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\Dtitle{p ��ɸ�Ϥˤ����� Eliassen-Palm Flux ���꼰��}
\Dauthor[�͸�����]{�͸�����}

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                  &= \overline{v} 
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$\displaystyle \begin{itemize}
     <tex2html_comment_mark> \item ��ư������
     <tex2html_comment_mark> \begin{align}
          \DD{u}{t}       &-  \left(f + \frac{u\tan\phi}{a}\right)v
                                         + \Dinv{a\cos\phi}\DP{\Phi}{\lambda} = X,\\
          \DD{v}{t}       &+  \left(f + \frac{u\tan\phi}{a}\right)u 
                                                    + \Dinv{a}\DP{\Phi}{\phi} = Y,
     \end{align}
     <tex2html_comment_mark> \item �ſ尵ʿ�ռ�
     <tex2html_comment_mark> \begin{align}
          \DP{\Phi}{p}    &=  -\alpha,
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     <tex2html_comment_mark> \item Ϣ³�μ�
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                                 + \DP{\omega}{p} = 0,
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     <tex2html_comment_mark> \item Ǯ͢���μ�
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\begin{subequations}\begin{align}
     \DP{}{t}(\overline{u} + u') &
           + \frac{\overline{u} + u'}{a\cos\phi}\DP{}{\lambda}(\overline{u} + u')
           + \frac{\overline{v} + v'}{a}\DP{}{\phi}(\overline{u} + u')
           + (\overline{\omega} + \omega')\DP{}{p}(\overline{u} + u')\\ 
       &- \left[f + \frac{\tan\phi}{a}(\overline{u} + u')\right](\overline{v} + v')
        + \Dinv{a\cos\phi}\DP{}{\lambda}(\overline{\Phi} + \Phi') = \overline{X} + X',\notag\\ \\
     \DP{}{t}(\overline{v} + v') &
           + \frac{\overline{u} + u'}{a\cos\phi}\DP{}{\lambda}(\overline{v} + v')
           + \frac{\overline{v} + v'}{a}\DP{}{\phi}(\overline{v} + v')
           + (\overline{\omega} + \omega')\DP{}{p}(\overline{v} + v')\notag\\ 
       &+ \left[f + \frac{\tan\phi}{a}(\overline{u} + u')\right](\overline{u} + u')
        + \Dinv{a}\DP{}{\phi}(\overline{\Phi} + \Phi') = \overline{Y} + Y',\notag\\ \\
    \DP{}{p}(\overline{\Phi} + \Phi')&
        =  -(\overline{\alpha} + \alpha'),\\
    \Dinv{a\cos\phi}&\left[\DP{}{\lambda}(\overline{u} + u')
        + \DP{}{\phi}\{(\overline{v} + v')\cos\phi\}\right]
        + \DP{}{p}[(\overline{\omega} + \omega')] = 0,\\
    \DP{}{t}(\overline{\theta} + \theta') &
           + \frac{\overline{u} + u'}{a\cos\phi}\DP{}{\lambda}(\overline{\theta} + \theta')
           + \frac{\overline{v} + v'}{a}\DP{}{\phi}(\overline{\theta} + \theta')
           + (\overline{\omega} + \omega')\DP{}{p}(\overline{\theta} + \theta')\notag\\ 
       &= \overline{Q} + Q'
   \end{align}\end{subequations}%
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\begin{subequations}\begin{align}
     \DP{\overline{u}}{t} &
         + \frac{\overline{u}}{a\cos\phi}\DP{\overline{u}}{\lambda}
         + \frac{\overline{v}}{a}\DP{\overline{u}}{\phi}
         + \overline{\omega}\DP{\overline{u}}{p}
         - f\overline{v} 
         - \frac{\tan\phi}{a}\overline{u}\overline{v}
