\batchmode


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


\usepackage{Dennou6}


\Dtitle[DCAPM2 Âè1Éô ¿ôÍý¥â¥Ç¥ë²½]{DCAPM3 \\[5mm]
          Âè1Éô \ ¿ôÍý¥â¥Ç¥ë²½\\[70mm]}
  \Dauthor[ÃÏµåÎ®ÂÎÅÅÇ¾¶æ³ÚÉô]{ÃÏµåÎ®ÂÎÅÅÇ¾¶æ³ÚÉô}
  %
\Dver{dcpam3-20070608} \Dmodify{2007}{06}{08}
  \Ddate[\Dmoddate ]{\DmoddateJ (DCPAM3-\Dversion )}

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


\makeindex




\usepackage[dvips]{color}


\pagecolor[gray]{.7}

\usepackage[latin1]{inputenc}



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$\displaystyle - \frac{1}{a(1-\mu^{2})}
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$\displaystyle \frac{u}{a \cos \varphi}
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$\displaystyle \frac{U}{a ( 1 -\mu^{2} )}
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$\displaystyle \frac{1}{a^{2}(1-\mu^{2})}
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\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
\lthtmldisplayA{displaymath385}%
\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_wrap6951}%

% latex2html id marker 6951
\setcounter{footnote}{2}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline564}%
$\nabla^{N_D}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath520}%
\begin{displaymath}
  {\cal D}(\zeta) = - K_{HD} 
                      \left[ (-1)^{N_D/2} \nabla^{N_D}
                              - \left( \frac{2}{a^2} \right)^{N_D/2} 
                      \right]
                    \zeta ,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath530}%
\begin{displaymath}
  {\cal D}(D) = - K_{HD} 
                      \left[ (-1)^{N_D/2} \nabla^{N_D}
                              - \left( \frac{2}{a^2} \right)^{N_D/2} 
                      \right]
                    D ,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath539}%
\begin{displaymath}
  {\cal D}(T) = - (-1)^{N_D/2} K_{HD} \nabla^{N_D} T ,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath545}%
\begin{displaymath}
  {\cal D}(q) = - (-1)^{N_D/2} K_{HD} \nabla^{N_D} q .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline566}%
$N_D$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline568}%
$\sim$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{section}
\stepcounter{Dchapter}
{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap6967}%

% latex2html id marker 6967
\setcounter{footnote}{3}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap6968}%

% latex2html id marker 6968
\setcounter{footnote}{3}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap6973}%

