\batchmode


\documentclass[a4j,twoside]{jreport}
\RequirePackage{ifthen}


\usepackage{Dennou6}


\Dtitle[DCAPM2 第1部 数理モデル化]{DCAPM2 \\[5mm]
          第1部 \ 数理モデル化\\[70mm]}
  \Dauthor[地球流体電脳倶楽部]{地球流体電脳倶楽部}
  %
\Dver{20050623-4} \Dmodify{2005}{06}{22}
  \Ddate[\Dmoddate ]{\DmoddateJ (DCPAM2-\Dversion )}

%
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\footnotetext[0]{#1}
\renewcommand{\thefootnote}{\arabic{footnote}}
} 


\makeindex




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  {\cal D}(\zeta) = - K_{HD} 
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$N_D$%
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$\sim$%
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$R^d$%
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$c_p^d$%
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$R$%
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$c_p$%
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$\displaystyle p^d$%
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$\displaystyle \rho^{d} R^d T,$%
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$\displaystyle p^v$%
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$\displaystyle \rho^{v} R^v T,$%
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$\bullet^d$%
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$\bullet^v$%
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$\displaystyle p$%
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$\displaystyle (\rho^d R^d + \rho^v R^v) T$%
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$\epsilon_v \equiv
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$\rho^v$%
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$S$%
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$\sigma_{ij}$%
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$\Phi^*$%
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$F'_i$%
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        \rho \DD{v_i}{t}
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$F_i$%
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$\Dvect{v}/2$%
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$\varepsilon$%
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$v_i$%
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$\DP{\Phi^*}{t}=0$%
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$\displaystyle v_i \DP{}{t} ( \rho v_i )
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$\displaystyle \DP{}{t} ( \rho v_i^2 )
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$\displaystyle \DP{}{t} ( \rho v_i^2 )
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$\displaystyle + \frac{1}{2} v_i^2 \DP{\rho}{t}
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$\displaystyle \DP{}{t} \left( \frac{1}{2} \rho v_i^2 \right)
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$\displaystyle \DP{}{t} \left( \frac{1}{2} \rho v_i^2 \right)
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$\displaystyle v_i \rho \DP{\Phi^*}{x_i}$%
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$\displaystyle \Phi^* \left\{ \DP{\rho}{t} + \DP{}{x_i}(\rho v_i) \right\}
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$Q^*$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline956}%
$\varepsilon = c_v T$%
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$c_p = c_v + R$%
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$T_v$%
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$\Dvect{\Omega}$%
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$\psi$%
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$\Dvect{A}$%
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$\displaystyle \mbox{回転系} \ \ \ \ $%
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\lthtmlinlinemathA{tex2html_wrap_indisplay5046}%
$\displaystyle \Dvect{i}' A'_x
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$\displaystyle \left( \DD{\Dvect{A}}{t} \right)_{\rm a}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5050}%
$\displaystyle \Dvect{i} \left( \DD{A_x}{t} \right)_{\rm a}
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5052}%
$\displaystyle \Dvect{i}' \left( \DD{A'_x}{t} \right)_{\rm a}
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5054}%
$\displaystyle \Dvect{i}' \left( \DD{A'_x}{t} \right)_{\rm r}
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5056}%
$\displaystyle \left( \DD{\Dvect{A}}{t} \right)_{\rm r}
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1224}%
$\Dvect{A}=\Dvect{r}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1226}%
$\Dvect{r}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1228}%
$\Dvect{v}_a \equiv (d\Dvect{r}/dt)_{\rm a}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1230}%
$\Dvect{v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1232}%
$\Dvect{v} \equiv (d\Dvect{r}/dt)_{\rm
r}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1138}%
\begin{displaymath}
  \Dvect{v}_a = \Dvect{v} + \Dvect{\Omega} \times \Dvect{r}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1234}%
$\Dvect{A}=\Dvect{v}_{\rm a}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1148}%
\begin{displaymath}
    \DD{\Dvect{v}_a}{t}
 =  \DD{\Dvect{v}}{t} + 2 \Dvect{\Omega} \times \Dvect{v}
    + \Dvect{\Omega} \times ( \Dvect{\Omega} \times \Dvect{r} ),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath1162}%
\begin{displaymath}
      \DD{\Dvect{v}}{t}
  = - \frac{1}{\rho} \Dgrad p 
    - 2 \Dvect{\Omega} \times \Dvect{v}
    - \Dvect{\Omega} \times ( \Dvect{\Omega} \times \Dvect{r} )
    + \Dgrad \Phi^* + \Dvect{F}. 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1236}%
$\Dvect{g} \equiv \Dgrad \Phi^* - \Dvect{\Omega}
\times ( \Dvect{\Omega} \times \Dvect{v})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1178}%
\begin{displaymath}
  \DD{\Dvect{v}}{t}
  = - \frac{1}{\rho} \Dgrad p 
    - 2 \Dvect{\Omega} \times \Dvect{v}
    + \Dvect{g} + \Dvect{F}, 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap5071}%

% latex2html id marker 5071
\setcounter{footnote}{10}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap5072}%