         + \Dinv{a\cos\phi}\DP{\overline{\Phi}}{\lambda}
         - \overline{X} =
  \\ &
           - \DP{u'}{t}
           - \frac{\overline{u}}{a\cos\phi}\DP{u'}{\lambda}
           - \frac{u'}{a\cos\phi}\DP{\overline{u}}{\lambda}
           - \frac{u'}{a\cos\phi}\DP{u'}{\lambda}\notag\\ &
           - \frac{\overline{v}}{a}\DP{u'}{\phi}
           - \frac{v'}{a}\DP{\overline{u}}{\phi}
           - \frac{v'}{a}\DP{u'}{\phi}\notag\\ &
           - \overline{\omega}\DP{u'}{p}
           - \omega'\DP{\overline{u}}{p}
           - \omega'\DP{u'}{p}\notag\\ &
           + fv'\notag\\ &
           + \frac{\tan\phi}{a}\overline{u}v'
           + \frac{\tan\phi}{a}u'\overline{v}
           + \frac{\tan\phi}{a}u'v'\notag\\ &
           - \Dinv{a\cos\phi}\DP{\Phi'}{\lambda}\notag\\ &
           + X',\\
     \DP{\overline{v}}{t} &
         + \frac{\overline{u}}{a\cos\phi}\DP{\overline{v}}{\lambda}
         + \frac{\overline{v}}{a}\DP{\overline{v}}{\phi}
         + \overline{\omega}\DP{\overline{v}}{p}
         + f\overline{u}
         + \frac{\tan\phi}{a}(\overline{u})^2
         + \Dinv{a}\DP{\overline{\Phi}}{\phi}
         - \overline{Y} =
  \notag\\ &
           - \DP{v'}{t}
           - \frac{\overline{u}}{a\cos\phi}\DP{v'}{\lambda}
           - \frac{u'}{a\cos\phi}\DP{\overline{v}}{\lambda}
           - \frac{u'}{a\cos\phi}\DP{v'}{\lambda}\notag\\ &
           - \frac{\overline{v}}{a}\DP{v'}{\phi}
           - \frac{v'}{a}\DP{\overline{v}}{\phi}
           - \frac{v'}{a}\DP{v'}{\phi}\notag\\ &
           - \overline{\omega}\DP{v'}{p}
           - \omega'\DP{\overline{v}}{p}
           - \omega'\DP{v'}{p}\notag\\ &
           - fu'\notag\\ &
           - 2\frac{\tan\phi}{a}\overline{u}u'
           - \frac{\tan\phi}{a}(u')^2\notag\\ &
           - \Dinv{a\cos\phi}\DP{\Phi'}{\phi}\notag\\ &
           + Y',\\
    \DP{\overline{\Phi}}{p} + \overline{\alpha}&
        = -\DP{\Phi'}{p} - \alpha',\\
     \Dinv{a\cos\phi}&\left[\DP{\overline{u}}{\lambda}
        + \DP{}{\phi}(\overline{v}\cos\phi)\right]
        + \DP{\overline{\omega}}{p} 
      = \notag\\ &
        - \Dinv{a\cos\phi}\left[
            \DP{u'}{\lambda}
          + \DP{}{\phi}(v'\cos\phi)
        \right]
        - \DP{\omega'}{p} ,\\
     \DP{\overline{\theta}}{t} &
         + \frac{\overline{u}}{a\cos\phi}\DP{\overline{\theta}}{\lambda}
         + \frac{\overline{v}}{a}\DP{\overline{\theta}}{\phi}
         + \overline{\omega}\DP{\overline{\theta}}{p}
         - \overline{Q} =
  \notag\\ &
           - \DP{\theta'}{t}
           - \frac{\overline{u}}{a\cos\phi}\DP{\theta'}{\lambda}
           - \frac{u'}{a\cos\phi}\DP{\overline{\theta}}{\lambda}
           - \frac{u'}{a\cos\phi}\DP{\theta'}{\lambda}\notag\\ &
           - \frac{\overline{v}}{a}\DP{\theta'}{\phi}
           - \frac{v'}{a}\DP{\overline{\theta}}{\phi}
           - \frac{v'}{a}\DP{\theta'}{\phi}
           - \overline{\omega}\DP{\theta'}{p}
           - \omega'\DP{\overline{\theta}}{p}
           - \omega'\DP{\theta'}{p}
           + Q'
   \end{align}\end{subequations}%