% latex2html id marker 6973
\setcounter{footnote}{6}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6978}%
$\displaystyle \DD{s}{z} < 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6980}%
$\displaystyle \DP{T}{z} - \frac{RT}{c_p p} \DP{p}{z} + \frac{L}{c_p} \DP{q^*}{z} < 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2374}%
$(\hat{q}, \hat{T})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2376}%
$(q, T)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6985}%
$\displaystyle q_{k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6987}%
$\displaystyle q^* (T_{k-1}, p_{k-1}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6988}%
$\displaystyle q_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6990}%
$\displaystyle q^{*} (T_{k}, p_{k})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6992}%
$\displaystyle T_{k-1} - T_{k}
+ \frac{L}{C_p}
\left\{ q^{*} (T_{k-1}, p_{k-1})  - q^{*} (T_{k}, p_{k}) \right\}
- \frac{R}{C_p} \frac{\Delta p_{k-1/2}}{p_{k-1/2}}
\frac{T_{k-1} + T_{k}}{2}
=0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6994}%
$\displaystyle (c_p T_{k} + L q_{k}) \Delta p_{k}
+ (c_p T_{k-1} + L q_{k-1}) \Delta p_{k-1}
=   (c_p \hat{T}_{k} + L \hat{q}_{k}) \Delta p_{k}
+ (c_p \hat{T}_{k-1} + L \hat{q}_{k-1}) \Delta p_{k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2378}%
$q_{k}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2380}%
$q_{k-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2382}%
$q \ll 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2384}%
$\Delta T_{k}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2386}%
$\Delta T_{k-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7003}%
$\displaystyle q^{*} (\hat{T}_{k},p_{k})
+ \left. \DP{q^{*}}{T} \right|_{\hat{T}_{k}}
\cdot \Delta T_{k},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7006}%
$\displaystyle q^{*} (\hat{T}_{k-1},p_{k-1})
+ \left. \DP{q^{*}}{T} \right|_{\hat{T}_{k-1}}
\cdot \Delta T_{k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2388}%
$T_{k-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7013}%
$\displaystyle q^{*} (\hat{T}_{k},p_{k})
+ \left. \DP{q^{*}}{T} \right|_{\hat{T}_{k}}
\cdot \Delta T_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2394}%
$\sum h =0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7016}%
$\displaystyle (c_p T_{k-1} + L q_{k-1}) \Delta p_{k-1}
- (c_p \hat{T}_{k-1} + L \hat{q}_{k-1}) \Delta p_{k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7018}%
$\displaystyle - (c_p T_{k} + L q_{k}) \Delta p_{k}
+ (c_p \hat{T}_{k} + L \hat{q}_{k}) \Delta p_{k},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7019}%
$\displaystyle \left\{ \Delta T_{k-1}
+ \frac{L}{c_p} (q_{k-1} - \hat{q}_{k-1} ) \right\}
\Delta p_{k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7021}%
$\displaystyle - \left\{ \Delta T_{k} + \frac{L}{c_p} (q_{k} - \hat{q}_{k}) \right\}
\Delta p_{k},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7023}%
$\displaystyle \left[   \Delta T_{k-1}
+ \frac{L}{c_p}
\left\{   q^{*} (\hat{T}_{k-1} )
+ \left. \DP{q^{*}}{T} \right|_{k-1}
\Delta T_{k-1}
- \hat{q}_{k-1}
\right\}
\right] \Delta p_{k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7024}%
$\displaystyle = - \left[   \Delta T_{k}
+ \frac{L}{c_p}
\left\{   q^{*} (T_{k})
+ \left. \DP{q^{*}}{T} \right|_{k}
\Delta T_{k}
- \hat{q}_{k}
\right\}
\right] \Delta p_{k},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7025}%
$\displaystyle \left\{  1+
\frac{L}{c_p}   \left. \DP{q^{*}}{T} \right|_{k-1}
\right\}
\Delta T_{k-1} \Delta p_{k-1}
+ \frac{L}{c_p}
\left\{   q^{*} (\hat{T}_{k-1} )
- \hat{q}_{k-1}
\right\}
\Delta p_{k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7026}%
$\displaystyle = - \left[   1
+ \frac{L}{c_p}
\left. \DP{q^{*}}{T} \right|_{k}
\right] \Delta T_{k}  \Delta p_{k}
- \frac{L}{c_p}
\left\{  q^{*} (\hat{T}_{k})
- \hat{q}_{k}
\right\}
\Delta p_{k},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7028}%
$\displaystyle \gamma_{k} \equiv \frac{L}{c_p} \left. \DP{q^{*}}{T} \right|_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7030}%
$\displaystyle \left\{  1 + \gamma_{k-1} \right\}
\Delta T_{k-1} \Delta p_{k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7031}%
$\displaystyle =
- \left(  1
+ \gamma_{k}
\right) \Delta T_{k}  \Delta p_{k}
+ \frac{L}{c_p}
\left[
\left\{ \hat{q}_{k-1} - q^{*} (\hat{T}_{k-1} ) \right\}
\Delta p_{k-1}
+ \left\{ \hat{q}_{k} - q^{*} (\hat{T}_{k}) \right\}
\Delta p_{k}
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7033}%
$\displaystyle \Delta \hat{Q} \equiv
\left\{ \hat{q}_{k-1} - q^{*} (\hat{T}_{k-1} ) \right\}
\Delta p_{k-1}
+ \left\{ \hat{q}_{k} - q^{*} (\hat{T}_{k}) \right\}
\Delta p_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7036}%
$\displaystyle \left\{  1 + \gamma_{k-1} \right\}
\Delta T_{k-1} \Delta p_{k-1}
=
- \left(  1
+ \gamma_{k}
\right) \Delta T_{k}  \Delta p_{k}
+ \frac{L}{c_p} \Delta \hat{Q},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7037}%
$\displaystyle \Delta T_{k-1}
=
- \frac{ 1 + \gamma_{k} }{ 1 + \gamma_{k-1}}
\frac{\Delta p_{k}}{\Delta p_{k-1}}
\Delta T_{k}
+ \frac{1}{ 1 + \gamma_{k-1}}
\frac{L}{c_p} \Delta \hat{Q} \frac{1}{\Delta p_{k-1}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2398}%
$T_{k}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7040}%
$\displaystyle \DP{S}{z} = 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2400}%
$q (T_{k-1}, p_{k-1})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2402}%
$q^* (T_{k-1}, p_{k-1})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7044}%
$\displaystyle T_{k-1} - T_{k}
+ \frac{L}{c_p}
\left\{ q (T_{k-1}, p_{k-1}) - q^{*} (T_{k}, p_{k}) \right\}
- \frac{R}{c_p}
\frac{\Delta p_{k-1/2}}{p_{k-1/2}}
\frac{T_{k-1} + T_{k}}{2}
= 0,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7045}%
$\displaystyle \hat{T}_{k-1} + \Delta T_{k-1}
- \left( \hat{T}_{k}  + \Delta T_{k} \right)
+ \frac{L}{c_p}
\left\{   q^{*} (\hat{T}_{k-1})
+ \left. \DP{q^{*}}{T} \right|_{k-1} \Delta T_{k-1}
- q^{*} (\hat{T}_{k})
- \left. \DP{q^{*}}{T} \right|_{k} \Delta T_{k}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7046}%
$\displaystyle \qquad
- \frac{R}{c_p}
\frac{\Delta p_{k-1/2}}{p_{k-1/2}}
\frac{\hat{T}_{k-1} + \Delta T_{k-1} + \hat{T}_{k} + \Delta T_{k}}{2}
= 0,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7047}%
$\displaystyle \hat{T}_{k-1} - \hat{T}_{k}
+ \frac{L}{c_p}
\left\{   q^{*} (\hat{T}_{k-1})
- q^{*} (\hat{T}_{k})
\right\}
- \frac{R}{c_p}
\frac{\Delta p_{k-1/2}}{p_{k-1/2}}