% latex2html id marker 5072
\setcounter{footnote}{10}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1729}%
$(\xi_1, \xi_2, \xi_3)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1731}%
$\bullet$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1733}%
$\Dvect{A}=(A_1, A_2, A_3)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1735}%
$h_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1737}%
$\Dvect{e}_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1326}%
\begin{displaymath}
  \Dgrad \bullet
    = \left( \frac{1}{h_1} \DP{\bullet}{\xi_1},
             \frac{1}{h_2} \DP{\bullet}{\xi_2}, 
             \frac{1}{h_3} \DP{\bullet}{\xi_3} \right),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1340}%
\begin{displaymath}
  \Ddiv \Dvect{A} 
  = \frac{1}{h_1 h_2 h_3} 
    \left[ \DP{}{\xi_1} ( h_2 h_3 A_1)
           +  \DP{}{\xi_2} ( h_1 h_3 A_2)
           +  \DP{}{\xi_3} ( h_1 h_2 A_3)
    \right],
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1351}%
\begin{displaymath}
    \nabla^2 \bullet 
  = \frac{1}{h_1 h_2 h_3} 
    \left[  \DP{}{\xi_1} 
              \left( \frac{h_2 h_3}{h_1} \DP{\bullet}{\xi_1} \right)
           + \DP{}{\xi_2}
              \left( \frac{h_1 h_3}{h_2} \DP{\bullet}{\xi_2} \right)
           + \DP{}{\xi_3}
              \left( \frac{h_1 h_2}{h_3} \DP{\bullet}{\xi_3} \right)
    \right],
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1373}%
\begin{displaymath}
  \Drot \Dvect{A}
  = \left(  \frac{1}{h_2 h_3}
            \left[ \DP{(h_3 A_3)}{\xi_2}  - \DP{(h_2 A_2)}{\xi_3}  \right],
            \frac{1}{h_3 h_1}
            \left[ \DP{(h_1 A_1)}{\xi_3}  - \DP{(h_3 A_3)}{\xi_1}  \right],
            \frac{1}{h_1 h_2}
            \left[ \DP{(h_2 A_2)}{\xi_1}  - \DP{(h_1 A_1)}{\xi_2}  \right]
   \right),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1394}%
\begin{displaymath}
  \DD{\bullet}{t} 
  = \DP{\bullet}{t}
    + \frac{v_1}{h_1} \DP{\bullet}{\xi_1}
    + \frac{v_2}{h_2} \DP{\bullet}{\xi_2}
    + \frac{v_3}{h_3} \DP{\bullet}{\xi_3},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1412}%
\begin{displaymath}
  \DD{\Dvect{v}}{t}
  =  \sum^3_{k=1} \Dvect{e}_k
      \left[ \DP{v_k}{t}
       + \sum^3_{j=1} \frac{v_k}{h_k} \DP{v_k}{\xi_j}
       + \left( -\frac{v_j}{h_j} \frac{1}{h_k} \DP{h_j}{\xi_k}
          +\frac{v_k}{h_k} \frac{1}{h_j} \DP{h_k}{\xi_j} \right) v_j
      \right].
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1739}%
$\Dvect{g}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1741}%
$(\xi_1, \xi_2, \xi_3) = (\lambda, \varphi, r)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1743}%
$(x_1, x_2, x_3)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5091}%
$\displaystyle x_1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5093}%
$\displaystyle r \cos \varphi \cos \lambda,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5094}%
$\displaystyle x_2$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5096}%
$\displaystyle r \cos \varphi \sin \lambda,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5097}%
$\displaystyle x_3$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5099}%
$\displaystyle r \sin \varphi,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1747}%
$\varphi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1751}%
$(\Dvect{e}_{\lambda}, \Dvect{e}_{\varphi},
\Dvect{e}_{r})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1753}%
$(u, v, w)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1447}%
\begin{displaymath}
  h_\lambda = r \cos \varphi, \ \ h_\varphi = r, \ \ h_r = 1.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1757}%
$\Dvect{A}=(A_{\lambda}, A_{\varphi}, A_r)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1452}%
\begin{displaymath}
  \Dgrad \bullet
 = \Dvect{e}_{\lambda} \frac{1}{r \cos \varphi} \DP{\bullet}{\lambda}
 + \Dvect{e}_{\varphi} \frac{1}{r} \DP{\bullet}{\varphi}
 + \Dvect{e}_r \DP{\bullet}{r}, 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1469}%
\begin{displaymath}
  \Ddiv \Dvect{A} 
  = \frac{1}{r^2 \cos \varphi} 
    \left[ r \DP{A_{\lambda}}{\lambda}
           + r \DP{}{\varphi} ( \cos \varphi A_{\varphi})
           +  \cos \varphi  \DP{}{r} ( r^2 A_r )
    \right],
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1481}%
\begin{displaymath}
    \nabla^2 \bullet 
  = \frac{1}{r^2 \cos \varphi} 
    \left[   \DP{}{\lambda} \left( \frac{1}{\cos \varphi}
           \DP{\bullet}{\lambda}\right) 
           + \DP{}{\varphi} \left( \cos \varphi \DP{\bullet}{\varphi} \right)
           + \DP{}{r} \left( r^2 \cos \varphi  \DP{\bullet}{r} \right)
    \right],
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5112}%
$\displaystyle \Drot \Dvect{A}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5114}%
$\displaystyle \Dvect{e}_{\lambda} \frac{1}{r}
\left[ \DP{A_r}{\varphi} - \DP{}{r}(r A_{\varphi})
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5115}%
$\displaystyle + \Dvect{e}_{\varphi} \frac{1}{r \cos \varphi}
\left[ \DP{}{r} (r \cos \varphi A_{\lambda}) -
\DP{A_r}{\lambda} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5116}%
$\displaystyle + \Dvect{e}_r \frac{1}{r \cos \varphi}
\left[ \DP{A_{\varphi}}{\lambda} - \DP{}{\varphi} (\cos
\varphi A_{\lambda}) \right],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1528}%
\begin{displaymath}
  \DD{\bullet}{t} 
  = \DP{\bullet}{t} + \frac{u}{r \cos \varphi} \DP{\bullet}{\lambda}
    + \frac{v}{r} \DP{\bullet}{\varphi}  + w \DP{\bullet}{r},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5119}%
$\displaystyle \DD{\Dvect{A}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5121}%
$\displaystyle \Dvect{e}_{\lambda} \left[
\DP{A_{\lambda}}{t} + \frac{u}{r \cos \varphi} \DP{A_{\lambda}}{\lambda}
+ \frac{v}{r} \DP{A_{\lambda}}{\varphi} + w \DP{A_{\lambda}}{r}
+ \frac{u}{r} A_r - \frac{u \tan \varphi}{r} A_{\varphi} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5122}%
$\displaystyle + \Dvect{e}_{\varphi} \left[
\DP{A_{\varphi}}{t} + \frac{u}{r \cos \varphi} \DP{A_{\varphi}}{\lambda}
+ \frac{v}{r} \DP{A_{\varphi}}{\varphi} + w \DP{A_{\varphi}}{r}
+ \frac{v}{r} A_r + \frac{u \tan \varphi}{r} A_{\lambda} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5123}%
$\displaystyle + \Dvect{e}_r \left[
\DP{A_r}{t} + \frac{u}{r \cos \varphi} \DP{A_r}{\lambda}
+ \frac{v}{r} \DP{A_r}{\varphi} + w \DP{A_r}{r}
- \frac{v}{r} A_{\varphi} - \frac{u}{r} A_{\lambda} \right].$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5126}%
$\displaystyle 2 \Dvect{\Omega} \times \Dvect{v}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5128}%
$\displaystyle 2 \Omega ( \Dvect{e}_{\varphi} \cos \varphi
+ \Dvect{e}_r \sin \varphi)
\times ( u \Dvect{e}_{\lambda} + v \Dvect{e}_{\varphi}
+ w \Dvect{e}_r)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5130}%
$\displaystyle ( 2 \Omega \cos \varphi w - 2 \Omega \sin \varphi v) \Dvect{e}_{\lambda}
+ 2 \Omega \sin \varphi u \Dvect{e}_{\varphi}
- 2 \Omega \cos \varphi u \Dvect{e}_r.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5132}%
$\displaystyle \DD{u}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5134}%
$\displaystyle - \frac{1}{\rho r \cos \varphi } \DP{p}{\lambda}
+  2 \Omega v \sin \varphi
-  2 \Omega w \cos \varphi
+  \frac{u v}{r} \tan \varphi
-  \frac{u w}{r}
+ F_\lambda,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5135}%
$\displaystyle \DD{v}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5137}%
$\displaystyle - \frac{1}{\rho r} \DP{p}{\varphi}
- 2 \Omega u \sin \varphi
- \frac{u^2}{r} \tan \varphi
- \frac{v w}{r}
+ F_\varphi,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5138}%
$\displaystyle \DD{w}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5140}%
$\displaystyle - \frac{1}{\rho} \DP{p}{r} -g
+ 2 \Omega u \cos \varphi
+ \frac{u^2}{r}
+ \frac{v^2}{r}
+ F_r.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1655}%
\begin{displaymath}
  \DD{\rho}{t} 
  + \frac{1}{r \cos \varphi} \DP{}{\lambda} ( u)
  + \frac{1}{r \cos \varphi} \DP{}{\varphi} ( \cos \varphi v)
  + \frac{1}{r^2} \DP{}{r} ( r^2 w )
  = 0.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1671}%
\begin{displaymath}
  \DD{}{t} T = \frac{1}{c_p^d \rho} \DD{p}{t} + \frac{Q^*}{c_p^d}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1687}%
\begin{displaymath}
  \DD{}{t}
     = \DP{}{t}
     + \frac{u}{r \cos \phi} \DP{}{\lambda}
     + \frac{v}{r} \DP{}{\phi}
     + w \DP{}{r},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap5146}%