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\begin{subequations}\begin{align}
     \DP{\overline{u}}{t}&
         + \Dinv{a}\overline{v}\DP{\overline{u}}{\phi}
         + \overline{\omega}\DP{\overline{u}}{p}
         - f\overline{v} 
         - \frac{\tan\phi}{a}\overline{u}\overline{v}
         - \overline{X} =
       \\ & \hspace{5em}
           - \Dinv{a\cos\phi}\overline{u'\DP{u'}{\lambda}}
           - \Dinv{a}\overline{v'\DP{u'}{\phi}}
           - \overline{\omega'\DP{u'}{p}}
           + \frac{\tan\phi}{a}\overline{u'v'},\\
     \DP{\overline{v}}{t}&
         + \frac{\overline{v}}{a}\DP{\overline{v}}{\phi}
         + \overline{\omega}\DP{\overline{v}}{p}
         + f\overline{u}
         + \frac{\tan\phi}{a}(\overline{u})^2
         + \Dinv{a}\DP{\overline{\Phi}}{\phi}
         - \overline{Y} =
      \notag\\ & \hspace{5em}
           - \Dinv{a\cos\phi}\overline{u'\DP{v'}{\lambda}}
           - \Dinv{a}\overline{{v'}\DP{v'}{\phi}}
           - \overline{\omega'\DP{v'}{p}}
           - \frac{\tan\phi}{a}\overline{(u')^2},\\
     \DP{\overline{\Phi}}{p} &+ \overline{\alpha} = 0,\\
     \Dinv{a\cos\phi}&\left[
        \DP{}{\phi}(\overline{v}\cos\phi)\right]
        + \DP{\overline{\omega}}{p} 
        = 0,\\
     \DP{\overline{\theta}}{t}&
         + \frac{\overline{v}}{a}\DP{\overline{\theta}}{\phi}
         + \overline{\omega}\DP{\overline{\theta}}{p}
         - \overline{Q} =
           - \Dinv{a\cos\phi}\overline{u'\DP{\theta'}{\lambda}}
           - \Dinv{a}\overline{v'\DP{\theta'}{\phi}}
           - \overline{\omega'\DP{\theta'}{p}}
   \end{align}\end{subequations}%
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\lthtmlinlinemathA{tex2html_wrap_indisplay1740}%
$\displaystyle \Dinv{a\cos\phi}\left[\DP{u'}{\lambda}
+ \DP{}{\phi}(v'\cos\phi)\right]
+ \DP{\omega'}{p}
= 0$%
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$ u' \times $%
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$\displaystyle \DP{\overline{u}}{t}$%
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\lthtmlinlinemathA{tex2html_wrap_indisplay1744}%
$\displaystyle + \Dinv{a}\overline{v}\DP{\overline{u}}{\phi}
         + \overline{\omega}\DP{\overline{u}}{p}
         - f\overline{v} 
         - \frac{\tan\phi}{a}\overline{u}\overline{v}
         - \overline{X} =\notag$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1745}%
$\displaystyle - \Dinv{a\cos\phi}\overline{u'\DP{u'}{\lambda}}
           - \Dinv{a}\overline{v'\DP{u'}{\phi}}
           - \overline{\omega'\DP{u'}{p}}\notag$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1746}%
$\displaystyle - \Dinv{a\cos\phi}\overline{u'\DP{u'}{\lambda}}
           - \Dinv{a}\overline{u'\DP{v'}{\phi}}
           - \overline{u'\DP{\omega'}{p}}
           + \frac{2\tan\phi}{a}\overline{u'v'}.$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1747}%
$\displaystyle - \Dinv{a\cos\phi}\overline{u'\DP{u'}{\lambda}}
           - \Dinv{a\cos\phi}\overline{u'\DP{u'}{\lambda}}$%
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\lthtmlinlinemathA{tex2html_wrap_indisplay1748}%
$\displaystyle = - \Dinv{a\cos\phi}\overline{\DP{(u')^2}{\lambda}}$%
