦�ʤ�ΤǤ���.
 ����, �����Ǥ�ȯ��$=$��ľ��ư�Ȥ����ͤ����򤷤Ƥ���Τ�,
 ���Υ�������󥰤�ֱ�ľ��ư��������󥰡פȸƤ�Ǥ���. 
}
����������
\footnote{
 ����Ū�ˤ�$R_1 \gg 1$�Ȥ�����������󥰤򤹤뤳�Ȥˤʤ�.
 �������뤳�ȤǱ��٤μ��Ǥ�ȯ��$D$���Ĥ�,
 Ǯ�ϳ���1ˡ§��ɬ�פȤʤ�.
},
���٤μ���ȯ���������褦�ˤʤ�.
�ޤ�, (4-46)�Ǥϲ�Ǯ�ι�ȱ�ľ��ư�ιब�Х�󥹤���褦�ˤʤ�.

�����ǹԤä�����������Ϥ�, ��Ǯ�˴ؤ��뤳�Ȥ�ޤ���ȤϤ���,
Ǯ�Ӥˤ�������פʱ�ư�����Ƥ򥫥С����ƤϤ��ʤ�.
{\bfseries ��ƻ����ӥ���}({\itshape Equatorial Kelvin wave})��
�����ӡ��ȤȽ����Ȥ������餫�����ä��Ȥϰ�ή���֥�������
\footnote{3-2���(4-4)����.}
�ǤϤ��ޤ��������ȤϽ���ʤ�
\footnote{Ǯ�Ӥ�, ���̤Υ����ӡ��Ȥ˴ؤ��Ƥϰ������ȤϽ����. }.
�ޤ��������ȤϤ����ǲ��ꤷ����Τ��⾮������ľ������������.






%\begin{center}
% {\bf 
% --------------------------------------
% ��ʸ�����ޤ�
% --------------------------------------
% } 
%\end{center}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%             �ʲ���Appendix             %%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%   Appendix �Ѥ� Counter, OutputFormat ������   %%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%   Set Counter (chapter, section etc. ) %%%%%%%%
%\setcounter{chapter}{2}
%\setcounter{section}{0}
%\setcounter{footnote}{0}
\setcounter{equation}{0}
%\setcounter{page}{1}
\setcounter{figure}{0}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%        Counter Output Format           %%%%%%%%
\def\theequation{A-\arabic{equation}}
%\def\thesection{\arabic{chapter}-\arabic{section}}
%\def\thesubsection{\arabic{chapter}-\arabic{section}-\arabic{subsection}}
\def\thefigure{A-\arabic{figure}}
\def\thetable{A-\arabic{table}}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%      Appendix        %%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%\subsection*{Appendix \qquad }

%\subsubsection*{}


%%%%%%%%              Text End                  %%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