% latex2html id marker 5146
\setcounter{footnote}{10}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap5147}%

% latex2html id marker 5147
\setcounter{footnote}{10}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap5148}%

% latex2html id marker 5148
\setcounter{footnote}{10}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath1792}%
\begin{displaymath}
0  =  - \frac{1}{\rho} \DP{p}{z} - g.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1986}%
$u,
v, w$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5155}%
$\displaystyle \DD{}{t} \left( \frac{1}{2} \Dvect{v}^2 \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5157}%
$\displaystyle u \DD{u}{t} + v \DD{v}{t} + w \DD{w}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5159}%
$\displaystyle u \biggl\{
- \frac{1}{\rho r \cos \varphi } \DP{p}{\lambda}
+  \underbrace{ 2 v \Omega \sin \varphi }_{(1)}
-  \underbrace{ 2 w \Omega \cos \varphi }_{(2)}
+  \underbrace{ \frac{u v}{r} \tan \varphi }_{(3)}
-  \underbrace{ \frac{u w}{r} }_{(4)}
+ F_\lambda \biggl\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5160}%
$\displaystyle + v \biggl\{ - \frac{1}{\rho r} \DP{p}{\varphi}
- \underbrace{ 2 \Omega u \sin \varphi }_{(1)}
- \underbrace{ \frac{u^2}{r} \tan \varphi }_{(3)}
- \underbrace{ \frac{v w}{r} }_{(5)}
+ F_\varphi \biggl\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5161}%
$\displaystyle + w \biggl\{ - \frac{1}{\rho} \DP{p}{r} -g
+ \underbrace{ 2 \Omega u \cos \varphi }_{(2)}
+ \underbrace{ \frac{u^2}{r} }_{(4)}
+ \underbrace{ \frac{v^2}{r} }_{(5)}
+ F_r \biggl\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5163}%
$\displaystyle - \frac{1}{\rho} \Dvect{v} \Dgrad{p} - g w
- \Dvect{v} \cdot \Dvect{F}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5169}%
$\displaystyle \frac{uv \tan \varphi}{r}
+ fv - \frac{1}{\rho r \cos \varphi} \DP{p}{\lambda}
+ F_{\lambda}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5172}%
$\displaystyle - \frac{u^2 \tan \varphi}{a}
- fu - \frac{1}{\rho r } \DP{p}{\varphi}
+ F_{\varphi}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1988}%
$f$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1990}%
$f \equiv 2\Omega \sin \varphi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1994}%
$a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1877}%
\begin{displaymath}
      \DD{\rho}{t} = - \rho \Ddiv \Dvect{v},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1882}%
\begin{displaymath}
      \DD{q}{t}  = S_q,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1886}%
\begin{displaymath}
      \DD{u}{t}  =  \frac{uv \tan \varphi}{a}
      + fv - \frac{1}{\rho a \cos \varphi} \DP{p}{\lambda}
      + F_{\lambda}, 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1897}%
\begin{displaymath}
      \DD{v}{t} 
 =  - \frac{u^2 \tan \varphi}{a}
     - fu - \frac{1}{\rho a } \DP{p}{\varphi}
      + F_{\varphi}, 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1908}%
\begin{displaymath}
0  =  - \frac{1}{\rho} \DP{p}{z} - g,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1914}%
\begin{displaymath}
      \DD{T}{t} = \frac{1}{c_p^d \rho} \DD{p}{t} + \frac{Q^*}{c_p^d},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1927}%
\begin{displaymath}
  \DD{}{t}
     = \DP{}{t}
      + \frac{u}{a \cos \varphi} \DP{}{\lambda}
      + \frac{v}{a} \DP{}{\varphi}
      + w \DP{}{z},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1943}%
\begin{displaymath}
  \Ddiv{\Dvect{v}}
 \equiv \frac{1}{a \cos \varphi} \DP{u}{\lambda}
  +  \frac{1}{a \cos \varphi} \DP{v}{\varphi}
     ( v \cos \varphi )
  + \DP{w}{z}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap5189}%

