%#!platex thesis.tex
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% thesis.tex ����
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%== ����
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% 200?/??/?? ???? ????   ����
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%%%%%%%%   Subtitle, Date, Filename Setting     %%%%%%%%
\markboth{�����������γƹ�ΰ�̣}{�����������γƹ�ΰ�̣}
%\Ddate{2003/01/15}
\Dfile{appendix-1.tex}
%\Dchapter{�����������γƹ�ΰ�̣}

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% ���ֹ����� 1-1, 1-2 ��ɽ�������礳���Υ����ȥ����Ȥ�Ϥ���
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% �ܼ��ˤ��ξϤ����ä���
%\addcontentsline{toc}{section}{�����������γƹ�ΰ�̣}
%\Dchapterhead

\section{�����������γƹ�ΰ�̣}
\Dseclab{�����������γƹ�ΰ�̣}

�ʲ��α��������� (\Dsecref{������������} ���
\Deqref{����������}��) �γƹ�ΰ�̣�ˤĤ��ƹͤ���.
%
\begin{eqnarray}
 \Deqlab{app-����������}
  \DD{(\zeta + f)}{t} =
  - (\zeta + f) \Ddiv \Dvect{V}
  - \Dvect{k} \cdot \nabla w \times \DP{\Dvect{V}}{z}
  + \Dvect{k} \cdot \nabla p \times \nabla \alpha
  + \Dvect{k} \cdot \nabla \times \Dvect{F}.
\end{eqnarray}


\subsection{ȯ���� (divergence term)}
\Dsubseclab{ȯ���� (divergence term)}

\Deqref{app-����������}�α�����1��
$-(\zeta + f) \Ddiv \Dvect{V}$��
{\bfseries ȯ����}({\itshape divergence term})�ȸƤФ��.
����ϲ�ž���Ƥ���������ѱ�ư�̤���¸���ʤ���, ���β�žȾ�¤�
�Ѳ�������ȳ�®�٤��Ѳ����뤳�Ȥ˻��Ƥ���.
ȯ�������Ǥ��뤳�Ȥ�, �����β�žȾ�¤����礹�뤳�Ȥ���������.
�դĤ�ŷ���ޤǸ�����褦���絬�Ϥʱ�ư�Ǥ����б���$(\zeta + f)$
�����Ǥ��뤫��, ȯ�������б��٤򸺾�����, ��«�����б��٤����ä�����
(\Dfigref{app-ȯ����}����).
%
\begin{figure}[htbp]
 %\vspace*{10mm}
 \begin{center}
  \Depsf[][60mm]{./eps/vorticity.eps}
 \end{center}
 \begin{quote}
  \caption{
  {\footnotesize ȯ���ȼ�«�ˤ�뱲�٤�ȯ��(���б��٤����Ȳ���)}
  }
  \Dfiglab{app-ȯ����}
 \end{quote}
\end{figure}
%