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$\displaystyle = 0,$%
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\lthtmlinlinemathA{tex2html_wrap_indisplay1750}%
$\displaystyle - \Dinv{a}\overline{v'\DP{u'}{\phi}}
           - \Dinv{a}\overline{u'\DP{v'}{\phi}}
           + \frac{2\tan\phi}{a}\overline{u'v'}$%
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$\displaystyle = -\Dinv{a\cos^2\phi}\DP{}{\phi}(\overline{v'u'}\cos^2\phi)$%
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{\newpage\clearpage
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$\displaystyle - \overline{\omega'\DP{u'}{p}}
           - \overline{u'\DP{\omega'}{p}}$%
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$\displaystyle = -\DP{}{p}(\overline{\omega'u'})$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1754}%
$\displaystyle \DP{\overline{u}}{t}
         + \Dinv{a}\overline{v}\DP{\overline{u}}{\phi}
         + \overline{\omega}\DP{\overline{u}}{p}
         - f\overline{v} 
         - \frac{\tan\phi}{a}\overline{u}\overline{v}
         - \overline{X} =
       \notag$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1755}%
$\displaystyle \hspace{5em}
 		-\Dinv{a\cos^2\phi}\DP{}{\phi}(\overline{v'u'}\cos^2\phi)
 		-\DP{}{p}(\overline{\omega'u'})$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1760}%
$\displaystyle \begin{itemize}
     <tex2html_comment_mark> \item ��ư������
     <tex2html_comment_mark> \begin{align}
       \DP{\overline{u}}{t}&
         + \Dinv{a}\overline{v}\DP{\overline{u}}{\phi}
         + \overline{\omega}\DP{\overline{u}}{p}
         - f\overline{v} 
         - \frac{\tan\phi}{a}\overline{u}\overline{v}
         - \overline{X} =
       \\ & \hspace{5em}
 		-\Dinv{a\cos^2\phi}\DP{}{\phi}(\overline{v'u'}\cos^2\phi)
 		-\DP{}{p}(\overline{\omega'u'})
          ,\\
        \DP{\overline{v}}{t}&
         + \frac{\overline{v}}{a}\DP{\overline{v}}{\phi}
         + \overline{\omega}\DP{\overline{v}}{p}
         + f\overline{u}
         + \frac{\tan\phi}{a}(\overline{u})^2
         + \Dinv{a}\DP{\overline{\Phi}}{\phi}
         - \overline{Y} =
       \notag\\ & \hspace{5em}
 		- \Dinv{a\cos\phi}\DP{}{\phi}(\overline{(v')^2}\cos\phi)
 		- \DP{}{p}(\overline{\omega'v'})
         - \overline{(u')^2}\frac{\tan\phi}{a},
     \end{align}
     <tex2html_comment_mark> \item �ſ尵ʿ�դμ�
     <tex2html_comment_mark> \begin{align}
         \DP{\overline{\Phi}}{p} + \overline{\alpha} = 0,
     \end{align}
     <tex2html_comment_mark> \item Ϣ³�μ�
     <tex2html_comment_mark> \begin{align}
         \Dinv{a\cos\phi}&\left[
        \DP{}{\phi}(\overline{v}\cos\phi)\right]
        + \DP{\overline{\omega}}{p} 
        = 0,
     \end{align}
     <tex2html_comment_mark> \item Ǯ͢���μ�
     <tex2html_comment_mark> \begin{align}
        \DP{\overline{\theta}}{t}
         + \frac{\overline{v}}{a}\DP{\overline{\theta}}{\phi}
         + \overline{\omega}\DP{\overline{\theta}}{p}
         - \overline{Q} =
 		- \Dinv{a\cos\phi}\DP{}{\phi}(\overline{v'\theta'}\cos\phi)
 		- \DP{}{p}(\overline{\omega'\theta'}).