% latex2html id marker 5189
\setcounter{footnote}{11}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap5190}%

% latex2html id marker 5190
\setcounter{footnote}{11}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmldisplayA{displaymath2033}%
\begin{displaymath}
  \sigma \equiv \frac{p}{p_s},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2038}%
\begin{displaymath} 
  \DP{\sigma}{z} = - \frac{g \sigma}{R^d T_v}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5206}%
$\displaystyle \DP{\bullet}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5208}%
$\displaystyle \DP{\sigma}{z} \DP{\bullet}{\sigma}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5210}%
$\displaystyle - \frac{g \sigma}{R^d T_v} \DP{\bullet}{\sigma}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5212}%
$\displaystyle \left( \DP{\bullet}{\lambda} \right)_z$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5214}%
$\displaystyle \left( \DP{\bullet}{\lambda} \right)_{\sigma}
- \DP{\sigma}{z} \DP{\bullet}{\sigma}
\left( \DP{z}{\lambda} \right)_{\sigma}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5216}%
$\displaystyle \left( \DP{\bullet}{\lambda} \right)_{\sigma}
+ \frac{g \sigma}{R^d T_v} \DP{\bullet}{\sigma}
\left( \DP{z}{\lambda} \right)_{\sigma},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5218}%
$\displaystyle \left( \DP{\bullet}{\varphi} \right)_z$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5220}%
$\displaystyle \left( \DP{\bullet}{\varphi} \right)_{\sigma}
- \DP{\sigma}{z} \DP{\bullet}{\sigma}
\left( \DP{z}{\varphi} \right)_{\sigma}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5222}%
$\displaystyle \left( \DP{\bullet}{\varphi} \right)_{\sigma}
+ \frac{g \sigma}{R^d T_v} \DP{\bullet}{\sigma}
\left( \DP{z}{\varphi} \right)_{\sigma}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5224}%
$\displaystyle \left( \DP{\bullet}{t} \right)_z$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5226}%
$\displaystyle \left( \DP{\bullet}{t} \right)_{\sigma}
- \DP{\sigma}{z} \DP{\bullet}{\sigma}
\left( \DP{z}{t} \right)_{\sigma}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5228}%
$\displaystyle \left( \DP{\bullet}{t} \right)_{\sigma}
+ \frac{g \sigma}{R^d T_v} \DP{\bullet}{\sigma}
\left( \DP{z}{t} \right)_{\sigma}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5230}%
$\displaystyle \left( \DD{\bullet}{t} \right)_z$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5232}%
$\displaystyle \left( \DP{\bullet}{t} \right)_z
+ \frac{u}{a \cos \varphi} \left( \DP{\bullet}{\lambda} \right)_z
+ \frac{v}{a} \left( \DP{\bullet}{\varphi} \right)_z
+ w \left( \DP{\bullet}{z} \right)_z$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5234}%
$\displaystyle \left( \DP{\bullet}{t} \right)_{\sigma}
+ \frac{u}{a \cos \varphi} \left( \DP{\bullet}{\lambda} \right)_{\sigma}
+ \frac{v}{a} \left( \DP{\bullet}{\varphi} \right)_{\sigma}
+ w \left( \DP{\bullet}{z} \right)_{\sigma}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5235}%
$\displaystyle + \frac{g \sigma}{R^d T_v} \left\{
\left( \DP{z}{t} \right)_{\sigma}
+ \frac{u}{a \cos \varphi} \left( \DP{z}{\lambda} \right)_{\sigma}
+ \frac{v}{a} \left( \DP{z}{\varphi} \right)_{\sigma}
-w \right\} \DP{\bullet}{\sigma}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5237}%
$\displaystyle \left( \DD{\bullet}{t} \right)_{\sigma}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2185}%
\begin{displaymath}
  \dot{\sigma} \equiv
    \frac{g \sigma}{R^d T_v} \left\{ 
    \left( \DP{z}{t} \right)_{\sigma}
   + \frac{u}{a \cos \varphi} \left( \DP{z}{\lambda} \right)_{\sigma}
   + \frac{v}{a} \left( \DP{z}{\varphi} \right)_{\sigma}
   -w \right\}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2619}%
$\Phi=gz$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2206}%
\begin{displaymath}
  \DP{\Phi}{\sigma}=-\frac{R^d T_v}{\sigma}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5249}%
$\displaystyle \frac{1}{\rho} \left( \DP{p}{\lambda} \right)_z$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5251}%
$\displaystyle \frac{1}{\rho} \left\{ \DP[][\sigma]{p}{\lambda}
+ \frac{g \sigma}{R^d T_v} \DP{p}{\sigma} \DP[][\sigma]{z}{\lambda}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5253}%
$\displaystyle \frac{R^d T_v}{p_s} \DP{p_s}{\lambda}
+ \frac{R^d T_v}{p} \frac{g \sigma}{R^d T_v} p_s \DP[][\sigma]{z}{\lambda}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5255}%
$\displaystyle R^d T_v \DP[][\sigma]{\pi}{\lambda} + \DP{\Phi}{\lambda},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2246}%
\begin{displaymath}
  \frac{1}{\rho} \left( \DP{p}{\varphi} \right)_z
 = R^d T_v \DP[][\sigma]{\pi}{\varphi} + \DP{\Phi}{\varphi}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2623}%
$\pi \equiv \ln p_s$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2256}%
\begin{displaymath}
               \DD{u}{t}  -f v - \frac{uv}{a} \tan \varphi
           = - \frac{1}{a \cos \varphi} \DP{\Phi}{\lambda}
             - \frac{R^d T_v}{a \cos \varphi} \DP{\pi}{\lambda}
             + F_{\lambda},
      \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2271}%
\begin{displaymath}
               \DD{v}{t} + fu + \frac{u^2}{a} \tan \varphi
           = - \frac{1}{a}  \DP{\Phi}{\varphi}
             - \frac{R^d T_v}{a}  \DP{\pi}{\varphi}
             + F_{\varphi}.
      \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5262}%
$\displaystyle \left( \Ddiv \Dvect{v} \right)_z$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5264}%
$\displaystyle \frac{1}{a \cos \varphi}
\left[   \DP[][\sigma]{u}{\lambda}