\frac{\hat{T}_{k-1} + \hat{T}_{k} }{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7048}%
$\displaystyle \qquad
+ \Delta T_{k-1} - \Delta T_{k}
+  \frac{L}{c_p} \left. \DP{q^{*}}{T} \right|_{k-1} \Delta T_{k-1}
- \frac{L}{c_p} \left. \DP{q^{*}}{T} \right|_{k} \Delta T_{k}
- \frac{R}{c_p}
\frac{\Delta p_{k-1/2}}{p_{k-1/2}}
\frac{\Delta T_{k-1} + \Delta T_{k}}{2}
= 0.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7050}%
$\displaystyle St \equiv
\hat{T}_{k-1} - \hat{T}_{k}
+ \frac{L}{c_p}
\left\{   q^{*} (\hat{T}_{k-1})
- q^{*} (\hat{T}_{k})
\right\}
- \frac{R}{c_p}
\frac{\Delta p_{k-1/2}}{p_{k-1/2}}
\frac{\hat{T}_{k-1} + \hat{T}_{k} }{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7052}%
$\displaystyle \Delta T_{k-1} - \Delta T_{k}
+ \gamma_{k-1} \Delta T_{k-1}
- \gamma_{k} \Delta T_{k}
- \frac{R}{c_p}
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
\Delta T_{k-1}
- \frac{R}{c_p}
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
\Delta T_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7053}%
$\displaystyle \qquad = - St,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7054}%
$\displaystyle \left( - 1 - \gamma_{k}
- \frac{R}{c_p}
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
\right)
\Delta T_{k}
+ \left(
1 + \gamma_{k-1}
- \frac{R}{c_p}
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
\right)
\Delta T_{k-1}
= - St$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2404}%
$p_{k-1/2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2406}%
$p_{k-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7059}%
$\displaystyle \left( - 1 - \gamma_{k}
- \frac{R}{c_p}
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
\right)
\Delta T_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7060}%
$\displaystyle + \left(
1 + \gamma_{k-1}
- \frac{R}{c_p}
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
\right)
\left(
- \frac{ 1 + \gamma_{k} }{ 1 + \gamma_{k-1}}
\frac{\Delta p_{k}}{\Delta p_{k-1}}
\Delta T_{k}
+ \frac{1}{ 1 + \gamma_{k-1}}
\frac{L}{c_p} \Delta \hat{Q} \frac{1}{\Delta p_{k-1}}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7061}%
$\displaystyle = - St$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2410}%
$\kappa = \frac{R}{c_p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7064}%
$\displaystyle \left( - 1 - \gamma_{k}
- \kappa
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
\right)
\Delta T_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7065}%
$\displaystyle + \left(
1 + \gamma_{k-1}
- \kappa
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
\right)
\left(
- \frac{ 1 + \gamma_{k} }{ 1 + \gamma_{k-1}}
\frac{\Delta p_{k}}{\Delta p_{k-1}}
\Delta T_{k}
+ \frac{1}{ 1 + \gamma_{k-1}}
\frac{L}{c_p} \Delta \hat{Q} \frac{1}{\Delta p_{k-1}}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7069}%
$\displaystyle \left[
\left( - 1 - \gamma_{k}  \right)
- \kappa
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
+
\left(
1 + \gamma_{k-1}
- \kappa
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
\right)
\left( - \frac{ 1 + \gamma_{k} }{ 1 + \gamma_{k-1}}
\frac{\Delta p_{k}}{\Delta p_{k-1}}
\right)
\right]
\Delta T_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7070}%
$\displaystyle = - St
- \left(
1 + \gamma_{k-1}
- \kappa
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
\right)
\frac{1}{ 1 + \gamma_{k-1}}
\frac{L}{c_p} \Delta \hat{Q} \frac{1}{\Delta p_{k-1}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7072}%
$\displaystyle \Delta T_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7073}%
$\displaystyle = \frac{
- St
- \left(
1 + \gamma_{k-1}
- \kappa
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
\right)
\frac{1}{ 1 + \gamma_{k-1}}
\frac{L}{c_p} \Delta \hat{Q} \frac{1}{\Delta p_{k-1}}
}{
\left( - 1 - \gamma_{k}  \right)
- \kappa
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
+
\left(
1 + \gamma_{k-1}
- \kappa
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
\right)
\left( - \frac{ 1 + \gamma_{k} }{ 1 + \gamma_{k-1}}
\frac{\Delta p_{k}}{\Delta p_{k-1}}
\right)
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7074}%
$\displaystyle = \frac{
St
+ \left(
1 + \gamma_{k-1}
- \kappa
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
\right)
\frac{1}{ 1 + \gamma_{k-1}}
\frac{L}{c_p} \Delta \hat{Q} \frac{1}{\Delta p_{k-1}}
}{
\left( 1 + \gamma_{k}  \right)
+ \kappa
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
+
\left(
1 + \gamma_{k-1}
- \kappa
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
\right)
\frac{ 1 + \gamma_{k} }{ 1 + \gamma_{k-1}}
\frac{\Delta p_{k}}{\Delta p_{k-1}}
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7075}%
$\displaystyle = \frac{
(1 + \gamma_{k-1}) \Delta p_{k-1} St
+ \left(
1 + \gamma_{k-1}
- \kappa
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
\right)
\frac{L}{c_p} \Delta \hat{Q}
}{
\left( 1 + \gamma_{k}  \right) (1 + \gamma_{k-1}) \Delta p_{k-1}
+ \kappa
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
(1 + \gamma_{k-1}) \Delta p_{k-1}
+
\left(
1 + \gamma_{k-1}
- \kappa
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
\right)
(1 + \gamma_{k})
\Delta p_{k}
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7076}%
$\displaystyle = \frac{
(1 + \gamma_{k-1}) \Delta p_{k-1} St
+ \left(
1 + \gamma_{k-1}
- \kappa
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
\right)
\frac{L}{c_p} \Delta \hat{Q}
}{
\left( 1 + \gamma_{k}  \right) (1 + \gamma_{k-1})
(\Delta p_{k-1} + \Delta p_{k})
+ \kappa
\frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
\left\{
(1 + \gamma_{k-1}) \Delta p_{k-1}
-  (1 + \gamma_{k}) \Delta p_{k}
\right\}
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2414}%
$l$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7080}%
$\displaystyle \DD{s}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7082}%
$\displaystyle - R_d \DD{}{t} (\ln p_d)
+ \left(1 + \frac{q}{1-q} \right) c_p
\DD{}{t} (\ln T)
+ l \DD{}{t} \frac{r}{T}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7084}%
$\displaystyle - R_d \DD{}{t} \left\{ \ln (p (1-q)) \right\}
+ \frac{1}{1-q} c_p
\DD{}{t} (\ln T)
+ l \DD{}{t} \left( \frac{1}{T} \frac{q}{1-q} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2416}%
$q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7089}%
$\displaystyle - R_d   \frac{1}{p (1-q)} \DD{}{t} \left\{ p (1-q) \right\}
+ \frac{1}{1-q} \frac{c_p}{T}
\DD{T}{t}
+ l
\left[
- \frac{1}{T^2} \DD{T}{t} \frac{q}{1-q}
+    \frac{1}{T} \DD{}{t} \left(  \frac{q}{1-q} \right)
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2418}%
$\DD{S}{z} =0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7092}%