     \end{align}
   \end{itemize}$%
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\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1768}%
$\displaystyle \begin{itemize}
     <tex2html_comment_mark> \item ��ư������
     <tex2html_comment_mark> \begin{align}&
       \DP{\overline{u}}{t}
         + \overline{v}^*\left[\Dinv{a\cos\phi}\DP{}{\phi}(\overline{u}\cos\phi) - f\right]
         + \overline{\omega}^*\DP{\overline{u}}{p}
         - \overline{X} =
         \Dinv{a \cos\phi}\Ddiv\Dvect{F},\\&
         \overline{u}\left(f+\overline{u}\frac{\tan\phi}{a}\right) 
                                    + \Dinv{a}\DP{}{\phi}\overline{\Phi} = G,
     \end{align}
     <tex2html_comment_mark> \item �ſ尵ʿ�դμ�
     <tex2html_comment_mark> \begin{align}
         \DP{\overline{\Phi}}{p} + \overline{\alpha} = 0,
     \end{align}
     <tex2html_comment_mark> \item Ϣ³�μ�
     <tex2html_comment_mark> \begin{align}
         \Dinv{a\cos\phi}&\left[
        \DP{}{\phi}(\overline{v}^*\cos\phi)\right]
        + \DP{\overline{\omega}^*}{p} 
        = 0,
     \end{align}
     <tex2html_comment_mark> \item Ǯ͢���μ�
     <tex2html_comment_mark> \begin{align}
        \DP{\overline{\theta}}{t}
         + \frac{\overline{v}^*}{a}\DP{\overline{\theta}}{\phi}
         + \overline{\omega}^*\DP{\overline{\theta}}{p}
         - \overline{Q} =
 		- \DP{}{p}
                 \left[
                       \left(
                         \overline{v'\theta'}\frac{\DP{\overline{\theta}}{\phi}}
                                  {a\DP{\overline{\theta}}{p}} + \overline{\omega'\theta'}
                       \right)
                 \right].
     \end{align}
   \end{itemize}$%
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% latex2html id marker 1773
$\displaystyle \begin{itemize}
     <tex2html_comment_mark> \item �ĺ��۴�
     <tex2html_comment_mark> \begin{align}
         \overline{v}^* &\equiv \overline{v} 
          - \DP{}{p}\left(\frac{\overline{v'\theta'}}
                          {\overline{\DP{\theta}{p}}}\right)\\ 
         \overline{\omega}^* &\equiv \overline{\omega} 
          + \Dinv{a \cos\phi}\DP{}{\phi}\left(\cos\phi\frac{\overline{v'\theta'}}
                          {\overline{\DP{\theta}{p}}}\right)\tag{\ref{residual_w}}
     \end{align}
     <tex2html_comment_mark> \item EP �ե�å���
     <tex2html_comment_mark> \begin{align*}
         {F_\phi} =& a
         \cos \phi \left(\DP{\overline{u}}{\overline{p}}
         \frac{\overline{v'\theta'}}{\DP{\overline{\theta}}{p}} - \overline{u'v'}\right)\tag{\ref{epflx_phi}}\\ 
         {F_p} =& a
         \cos \phi \left(\left[ f - \frac{\DP{\overline{u}\cos \phi}{\phi}}{a\cos\phi} \right]
        \frac{\overline{v'\theta'}}{\DP{\overline{\theta}}{p}} - \overline{u'\omega'}\right)\tag{\ref{epflx_p}}.
     \end{align*}
     <tex2html_comment_mark> \item \Ddiv
     <tex2html_comment_mark> \begin{align}
       \Ddiv{} = \Dinv{a \cos \phi} \DP{\cos \phi}{\phi} + \DP{}{p}\tag{\ref{div}}
     \end{align}
   \end{itemize}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1777}%
$\displaystyle \DP{\overline{u}}{t}
         + \overline{v}^*\left[\Dinv{a\cos\phi}\DP{}{\phi}(\overline{u}\cos\phi) - f\right]
         + \overline{\omega}^*\DP{\overline{u}}{p}
         - \overline{X} =
         \Dinv{\sigma \cos\phi}\Ddiv\Dvect{\hat{F}}.$%
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\stepcounter{section}
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$ T$%
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$\displaystyle \theta$%
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$\displaystyle = T \left(\frac{p_{00}}{p}\right)^\kappa, \kappa = R/C_p$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1791}%
$ R$%
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\end{document}