+ \frac{g \sigma}{R^d T_v} \DP{u}{\sigma}
\DP[][\sigma]{z}{\lambda} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5265}%
$\displaystyle + \frac{1}{a \cos \varphi}
\left[   \left( \DP{}{\varphi} (v \cos \varphi) \right)_{\sigma}
+ \frac{g \sigma}{R^d T_v} \DP{}{\sigma} ( v \cos \varphi)
\DP[][\sigma]{z}{\lambda} \right]
- \frac{g \sigma}{R^d T_v} \DP{}{\sigma} \left( \DD{z}{t}
\right)_{\sigma}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5268}%
$\displaystyle + \frac{1}{a \cos \varphi}
\left[  \left( \DP{}{\varphi} (v \cos \varphi) \right)_{\sigma}
+ \frac{g \sigma}{R^d T_v}\DP{}{\sigma} ( v \cos \varphi)
\DP[][\sigma]{z}{\lambda} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5269}%
$\displaystyle - \frac{g \sigma}{R^d T_v} \DP{}{\sigma} \left[
\DP[][\sigma]{z}{t} + \frac{u}{a \cos \varphi}
\DP[][\sigma]{z}{\lambda}
+ \frac{v}{a} \DP[][\sigma]{z}{\varphi}
+ \dot{\sigma} \DP{z}{\sigma}
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5271}%
$\displaystyle \frac{1}{a \cos \varphi} \DP[][\sigma]{u}{\lambda}
+ \frac{1}{a \cos \varphi} \left( \DP{}{\varphi} (v \cos
\varphi) \right)_{\sigma}
+ \DP{\dot{\sigma}}{\sigma}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5272}%
$\displaystyle - \frac{g \sigma}{R^d T_v} \left[ \DP{}{\sigma} \DP[][\sigma]{z}{t}
+ \frac{u}{a \cos \varphi} \DP{}{\sigma}
\DP[][\sigma]{z}{\lambda}
+ \frac{v}{a} \DP{}{\sigma} \DP[][\sigma]{z}{\varphi}
+ \dot{\sigma} \DP{}{\sigma} \DP[][]{z}{\sigma} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5274}%
$\displaystyle ( \Ddiv{\Dvect{v}_H})_{\sigma} + \DP{\dot{\sigma}}{\sigma}
+ \DP{\sigma}{z}
\left( \DD{}{t} \DP{z}{\sigma} \right)_{\sigma}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2401}%
\begin{displaymath}
   \Ddiv{\Dvect{v}_H} 
     \equiv \frac{1}{a \cos \varphi}
           \DP[][\sigma]{u}{\lambda} 
         + \frac{1}{a \cos \varphi} \left( \DP{}{\varphi} (v \cos
           \varphi ) \right)_{\sigma}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5278}%
$\displaystyle \frac{1}{\rho} \left( \DD{\rho}{t} \right)_z
+ \left( \Ddiv{\Dvect{v}} \right)_z$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5280}%
$\displaystyle \frac{1}{\rho} \left( \DD{\rho}{t} \right)_{\sigma}
+ \left( \Ddiv{\Dvect{v}_H} \right)_{\sigma}
+ \DP{\dot{\sigma}}{\sigma}
+ \DP{\sigma}{z} \left( \DD{}{t} \DP{z}{\sigma} \right)_{\sigma}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5282}%
$\displaystyle \frac{1}{\rho} \left( \DD{\rho}{t} \right)_{\sigma}
+ \left( \Ddiv{\Dvect{v}_H} \right)_{\sigma}
+ \DP{\dot{\sigma}}{\sigma}
+ \frac{\rho}{p_s} \left( \DD{}{t} \frac{p_s}{\rho} \right)_{\sigma}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5284}%
$\displaystyle \left( \DD{\ln p_s}{t} \right)_{\sigma}
+ \left( \Ddiv{\Dvect{v}_H} \right)_{\sigma}
+ \DP{\dot{\sigma}}{\sigma}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2459}%
\begin{displaymath}
            \DD{\pi}{t}
          + \Ddiv{\Dvect{v}_H} 
          + \DP{\dot{\sigma}}{\sigma}
        = 0.
      \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5289}%
$\displaystyle \frac{1}{c_p^d \rho} \DD{p}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5291}%
$\displaystyle \frac{1}{c_p^d \rho} \left\{ \DP{p}{t}
+ \Dvect{v}_H \cdot \nabla_{\sigma} p
+ \dot{\sigma}  \DP{p}{\sigma} \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5293}%
$\displaystyle \frac{1}{c_p^d \rho} \left\{ \sigma \DP{p_s}{t}
+ \sigma \Dvect{v}_H \cdot \nabla_{\sigma} p_s
+ \dot{\sigma}  p_s \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5295}%
$\displaystyle \frac{R^d T_v}{c_p^d} \left\{   \DP{\pi}{t}
+ \Dvect{v}_H \cdot \nabla_{\sigma} \pi
+ \frac{\dot{\sigma}}{\sigma} \right\}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2499}%
\begin{displaymath}
            \Dvect{v}_H \cdot \nabla_{\sigma} 
        =   \frac{u}{a \cos \varphi} \DP{}{\lambda}
          + \frac{v}{a} \DP{}{\varphi}.
      \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2511}%
\begin{displaymath}
                \DD{T}{t} 
        =     \frac{R^d T_v}{c_p^d}
                \left\{   \DP{\pi}{t} 
                        + \Dvect{v}_H \cdot \nabla_{\sigma} \pi
                        + \frac{\dot{\sigma}}{\sigma} \right\}
                        + \frac{Q^*}{c_p^d}.
      \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath2527}%
\begin{displaymath}
  \Phi = \Phi_s (\lambda, \varphi)   \ \ \ \ {\rm at} \ \ \sigma=1.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2631}%
$\Phi_s$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2635}%
$\Phi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
\stepcounter{subsubsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2639}%
$\sigma=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2641}%
$\sigma=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2645}%
$\pi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2537}%
\begin{displaymath}
   \frac{\partial \pi}{\partial t}
   = - \int_{0}^{1} \Dvect{v}_{H} \cdot \nabla_{\sigma} \pi d \sigma
     - \int_{0}^{1} D  d \sigma.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2649}%
$\Ddiv{\Dvect{v}_H}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2651}%
$D$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2659}%
$\sigma=\sigma$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2551}%
\begin{displaymath}
   \dot{\sigma} 
   = - \sigma 
     \frac{\partial \pi}{\partial t}
     - \int_{0}^{\sigma} D d \sigma
     - \int_{0}^{\sigma} 
         \Dvect{v}_{H} \cdot \nabla_{\sigma} \pi d \sigma.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap5323}%