$\displaystyle - \frac{R_d}{p (1-q)} \DD{}{z} \left\{ p (1-q) \right\}
+ \frac{1}{1-q} \frac{c_p}{T}
\DD{T}{z}
- \frac{l}{T^2} \frac{q}{1-q} \DD{T}{z}
+ \frac{l}{T} \DD{}{z} \left(  \frac{q}{1-q} \right)
= 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2420}%
$dS=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7095}%
$\displaystyle - \frac{R_d}{p (1-q)} \DD{}{z} \left\{ p (1-q) \right\}
+ \frac{1}{1-q} \frac{c_p}{T}
\DD{T}{z}
- \frac{l}{T^2} \frac{q}{1-q} \DD{T}{z}
+ \frac{l}{T}
\frac{\DD{q}{z} (1-q) - q \DD{}{z}(1-q)}
{(1-q)^2}
= 0,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7096}%
$\displaystyle - \frac{R_d}{p (1-q)} \DD{}{z} \left\{ p (1-q) \right\}
+ \frac{1}{1-q} \frac{c_p}{T}
\DD{T}{z}
- \frac{l}{T^2} \frac{q}{1-q} \DD{T}{z}
+ \frac{l}{T} \frac{1}{(1-q)} \DD{q}{z}
+ \frac{l}{T}  \frac{q}{(1-q)^2}  \DD{q}{z}
= 0.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2422}%
$T^2(1-q)^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7099}%
$\displaystyle - \frac{R_d}{p} T^2 (1-q)  \DD{}{z} \left\{ p (1-q) \right\}
+ c_p T (1-q)
\DD{T}{z}
- l q (1-q)  \DD{T}{z}
+ l T (1-q) \DD{q}{z}
+ l T q \DD{q}{z}
= 0,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7100}%
$\displaystyle - \frac{R_d}{p} T^2 (1-q)  \DD{}{z} \left\{ p (1-q) \right\}
+ c_p T (1-q)
\DD{T}{z}
- l q (1-q)  \DD{T}{z}
+ l T \DD{q}{z}
= 0,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2424}%
$dz$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7103}%
$\displaystyle - \frac{R_d}{p} T^2 (1-q)  d \left\{ p (1-q) \right\}
+ c_p T (1-q)
dT
- l q (1-q)  dT
+ l T dq
= 0,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7105}%
$\displaystyle - \frac{R_d}{p_{k-1/2}} T_{k-1/2}^2 (1-q_{k-1/2})
\left[ p_{k-1} (1-q_{k-1}) - p_{k} (1-q_{k}) \right]
+ c_p (1-q_{k-1/2}) T_{k-1/2}
(T_{k-1} - T_{k})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7106}%
$\displaystyle \qquad
- l q_{k-1/2} (1-q_{k-1/2})  (T_{k-1} - T_{k})
+ l T_{k-1/2} (q_{k-1} - q_{k})
= 0,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7108}%
$\displaystyle T_{k-1/2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7110}%
$\displaystyle \frac{T_{k-1} + T_{k}}{2},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7111}%
$\displaystyle q_{k-1/2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7113}%
$\displaystyle \frac{q_{k-1} + q_{k}}{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2426}%
$T_{k-1/2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7117}%
$\displaystyle - \frac{R_d}{p_{k-1/2}}
\left( \frac{T_{k-1} + T_{k}}{2} \right)^2
\left( 1 - \frac{q_{k-1} + q_{k}}{2} \right)
\left[ p_{k-1} (1-q_{k-1}) - p_{k} (1-q_{k}) \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7118}%
$\displaystyle \qquad
+ c_p \left( 1 - \frac{q_{k-1} + q_{k}}{2} \right)
\frac{T_{k-1} + T_{k}}{2}
(T_{k-1} - T_{k})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7119}%
$\displaystyle \qquad
- l \frac{q_{k-1} + q_{k}}{2}
\left( 1 - \frac{q_{k-1} + q_{k}}{2} \right)  (T_{k-1} - T_{k})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7120}%
$\displaystyle \qquad
+ l \frac{T_{k-1} + T_{k}}{2} (q_{k-1} - q_{k})
= 0,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7121}%
$\displaystyle - \frac{R_d}{c_p}
\left( \frac{T_{k-1} + T_{k}}{2} \right)^2
\left( 1 - \frac{q_{k-1} + q_{k}}{2} \right)
\left[   \frac{p_{k-1}}{p_{k-1/2}}  (1-q_{k-1})
- \frac{p_{k}}{p_{k-1/2}}  (1-q_{k})
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7122}%
$\displaystyle \qquad
+ \left( 1 - \frac{q_{k-1} + q_{k}}{2} \right)
\frac{T_{k-1} + T_{k}}{2}
(T_{k-1} - T_{k})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7123}%
$\displaystyle \qquad
- \frac{L}{c_p} \frac{q_{k-1} + q_{k}}{2}
\left( 1 - \frac{q_{k-1} + q_{k}}{2} \right)  (T_{k-1} - T_{k})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7124}%
$\displaystyle \qquad
+ \frac{L}{c_p} \frac{T_{k-1} + T_{k}}{2} (q_{k-1} - q_{k})
= 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2430}%
$L$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7128}%
$\displaystyle - \frac{R_d}{c_p}  \frac{1}{4}
\left(
\hat{T}_{k-1} + \Delta T_{k-1} + \hat{T}_{k} + \Delta T_{k}
\right)^2$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7129}%
$\displaystyle \qquad
\times
\left\{   1
- \frac{1}{2}
\left(   q^{*} (\hat{T}_{k-1})
+ \left. \DP{q^{*}}{T} \right|_{k-1} \Delta T_{k-1}
+ q^{*} (\hat{T}_{k})
+ \left. \DP{q^{*}}{T} \right|_{k} \Delta T_{k} \right)
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7130}%
$\displaystyle \qquad
\times
\left[ \frac{p_{k-1}}{p_{k-1/2}}
\left( 1 - q^{*} (\hat{T}_{k-1})
- \left. \DP{q^{*}}{T} \right|_{k-1} \Delta T_{k-1} \right)
- \frac{p_{k}}{p_{k-1/2}}  \left( 1-q^{*} (\hat{T}_{k}) - \left. \DP{q^{*}}{T} \right|_{k} \Delta T_{k}
\right)
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7131}%
$\displaystyle \quad
+ \left\{ 1 - \frac{1}{2} \left( q^{*} (\hat{T}_{k-1}) + \left. \DP{q^{*}}{T} \right|_{k-1} \Delta T_{k-1} + q^{*} (\hat{T}_{k}) + \left. \DP{q^{*}}{T} \right|_{k} \Delta T_{k} \right) \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7132}%
$\displaystyle \qquad
\times
\frac{1}{2} \left( \hat{T}_{k-1} + \Delta T_{k-1} + \hat{T}_{k} + \Delta T_{k} \right)
(\hat{T}_{k-1} + \Delta T_{k-1} - \hat{T}_{k} - \Delta T_{k})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7133}%
$\displaystyle \quad
- \frac{L}{c_p} \frac{1}{2} \left( q^{*} (\hat{T}_{k-1}) + \left. \DP{q^{*}}{T} \right|_{k-1} \Delta T_{k-1} + q^{*} (\hat{T}_{k}) + \left. \DP{q^{*}}{T} \right|_{k} \Delta T_{k} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7135}%
$\displaystyle \qquad
\times
(\hat{T}_{k-1} + \Delta T_{k-1} - \hat{T}_{k} - \Delta T_{k})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7136}%
$\displaystyle \quad
+ \frac{L}{c_p}
\frac{1}{2}
\left( \hat{T}_{k-1} + \Delta T_{k-1} + \hat{T}_{k} + \Delta T_{k} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7137}%
$\displaystyle \qquad
\times
\left( q^{*} (\hat{T}_{k-1}) + \left. \DP{q^{*}}{T} \right|_{k-1} \Delta T_{k-1} - q^{*} (\hat{T}_{k}) - \left. \DP{q^{*}}{T} \right|_{k} \Delta T_{k} \right)
= 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7139}%
$\displaystyle MM$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7141}%
$\displaystyle 1  - \frac{1}{2} q^{*} (\hat{T}_{k-1})
- \frac{1}{2} q^{*} (\hat{T}_{k}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7142}%
$\displaystyle D_{k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7144}%
$\displaystyle \left. \DP{q^{*}}{T} \right|_{k-1},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7147}%
