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\section{�Х�󥹥����ƥ�}

\begin{itembox}[l]{����}
 \Dparskip  \vspace{-6mm}
 ���ѵ��Ϥ������, Ǯ��, �ڤ��������Ϥ����Ƥ�ޤॹ��������Ϥ򤪤��ʤ�
 ��{\bfseries �Х�󥹥����ƥ�}({\itshape balance system})�ˤĤ���
 ��������.

 �Х�󥹥����ƥ�Ϥ��줾��ε��ϤǤΥ���������Ϥ���Ȥ���Ƥ���¿����
 ��򤽤Τޤ޻Ĥ�����ΤǤ���.
 ������, ���Τ���˲򤯤��Ȥ��񤷤�, ���Ͽ���ͽ��ˤϤۤȤ�ɻȤ��Ƥ�
 �ʤ�.
\end{itembox}

�͡������̤ʾ����θ�������Ƥι��ޤ�, ���ѵ��Ϥα�ư�˴ؤ��Ƥ�
��������Τ˵��ҤǤ���褦��, ��깭�����Ӥ���ä��������Ϥ������
˾�ޤ���.
���ѵ��ϲ��Ϥˤ����ƥ�������$R_O$�ʾ�����Ƥι��
�Ĥ����ޤޤ��������ϤȤ���, {\bfseries �Х�󥹥����ƥ�}
({\itshape balance system})������.
�Х�󥹥����ƥ�ϰʲ��Τ褦�˵��Ҥ����.
%
\begin{eqnarray}
 \DP{\zeta}{t} + (\Dvect{V}_{\Psi} + \Dvect{V}_{\chi}) \cdot
  \nabla (\zeta + f) + \omega \DP{\zeta}{p}
  \hspace{40mm} & &
  \nonumber \\
  + (f + \zeta) D + \Dvect{k} \cdot \nabla \omega \times
  \DP{\Dvect{V}_{\Psi}}{p} &=& 0,
  \\
 \Ddiv (\Dvect{V}_{\Psi} \cdot \nabla \Dvect{V}_{\Psi})
  + \Dlapla \phi - f \zeta - \Dvect{k} \times \nabla f \cdot \Dvect{V}_{\Psi}
  &=& 0,
  \\
 \DP{}{t} \DP{\phi}{p} + (\Dvect{V}_{\Psi} + \Dvect{V}_{\chi}) \cdot \nabla
  \DP{\phi}{p} + \frac{\omega}{p} \DP{}{p}
  \left[
   p \DP{\phi}{p} - \kappa \phi
  \right]
  &=& 0,
  \\
 D + \DP{\omega}{p} &=& 0.
\end{eqnarray}
%
¾�δط����ϰʲ��Τ褦�ˤʤ�.
%
\begin{eqnarray}
 \Dvect{V}_{\Psi} = \Dvect{k} \times \nabla \Psi, \quad
  \Dvect{V}_{\chi} = \nabla \chi,
  \\
 \zeta = \Dlapla \Psi, \quad \hspace{7mm}
  D = \Dlapla \chi.
  \nonumber 
\end{eqnarray}
%
�����������������Ѥ������ʤ���, ���Ϻ�ɸ�Ϥǵ��Ҥ���Ƥ���.
������������ͣ����Ȥ��줿���, ����ȯ����ʬ��ޤ�Ω���夬���ΰ���
\footnote{
 ����Ū�ˤ�(4-43)�κǸ�ι�Ǥ���
 $\Dvect{k} \cdot \nabla \dot{Z} \times (\partial \Dvect{V}_{\chi} /
 \partial Z)$�Ǥ���.
}
�Ǥ���.
ȯ���������Ǥ�����ȯ����ʬ�˰�¸�������Ƥι����Ȥ���.
���η��, ȯ����������$\Psi$��$\phi$�ι�Τߤǵ��ҤǤ���褦�ˤʤä�.
���μ���{\bfseries �Х��������}({\itshape balance equation})��
�ƤФ��
\footnote{3-5���(4-81)�ǰ������о줷�����Ǥ���.}.
Ǯ�ϳ���1ˡ§�����Ƥιब�Ĥä��ޤޤǤ���.
�ʤ�, ��Ǯ���໤�Ϥιब¾�ι�Υ���������Ʊ�����������礭�����,
�����ι�⤳�μ��˲ä�����.

�Х�󥹥����ƥ�ϥ���������Ϥ���Ƥ���Τǽ�����֤ξ����ʸ�����
�Ҵ��ǤϤʤ�. �ޤ�, �Х�󥹥����ƥ��ȯ���������ˤ�����ȯ���θ��ۤ�
̵�뤷�Ƥ��뤿��˽����Ȥ�¸�ߤ�����ʤ�.
���ѵ��Ϥα�ư�ˤ�����, ̵�뤵�����ǺǤ��礭����Υ���������${R_O}^2$
�Ǥ���
\footnote{
 3-4��Ρ�����ٲ��ϡפǤ�$R_O$�ʲ��Υ��������ι����Ȥ��Ƥ���
 ($R_O \sim 0.1$).
 ����Ϥ������ľ��������������⽦���褦�ˤ���.
}.
����ˤ��, �Х����������Ǯ��, �ڤ��������ϤǤΥ���������Ϥ�����줿
���Ƥι��ޤ�.
ͣ����㳰��$- \Dvect{k} \times \nabla f \cdot \Dvect{V}_{\chi}$�ι�Ǥ���.
���ι���������Ϥα�ư��ȯ����������ɬ�פˤʤ�\footnote{(4-84)������.}.
���ι��(4-87)�˲ä��Ƥ⥨�ͥ륮����¸§�ˤϱƶ���ڤܤ��ʤ�.
������, ���ι��¸�ߤ��������Ϥβ�����Τ���ˤ���.
���Ϲ�ή�������ϤǤ�$f$����ʬ����Ƥ��ʤ��¤��������֤��������Ƥ�����,
�Х����������$f$���Ѳ������ƴޤ�Ǥ���.
$f$���Ѳ���, �絬�Ϥ��ΰ��ͽ¬��Ԥ������ä˽��פˤʤ�.

�Թ��ʻ���, �Х�󥹥����ƥ�ϲ򤯤Τ������񤷤�. ����ϥХ�󥹥����ƥ�
������Ū�ʷ�
\footnote{����Ū�ˤϥХ���������Ǥ���(4-87)�Τ��Ȥ���äƤ���.}
�򤷤Ƥ��뤫��Ǥ���.
���Ϲ�ή�������ϤȤϰ㤤, ���μ�����ϴ�ñ�ʥݥƥ󥷥�뱲����������
����������Ƴ�����Ͻ���ʤ�.
����˲ä�, �Х�󥹥����ƥ��{\bfseries ����ӥ���}({\itshape Kelvin wave})
�Τ褦�ʽ��פ�Ǯ�ӽ۴ı�ư�򵭽ҤǤ��ʤ�.
���, �Х�󥹥����ƥ�Ͽ���ͽ��ˤϤ��ޤ�Ȥ������̵��.
����, ���Ϲ�ή�������Ϥ�����줿��̤������Τʤ�Τ��ߤ������ˤ�
�ץ�ߥƥ����������Ϥ��Ȥ���.
������, �Х����������ޤ�, �ץ�ߥƥ����������Ϥν���ͤ������
�����Ĥ����ϳإץ����������򤹤뤳�Ȥν����ˤϤʤäƤ���.



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