% latex2html id marker 5323
\setcounter{footnote}{11}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap5324}%

% latex2html id marker 5324
\setcounter{footnote}{11}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath2719}%
\begin{displaymath}
\zeta \equiv \frac{1}{a \cos \varphi} \DP{v}{\lambda}
         - \frac{1}{a \cos \varphi} \DP{}{\varphi} ( u \cos \varphi).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2729}%
\begin{displaymath}
D \equiv \frac{1}{a \cos \varphi} \DP{u}{\lambda}
         + \frac{1}{a \cos \varphi} \DP{}{\varphi} ( v \cos \varphi).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3503}%
$u$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3505}%
$\frac{1}{a \cos \varphi} \DP{}{\varphi} \cos
\varphi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3507}%
$v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3509}%
$\frac{1}{a \cos \varphi} \DP{}{\lambda}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5335}%
$\displaystyle \DP{\zeta}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5337}%
$\displaystyle - \frac{1}{a \cos \varphi} \DP{}{\varphi}
( \zeta v \cos  \varphi )
-  \frac{1}{a \cos \varphi} \DP{}{\lambda}
( \zeta u )$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5338}%
$\displaystyle - \frac{1}{a \cos \varphi} \DP{}{\lambda}
\left[   \dot{\sigma} \DP{v}{\sigma}
+ \frac{R^d T_v}{a p_s} \DP{p_s}{\varphi}
- F_{\varphi} + f u \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5339}%
$\displaystyle - \frac{1}{a \cos \varphi} \DP{}{\varphi}
\left[   - \cos \varphi \dot{\sigma} \DP{u}{\sigma}
- \frac{R^d T_v}{a p_s} \DP{p_s}{\lambda}
+ F_{\lambda} \cos \varphi + f v \cos \varphi \right].$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5346}%
$\displaystyle \DP{D}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5348}%
$\displaystyle \frac{1}{a \cos \varphi} \DP{}{\lambda}
( \zeta v )
-  \frac{1}{a \cos \varphi} \DP{}{\varphi}
( \zeta u \cos \varphi)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5349}%
$\displaystyle - \frac{1}{a \cos \varphi} \DP{}{\lambda}
\left[   \dot{\sigma} \DP{u}{\sigma}
+ \frac{R^d T_v}{a \cos \varphi p_s} \DP{p_s}{\lambda}
- F_{\lambda} - f v \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5350}%
$\displaystyle - \frac{1}{a \cos \varphi} \DP{}{\varphi}
\left[    \cos \varphi \dot{\sigma} \DP{v}{\sigma}
+ \frac{R^d T_v}{a p_s} \DP{p_s}{\varphi} \cos \varphi
- F_{\varphi} \cos \varphi + f u \cos \varphi \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5351}%
$\displaystyle - \nabla^2_{\sigma} ( \Phi + KE).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5353}%
$\displaystyle \nabla^2_{\sigma}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5355}%
$\displaystyle \frac{1}{a^2 \cos^2 \varphi} \DP[2]{}{\lambda}
+ \frac{1}{a^2 \cos \varphi} \DP{}{\varphi} ( \cos
\varphi \DP{}{\varphi} ),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5356}%
$\displaystyle KE$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5358}%
$\displaystyle \frac{u^2 + v^2}{2}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3519}%
$\mu \equiv \sin \varphi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3521}%
$u, v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3523}%
$U \equiv u
\cos \phi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3525}%
$V \equiv \cos \phi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3529}%
$\zeta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5374}%
$\displaystyle \frac{1}{a \cos \varphi} \DP{v}{\lambda}
- \frac{1}{a \cos \varphi} \DP{}{\varphi} ( u \cos \varphi)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5376}%
$\displaystyle \frac{1}{a \cos^2 \varphi} \DP{v \cos \phi}{\lambda}
- \frac{1}{a \cos \varphi} \DP{}{\varphi} ( u \cos \varphi)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5378}%
$\displaystyle \frac{1}{a ( 1- \mu^2 )} \DP{V}{\lambda}
- \frac{1}{a} \DP{U}{\mu},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5382}%
$\displaystyle \frac{1}{a \cos \varphi} \DP{u}{\lambda}
+ \frac{1}{a \cos \varphi} \DP{}{\varphi} ( v \cos \varphi)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5384}%
$\displaystyle \frac{1}{a \cos^2 \varphi} \DP{u \cos \phi}{\lambda}
+ \frac{1}{a \cos \varphi} \DP{}{\varphi} ( v \cos \varphi)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5386}%
$\displaystyle \frac{1}{a ( 1-\mu^2)} \DP{U}{\lambda}
+ \frac{1}{a} \DP{V}{\mu}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5388}%
$\displaystyle \frac{u}{a \cos\phi}\DP{\bullet}{\lambda}
+ \frac{v}{a} \DP{\bullet}{\phi}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5390}%
$\displaystyle \frac{1}{a \cos^2 \phi}
\left\{ \DP{}{\lambda} (u \cos \phi \bullet)
- \bullet \DP{}{\lambda} ( u \cos \phi ) \right\}
\frac{1}{a \cos \phi}
\left\{ \DP{}{\phi} (v \cos \phi \bullet)
- \bullet \DP{}{\phi} ( v \cos \phi ) \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5392}%
$\displaystyle \frac{1}{a (1-\mu^2)} \DP{}{\lambda} (U\bullet)
-\frac{\bullet}{a (1-\mu^2)} \DP{U}{\lambda}
+\frac{1}{a \mu} \DP{}{\phi} (V\bullet)
-\frac{\bullet}{a} \DP{V}{\mu}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5394}%