$\displaystyle \left. \DP{q^{*}}{T} \right|_{k},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7148}%
$\displaystyle TP$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7150}%
$\displaystyle \hat{T}_{k-1} + \hat{T}_{k},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7151}%
$\displaystyle TM$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7153}%
$\displaystyle \hat{T}_{k-1} - \hat{T}_{k},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7154}%
$\displaystyle M_{k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7156}%
$\displaystyle 1 - q^{*} (\hat{T}_{k-1}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7157}%
$\displaystyle M_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7159}%
$\displaystyle 1 - q^{*} (\hat{T}_{k}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7160}%
$\displaystyle F$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7162}%
$\displaystyle \frac{R_d}{c_p},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7163}%
$\displaystyle E$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7165}%
$\displaystyle \frac{L}{c_p},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7166}%
$\displaystyle QP$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7168}%
$\displaystyle q^{*} (\hat{T}_{k-1}) + q^{*} (\hat{T}_{k}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7169}%
$\displaystyle QM$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7171}%
$\displaystyle q^{*} (\hat{T}_{k-1}) - q^{*} (\hat{T}_{k}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7172}%
$\displaystyle P_{k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7174}%
$\displaystyle \frac{p_{k-1}}{p_{k-1/2}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7175}%
$\displaystyle P_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7177}%
$\displaystyle \frac{p_{k}}{p_{k-1/2}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7179}%
$\displaystyle - \frac{F}{4}
\left( TP + \Delta T_{k-1} + \Delta T_{k}
\right)^2
\left\{   MM
- \frac{1}{2} D_{k-1} \Delta T_{k-1}
- \frac{1}{2} D_{k} \Delta T_{k}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7180}%
$\displaystyle \qquad
\times
\left[   P_{k-1} \left( M_{k-1}  - D_{k-1} \Delta T_{k-1}  \right)
- P_{k} \left( M_{k} - D_{k} \Delta T_{k} \right)
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7181}%
$\displaystyle \quad
+ \frac{1}{2}
\left\{ MM - \frac{1}{2} \left( D_{k-1} \Delta T_{k-1}
+ D_{k} \Delta T_{k} \right)
\right\}
\left( TP + \Delta T_{k-1} + \Delta T_{k} \right)
(TM + \Delta T_{k-1} - \Delta T_{k})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7182}%
$\displaystyle \quad
- \frac{E}{2}
\left( QP + D_{k-1} \Delta T_{k-1} + D_{k} \Delta T_{k} \right)
\left\{  MM - \frac{1}{2} \left( D_{k-1} \Delta T_{k-1} + D_{k} \Delta T_{k} \right) \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7183}%
$\displaystyle \qquad
\times
(TM + \Delta T_{k-1} - \Delta T_{k})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7184}%
$\displaystyle \quad
+ \frac{E}{2}
\left( TP + \Delta T_{k-1} + \Delta T_{k} \right)
\left( QM + D_{k-1} \Delta T_{k-1} - D_{k} \Delta T_{k} \right)
= 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2434}%
$\Delta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7187}%
$\displaystyle - \frac{F}{4}
\left\{ TP^2  + 2 TP \cdot (\Delta T_{k-1} + \Delta T_{k}) \right\}
\left(   MM
- \frac{1}{2} D_{k-1} \Delta T_{k-1}
- \frac{1}{2} D_{k} \Delta T_{k}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7188}%
$\displaystyle \qquad
\times
\left(   P_{k-1} M_{k-1}  - P_{k-1} D_{k-1} \Delta T_{k-1}
- P_{k} M_{k} + P_{k} D_{k} \Delta T_{k}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7189}%
$\displaystyle \quad
+ \frac{1}{2}
\left( MM  - \frac{1}{2} D_{k-1} \Delta T_{k-1}
- \frac{1}{2} D_{k} \Delta T_{k}
\right)
\left\{ TP \cdot TM  + (\Delta T_{k-1} + \Delta T_{k}) TM
+ ( \Delta T_{k-1} - \Delta T_{k}) TP
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7190}%
$\displaystyle \quad
- \frac{E}{2}
\left( QP + D_{k-1} \Delta T_{k-1} + D_{k} \Delta T_{k} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7191}%
$\displaystyle \qquad
\times
\left\{   MM \cdot TM
+ ( \Delta T_{k-1} - \Delta T_{k}) MM
+ \left(- \frac{1}{2} D_{k-1} \Delta T_{k-1} - \frac{1}{2} D_{k} \Delta T_{k}\right)TM  \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7192}%
$\displaystyle \quad
+ \frac{E}{2}
\left\{   TP \cdot QM
+  \left(  D_{k-1} \Delta T_{k-1} - D_{k} \Delta T_{k} \right) TP
+ (\Delta T_{k-1} + \Delta T_{k}) QM
\right\}
= 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7194}%
$\displaystyle - \frac{F}{4}
\left\{   TP^2 \cdot MM
- \frac{1}{2} TP^2
\left(
D_{k-1} \Delta T_{k-1}
+  D_{k} \Delta T_{k}
\right)
+ 2 TP \cdot MM (\Delta T_{k-1} + \Delta T_{k})
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7195}%
$\displaystyle \quad
\times
\left\{  \left( P_{k-1} M_{k-1} - P_{k} M_{k} \right)
- P_{k-1} D_{k-1} \Delta T_{k-1}
+ P_{k} D_{k} \Delta T_{k}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7196}%
$\displaystyle + \frac{1}{2}
\left\{
MM \cdot TP \cdot TM
+ \left\{
(\Delta T_{k-1} + \Delta T_{k}) TM
+ ( \Delta T_{k-1} - \Delta T_{k}) TP
\right\} MM
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7197}%
$\displaystyle \quad \left.
- TP \cdot TM
\left(   \frac{1}{2} D_{k-1} \Delta T_{k-1}
+ \frac{1}{2} D_{k} \Delta T_{k}
\right)
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7198}%
$\displaystyle - \frac{E}{2}
\left\{   QP  \cdot MM \cdot TM
+ MM \cdot QP ( \Delta T_{k-1} - \Delta T_{k})
+ TM \cdot  QP
\left( - \frac{1}{2} D_{k-1} \Delta T_{k-1}
- \frac{1}{2} D_{k} \Delta T_{k}
\right)
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7199}%
$\displaystyle \quad \left.
+ MM \cdot TM (D_{k-1} \Delta T_{k-1} + D_{k} \Delta T_{k} )
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7200}%
$\displaystyle + \frac{E}{2}
\left\{   TP \cdot QM
+ (  TP \cdot D_{k-1} + QM ) \Delta T_{k-1}
+ ( - TP \cdot D_{k}  + QM )  \Delta T_{k}
\right\}
= 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7202}%
$\displaystyle - \frac{F}{4}
\left[   TP^2 \cdot MM \left( P_{k-1} M_{k-1} - P_{k} M_{k} \right)
+ TP^2 \cdot MM
\left\{
- P_{k-1} D_{k-1} \Delta T_{k-1}
+ P_{k} D_{k} \Delta T_{k}
\right\}
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7203}%
$\displaystyle \qquad \left.
+ \left( P_{k-1} M_{k-1} - P_{k} M_{k} \right)
\left\{   - \frac{1}{2} TP^2
\left(
D_{k-1} \Delta T_{k-1}
+  D_{k} \Delta T_{k}
\right)
+ 2 TP \cdot MM (\Delta T_{k-1} + \Delta T_{k})
\right\}
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7205}%