\subsection{Ω������ (tilting term)}
\Dsubseclab{Ω������ (tilting term)}

\Deqref{app-����������}�α�����2��
$- \Dvect{k} \cdot \nabla w \times \partial \Dvect{V} / \partial z$
��{\bfseries Ω������}({\itshape tilting term}
or {\itshape twisting term})�ȸƤФ��
\footnote{
 {\bfseries ���й�}�Ȥ�ƤФ��.
}.
��ľ®�٤�ʿ����ǰ��ͤǤʤ�����, �Ϥ��ʿ�����˸����Ƥ������μ���
��ľ������Ω���夬��, ���٤α�ľ��ʬ���Ѳ�������̤򼨤�
\footnote{
 ������⼫���ʤ��Ȥ�����ľ®�٤����ͤʾ��ϱ���Ω���夬�뤳�Ȥ�
 ̵������, ���ι�Ͼ��Ǥ���.
}.
$- \Dvect{k} \cdot \nabla w \times \partial \Dvect{V} / \partial z$
�򥹥��顼ɽ�������
$\displaystyle - \DP{w}{x} \DP{v}{z} + \DP{w}{y} \DP{u}{z}$
�Ȥʤ�.
�ޤ�, $\displaystyle - \DP{w}{x} \DP{v}{z}$�ι��ͤ���.
�����Ǥ�$v$����ˤ����ˤĤ�Ƹ�����, $w$��$x$���������ä��Ƥ������
�ͤ���. ���ξ��,
$\displaystyle - \DP{w}{x} \DP{v}{z}$�����Ȥʤ�,
���б���$(\zeta + f)$�����ä���.
�����\Dfigref{app-Ω���夬���}�ǹͤ��Ƥߤ�.
%
\begin{figure}[htb]
 \begin{center}
  \Depsf[][]{./eps/tilte.eps}
 \end{center}
 \begin{quote}
  \caption{
  {\footnotesize $v$��$z$�����Ѳ��ˤ�ä�$x$������ʿ�Ԥʱ��ɤ�����,
  ���줬�����$w$��$x$�������Ѳ��ˤ�ä�Ω���夬�äƱ�ľ������
  ������ʬ����.}
  }
 \Dfiglab{app-Ω���夬���}
 \end{quote}
\end{figure}
%
$\partial v / \partial z$����Ǥ��뤳�Ȥ���ޤˤ���褦��$x$������
���Ӥ뱲�δɤ��Ǥ���. �����$\partial w/ \partial x$�����Ǥ��뤳�Ȥ���
���α��ɤ��ޤ�������������˲�ž��, Ω���夬��.
���β�ž��������ͤ���, ���η�̱��٤����ä��뤳�Ȥ��狼�������.
$(\partial w / \partial y) (\partial u / \partial z)$�ι�˴ؤ��Ƥ�
Ʊ�ͤ˹ͤ��뤳�Ȥ��Ǥ���.
���ʤߤˤ��ι�ϥ᥽���ݤ�ε����ȯ�������������˽��פ������̤�����
�餷��.

\subsection{����Υ��ɹ� (solenoidal term)}
\Dsubseclab{����Υ��ɹ� (solenoidal term)}

\Deqref{app-����������}�α�����3��
$\Dvect{k} \cdot \nabla p \times \nabla \alpha$��
{\bfseries ����Υ��ɹ�}({\itshape solenoidal term})�ȸƤФ��.
�����\Dfigref{app-����Υ��ɹ�}�ǹͤ���ȴ�ñ�Ǥ���.
%
%\begin{figure}[htb]
% \begin{center}
%  \Depsf[][]{./eps/solenoid.eps}
% \end{center}
% \begin{quote}
%  \caption{
%  {\footnotesize (a)�Ǥ���$p$�̤���$\alpha$�̤��򺹤��Ƥ��뤿��,
%  ����������. ������Ф�, (b)�Ǥ���$p$�̤���$\alpha$�̤�
%  ʿ�ԤˤʤäƤ��뤿�ᱲ�������ʤ�.
%  (Peixoto, J. P. and A. H. Oort, 1992:
%   Physics of Climate.
%   {\itshape Springer-Verlag}, 520pp. ���)}
%  }
%  \Dfiglab{app-����Υ��ɹ�}
% \end{quote}
%\end{figure}
%
(a)�Ǥ���$p$�̤���$\alpha$�̤��򺹤��Ƥ���.
���ϸ��ۤˤ�ä�ή�줬������������, ���κݤ�(a)�Τ褦��̩�ٹ�¤��
�ʤäƤ����, ̩�٤κ��ˤ�ä�ή��˺����Ǥ�, 
���η�̤Ȥ��Ʊ���������.
���줬����Υ��ɹ�θ��̤Ǥ���.
������Ф���(b)�Ǥ���$p$�̤���$\alpha$�̤�ʿ�ԤˤʤäƤ���.
���ξ��ˤ�ή��˺��ϤǤ���, ���������ʤ�.

���ʤߤ�, ��ľ��ɸ��$p$��Ȥä����, �����Τ褦��
$\nabla_p p = 0$�Ȥʤ�, ����Υ��ɹ�Ͼ��Ǥ���.
���������κǸ�Ǥ�Ҥ٤��Ƥ��뤳�ȤǤ���.


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