$\displaystyle \frac{1}{a (1-\mu^2)} \DP{}{\lambda} (U\bullet)
+\frac{1}{a \mu} \DP{}{\phi} (V\bullet)
+\bullet D.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5398}%
$\displaystyle + \frac{u \cos \phi }{a \cos^2 \phi}\DP{\bullet}{\lambda}
+ \frac{v \cos \phi }{a \cos \phi } \DP{\bullet}{\phi}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5400}%
$\displaystyle + \frac{U}{a (1-\mu^2)} \DP{\bullet}{\lambda}
+ \frac{V}{a} \DP{\bullet}{\mu}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5402}%
$\displaystyle \Dvect{v}_H \cdot \Dgrad_{\sigma} \bullet.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2974}%
\begin{displaymath}
  \DP{\pi}{t} + \Dvect{v}_H \cdot \Dgrad_{\sigma} \pi 
    = -\Dgrad_{\sigma} \cdot \Dvect{v}_H - \DP{\dot{\sigma}}{\sigma}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5410}%
$\displaystyle -\frac{1}{a}\DP{}{\mu} ( \zeta V )
-\frac{1}{a (1-\mu^2)} \DP{}{\lambda} ( \zeta U )$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5411}%
$\displaystyle - \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[   \dot{\sigma} \DP{V}{\sigma}
+ \frac{R^d T_v}{a} (1-\mu^2) \DP{\pi}{\mu}
- F_{\varphi} \cos \varphi + f U \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5412}%
$\displaystyle - \frac{1}{a} \DP{}{\mu}
\left[   - \dot{\sigma} \DP{U}{\sigma}
- \frac{R^d T_v}{a} \DP{\pi}{\lambda}
+ F_{\lambda} \cos \varphi + fV \right].$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5416}%
$\displaystyle \frac{1}{a (1-\mu^2)} \DP{}{\lambda} ( \zeta V )
-  \frac{1}{a} \DP{}{\mu}
( \zeta U )$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5417}%
$\displaystyle - \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[   \dot{\sigma} \DP{U}{\sigma}
+ \frac{R^d T_v}{a} \DP{\pi}{\lambda}
- F_{\lambda} \cos \varphi - f V \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5418}%
$\displaystyle - \frac{1}{a} \DP{}{\mu}
\left[ \dot{\sigma} \DP{V}{\sigma}
+ \frac{R^d T_v}{a} ( 1-\mu^2 ) \DP{\pi}{\mu}
- F_{\varphi} \cos \varphi + f U \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5421}%
$\displaystyle \DP{T}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5423}%
$\displaystyle - \frac{1}{a(1-\mu^{2})} \DP{UT}{\lambda}
- \frac{1}{a}
\DP{VT}{\mu}
+ T D$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5424}%
$\displaystyle - \dot{\sigma}
\DP{T}{\sigma}
+ \kappa T \left( \DP{\pi}{t}
+ \Dvect{v}_{H} \cdot \nabla_{\sigma} \pi
+ \frac{ \dot{\sigma} }{ \sigma }
\right)
+ \frac{Q^*}{C_{p}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5426}%
$\displaystyle \DP{q}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5428}%
$\displaystyle - \frac{1}{a(1-\mu^{2})}
\DP{Uq}{\lambda}
- \frac{1}{a}
\DP{Vq}{\mu}
+ q D$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5429}%
$\displaystyle - \dot{\sigma} \frac{\partial q }{\partial \sigma}
+ S_{q}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3543}%
$\bar{T}_v(\sigma)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3545}%
$T'_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5436}%
$\displaystyle - \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ + \frac{R^d T_v}{a} (1-\mu^2) \DP{\pi}{\mu} \right]
- \frac{1}{a} \DP{}{\mu}
\left[ - \frac{R^d T_v}{a} \DP{\pi}{\lambda} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5438}%
$\displaystyle - \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ + \frac{R^d \bar{T}_v}{a} (1-\mu^2) \DP{\pi}{\mu} \right]
- \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ + \frac{R^d T'_v}{a} (1-\mu^2) \DP{\pi}{\mu} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5439}%
$\displaystyle - \frac{1}{a} \DP{}{\mu}
\left[ - \frac{R^d \bar{T}_v}{a} \DP{\pi}{\lambda} \right]
- \frac{1}{a} \DP{}{\mu}
\left[ - \frac{R^d T'_v}{a} \DP{\pi}{\lambda} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5441}%
$\displaystyle - \frac{1}{a} \frac{R^d \bar{T}_v}{a}
\frac{\partial^2 \pi}{\partial \lambda \partial \mu}
- \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ + \frac{R^d T'_v}{a} (1-\mu^2) \DP{\pi}{\mu} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5442}%
$\displaystyle + \frac{1}{a} \frac{R^d \bar{T}_v}{a}
\frac{\partial^2 \pi}{\partial \mu \partial \lambda}
- \frac{1}{a} \DP{}{\mu}
\left[ - \frac{R^d T'_v}{a} \DP{\pi}{\lambda} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5444}%
$\displaystyle - \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ + \frac{R^d T'_v}{a} (1-\mu^2) \DP{\pi}{\mu} \right]
- \frac{1}{a} \DP{}{\mu}
\left[ - \frac{R^d T'_v}{a} \DP{\pi}{\lambda} \right].$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5447}%
$\displaystyle - \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ \frac{R^d T_v}{a} \DP{\pi}{\lambda} \right]
- \frac{1}{a} \DP{}{\mu}
\left[ \frac{R^d T_v}{a} ( 1-\mu^2 ) \DP{\pi}{\mu} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5449}%
$\displaystyle - \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ \frac{R^d \bar{T}_v}{a} \DP{\pi}{\lambda} \right]
- \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ \frac{R^d T'_v}{a} \DP{\pi}{\lambda} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5450}%
$\displaystyle - \frac{1}{a} \DP{}{\mu}