$\displaystyle \qquad \left.
- TP \cdot TM
\left(   \frac{1}{2} D_{k-1} \Delta T_{k-1}
+ \frac{1}{2} D_{k} \Delta T_{k} \right)
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7207}%
$\displaystyle \qquad \left.
+ MM \cdot TM (D_{k-1} \Delta T_{k-1} + D_{k} \Delta T_{k} )
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7212}%
$\displaystyle - \frac{F}{4}
\left[   TP^2 \cdot MM \left( P_{k-1} M_{k-1} - P_{k} M_{k} \right)
- TP^2 \cdot MM P_{k-1} D_{k-1} \Delta T_{k-1}
+ TP^2 \cdot MM P_{k} D_{k} \Delta T_{k}
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7213}%
$\displaystyle \qquad \left.
- \frac{1}{2} \left( P_{k-1} M_{k-1} - P_{k} M_{k} \right)  TP^2 D_{k-1} \Delta T_{k-1}
- \frac{1}{2} \left( P_{k-1} M_{k-1} - P_{k} M_{k} \right)  TP^2  D_{k} \Delta T_{k}
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7214}%
$\displaystyle \qquad \left.
+ 2 \left( P_{k-1} M_{k-1} - P_{k} M_{k} \right)   TP \cdot MM \Delta T_{k-1}
+ 2 \left( P_{k-1} M_{k-1} - P_{k} M_{k} \right)   TP \cdot MM \Delta T_{k}
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7215}%
$\displaystyle + \frac{1}{2}
\left\{   MM \cdot TP \cdot TM
+ TM \cdot MM \Delta T_{k-1} + TM \cdot MM \Delta T_{k}
+ TP \cdot MM \Delta T_{k-1} - TP \cdot MM \Delta T_{k}
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7216}%
$\displaystyle \qquad \left.
- TP \cdot TM  \frac{1}{2} D_{k-1} \Delta T_{k-1}
- TP \cdot TM \frac{1}{2} D_{k} \Delta T_{k}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7217}%
$\displaystyle - \frac{E}{2}
\left\{   QP  \cdot MM \cdot TM
+ MM \cdot QP \Delta T_{k-1}
- MM \cdot QP \Delta T_{k}
- TM \cdot  QP \frac{1}{2} D_{k-1} \Delta T_{k-1}
- TM \cdot  QP\frac{1}{2} D_{k} \Delta T_{k}
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7218}%
$\displaystyle \qquad \left.
+ MM \cdot TM D_{k-1} \Delta T_{k-1}
+ MM \cdot TM D_{k} \Delta T_{k}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7221}%
$\displaystyle - \frac{F}{4} TP^2 \cdot MM \left( P_{k-1} M_{k-1} - P_{k} M_{k} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7222}%
$\displaystyle - \frac{F}{4}
\left\{
- TP^2 \cdot MM \cdot P_{k-1} \cdot D_{k-1}
+ \left( P_{k-1} M_{k-1} - P_{k} M_{k} \right)
\left(- \frac{1}{2} TP^2 \cdot D_{k-1} + 2 TP \cdot MM \right)
\right\} \Delta T_{k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7223}%
$\displaystyle - \frac{F}{4}
\left\{
TP^2 \cdot MM \cdot P_{k} \cdot D_{k}
+ \left( P_{k-1} M_{k-1} - P_{k} M_{k} \right)
\left( - \frac{1}{2} TP^2 \cdot  D_{k} + 2 TP \cdot MM \right)
\right\} \Delta T_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7224}%
$\displaystyle + \frac{1}{2} MM \cdot TP \cdot TM$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7225}%
$\displaystyle + \frac{1}{2}
\left\{
TM \cdot MM + TP \cdot MM
- \frac{1}{2} TP \cdot TM \cdot D_{k-1}
\right\} \Delta T_{k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7226}%
$\displaystyle + \frac{1}{2}
\left\{
TM \cdot MM - TP \cdot MM
- \frac{1}{2} TP \cdot TM  \cdot D_{k}
\right\} \Delta T_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7227}%
$\displaystyle - \frac{E}{2} QP  \cdot MM \cdot TM$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7228}%
$\displaystyle - \frac{E}{2}
\left(
MM \cdot QP - \frac{1}{2} TM \cdot QP \cdot D_{k-1}
+ MM \cdot TM \cdot D_{k-1}
\right) \Delta T_{k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7229}%
$\displaystyle - \frac{E}{2}
\left(
- MM \cdot QP - \frac{1}{2} TM \cdot  QP \cdot D_{k}
+ MM \cdot TM \cdot D_{k}
\right) \Delta T_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7230}%
$\displaystyle + \frac{E}{2} TP \cdot QM
+ \frac{E}{2} ( TP \cdot D_{k-1} + QM ) \Delta T_{k-1}
+ \frac{E}{2} ( - TP \cdot D_{k} + QM ) \Delta T_{k}
= 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2440}%
$St$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7233}%
$\displaystyle St$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7235}%
$\displaystyle \frac{F}{4} TP^2 \cdot MM \left( P_{k-1} M_{k-1} - P_{k} M_{k} \right)
- \frac{1}{2} MM \cdot TP \cdot TM$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7236}%
$\displaystyle + \frac{E}{2} QP  \cdot MM \cdot TM
- \frac{E}{2} TP \cdot QM$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7237}%
$\displaystyle B$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7239}%
$\displaystyle - \frac{F}{4}
\left\{
- TP^2 \cdot MM \cdot P_{k-1} \cdot D_{k-1}
+ \left( P_{k-1} M_{k-1} - P_{k} M_{k} \right)
\left(- \frac{1}{2} TP^2 \cdot D_{k-1} + 2 TP \cdot MM \right)
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7240}%
$\displaystyle + \frac{1}{2}
\left\{
TM \cdot MM + TP \cdot MM
- \frac{1}{2} TP \cdot TM \cdot D_{k-1}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7241}%
$\displaystyle - \frac{E}{2}
\left(
MM \cdot QP - \frac{1}{2} TM \cdot QP \cdot D_{k-1}
+ MM \cdot TM \cdot D_{k-1}
\right)
+ \frac{E}{2} ( TP \cdot D_{k-1} + QM )$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7242}%
$\displaystyle C$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7244}%
$\displaystyle - \frac{F}{4}
\left\{
TP^2 \cdot MM \cdot P_{k} \cdot D_{k}
+ \left( P_{k-1} M_{k-1} - P_{k} M_{k} \right)
\left( - \frac{1}{2} TP^2 \cdot  D_{k} + 2 TP \cdot MM \right)
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7245}%
$\displaystyle + \frac{1}{2}
\left\{
TM \cdot MM - TP \cdot MM
- \frac{1}{2} TP \cdot TM  \cdot D_{k}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7246}%
$\displaystyle - \frac{E}{2}
\left(
- MM \cdot QP - \frac{1}{2} TM \cdot  QP \cdot D_{k}
+ MM \cdot TM \cdot D_{k}
\right)
+ \frac{E}{2} ( - TP \cdot D_{k} + QM )$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7248}%
$\displaystyle B \Delta T_{k-1} + C \Delta T_{k} = St$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7251}%
$\displaystyle \Delta T_{k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7253}%
$\displaystyle - \frac{1 + \gamma_{k}}{1+\gamma_{k-1}}
\frac{\Delta p_{k}}{\Delta p_{k-1}} \Delta T_{k}
+ \frac{1}{1+\gamma_{k-1}}
\frac{L}{c_p}
\Delta \hat{Q}
\frac{1}{\Delta p_{k-1}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7255}%
$\displaystyle \alpha \Delta T_{k} + \beta$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7257}%
$\displaystyle B \left( \alpha \Delta T_{k} + \beta \right)  + C T_{k} = St$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7260}%
$\displaystyle T_{k} = \frac{St - \beta B }{C + \alpha B}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{Dchapter}
{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7263}%

% latex2html id marker 7263
\setcounter{footnote}{6}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7265}%

% latex2html id marker 7265
\setcounter{footnote}{6}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2577}%
$N_S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2579}%
$F_S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7271}%
$\displaystyle F_S(z)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7273}%
$\displaystyle \sum_i^{N_S} a_i
\left[
(1-\alpha_A) F_S^I
\exp \left( - \tau_{S,i}(z) \sec \zeta \right)
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7274}%
$\displaystyle \left. - \alpha_g (1-\alpha_A) F_S^I
\exp \left( - \tau_{S,i}(0) \sec \zeta \right)
\exp \left( - ( \tau_{S,i}(0)-\tau_i(z) ) \sec \zeta_0 \right)
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2581}%
$F_S^I$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2583}%
$\zeta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2585}%
$\zeta_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2587}%
$\sec \zeta_0 = 1.66$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2589}%
$\alpha_A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2591}%
$\alpha_g$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2593}%
$\tau_{S,i}(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2544}%
\begin{displaymath}
\tau_{S,i}(z) = \int_z^\infty k_{S,i} \rho q dz 
          + \int_z^\infty \bar{k}_{S,i} \rho dz
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2595}%
$k_{S,i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2597}%
$i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2599}%
$\bar{k}_{S,i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2605}%
$a_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2554}%
\begin{displaymath}
F_S(0) = \sum_i^{N_S} a_i 
         (1-\alpha_g) (1-\alpha_A) F_S^I 
          \exp ( - \tau_{S,i}(0)\sec \zeta ) ,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2611}%
$S_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2613}%
$r_S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2559}%
\begin{displaymath}
F_S^I = - S_0 r_S^{-2} \cos \zeta .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2562}%
\begin{displaymath}
\cos \zeta = \cos \varphi \cos \delta_S \cos H
           + \sin \varphi \sin \delta_S
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2619}%
$\delta_S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2621}%
$H$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