\left[ \frac{R^d \bar{T}_v}{a} ( 1-\mu^2 ) \DP{\pi}{\mu} \right]
- \frac{1}{a} \DP{}{\mu}
\left[ \frac{R^d T'_v}{a} ( 1-\mu^2 ) \DP{\pi}{\mu} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5452}%
$\displaystyle - \frac{1}{a^2 (1-\mu^2)} \DP[2]{}{\lambda}
( R^d \bar{T}_v \pi )
- \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ \frac{R^d T'_v}{a} \DP{\pi}{\lambda} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5453}%
$\displaystyle - \frac{1}{a^2} \DP{}{\mu}
\left[ (1-\mu^2) \DP{}{\mu} ( R^d \bar{T}_v \pi ) \right]
- \frac{1}{a} \DP{}{\mu}
\left[ \frac{R^d T'_v}{a} ( 1-\mu^2 ) \DP{\pi}{\mu} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5455}%
$\displaystyle - \Dgrad^2_{\sigma} ( R^d \bar{T}_v \pi )
- \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ \frac{R^d T'_v}{a} \DP{\pi}{\lambda} \right]
- \frac{1}{a} \DP{}{\mu}
\left[ \frac{R^d T'_v}{a} ( 1-\mu^2 ) \DP{\pi}{\mu} \right].$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5459}%
$\displaystyle - \frac{1}{a(1-\mu^{2})} \DP{U \bar{T}}{\lambda}
- \frac{1}{a(1-\mu^{2})} \DP{UT'}{\lambda}
- \frac{1}{a} \DP{V \bar{T}}{\mu}
- \frac{1}{a} \DP{VT'}{\mu}
+ \bar{T} D
+ T' D$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5461}%
$\displaystyle - \frac{\bar{T}}{a(1-\mu^{2})} \DP{U}{\lambda}
- \frac{1}{a(1-\mu^{2})} \DP{UT'}{\lambda}
- \frac{\bar{T}}{a} \DP{V}{\mu}
- \frac{1}{a} \DP{VT'}{\mu}
+ \bar{T} \left[ \frac{1}{a(1-\mu^{2})} \DP{U}{\lambda}
+ \frac{\bar{1}}{a} \DP{V}{\mu}         \right]
+ T' D$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5463}%
$\displaystyle - \frac{1}{a(1-\mu^{2})} \DP{UT'}{\lambda}
- \frac{1}{a} \DP{VT'}{\mu}
+ T' D.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3365}%
\begin{displaymath}
  \DP{\zeta}{t}
  = -\frac{1}{a (1-\mu^2)} \DP{VA}{\lambda}
      -\frac{1}{a} \DP{UA}{\mu},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3377}%
\begin{displaymath}
  \DP{D}{t}
  = \frac{1}{a (1-\mu^2)} \DP{UA}{\lambda}
    -  \frac{1}{a} \DP{VA}{\mu} 
    - \Dgrad^2_{\sigma} ( \Phi + R \bar{T}_v \pi + KE ).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5473}%
$\displaystyle UA$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5475}%
$\displaystyle ( \zeta + f ) V
- \dot{\sigma} \DP{U}{\sigma}
- \frac{RT'}{a}
\DP{\pi}{\lambda}
+ F_{\lambda} \cos \varphi$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5476}%
$\displaystyle VA$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5478}%
$\displaystyle - ( \zeta + f ) U
- \dot{\sigma} \DP{V}{\sigma}
- \frac{RT'}{a} ( 1 - \mu^{2} )
\DP{\pi}{\mu}
+ F_{\varphi} \cos \varphi.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5482}%
$\displaystyle - \frac{1}{a(1-\mu^{2})} \DP{UT'}{\lambda}
- \frac{1}{a} \DP{VT'}{\mu}
+ T' D
- \dot{\sigma}
\DP{T}{\sigma}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5483}%
$\displaystyle \qquad
+ \kappa T \left( \DP{\pi}{t}
+ \Dvect{v}_{H} \cdot \nabla_{\sigma} \pi
+ \frac{ \dot{\sigma} }{ \sigma }
\right)
+ \frac{Q^*}{C_p^d}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3434}%
\begin{displaymath}
  \DP{q}{t}
    = - \frac{1}{a(1-\mu^{2})} 
               \DP{Uq}{\lambda}
          - \frac{1}{a}
               \DP{Vq}{\mu}
          + q D 
       - \dot{\sigma} \frac{\partial q }{\partial \sigma}
          + S_{q}.
\end{displaymath}%
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$c_p \mathcal{D}(\Dvect{v})$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3559}%
$Q^*=Q+c_p \mathcal{D}(\Dvect{v})$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3561}%
$\mathcal{D}(\zeta)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3563}%
$\mathcal{D}(D)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3565}%
$\mathcal{D}(T)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3567}%
$\mathcal{D}(q)$%
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\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3664}%
$\times 10^6$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3666}%
$g$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3668}%
$^{-2}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3670}%
$C_p$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3672}%
$^{-1}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3682}%
$L$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3688}%
$C_v$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3694}%
$R_v$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3700}%
$d_{H_2O}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3706}%
$^{\circ}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3708}%
$e^*$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3710}%
$\sigma_{SB}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3714}%
$^{-4}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3716}%
$\times 10^{-8}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3718}%
$k$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3720}%
$\epsilon_v$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3722}%
$\delta_v = \epsilon_v^{-1} - 1$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3724}%
$\kappa = R/C_p$%
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\end{document}