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

{\newpage\clearpage
\lthtmldisplayA{displaymath2564}%
\begin{displaymath}
\overline{F_S^I} \simeq - S_0 ( 0.127 + 0.183 \cos^2 \varphi ) ,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2567}%
\begin{displaymath}
\overline{\cos \zeta} \simeq 0.410 + 0.590 \cos^2 \varphi .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7304}%

% latex2html id marker 7304
\setcounter{footnote}{6}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2690}%
$N_R$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2692}%
$F_R$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2654}%
\begin{displaymath}
F_R(z) =   \left( \pi B(T_g) - \pi B(T_s) \right) {\cal T}^f(z,0)
          +        \pi B(T(z_T))                  {\cal T}^f(z,z_T)
          - \int_0^{z_T} \DD{\pi B}{\xi} {\cal T}^f(z,\xi) d \xi 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2694}%
${\cal T}^f(z_1,z_2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2696}%
$z=z_1,z_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2698}%
$\pi B \equiv \sigma_{SB} T^4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2666}%
\begin{displaymath}
{\cal T}^f(z_1,z_2) 
   = \sum_{i=1}^{N_R} b_i 
       \exp \left( - \delta_R | \tau_{R,i}(z_1) - \tau_{R,i}(z_2) | 
            \right)
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2702}%
$\tau_i(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2673}%
\begin{displaymath}
\tau_{R,i}(z) = \int_z^\infty k_{R,i} \rho q dz 
              + \int_z^\infty \bar{k}_{R,i} \rho dz
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2704}%
$k_{R,i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2708}%
$\bar{k}_{R,i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2714}%
$b_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2718}%
$\delta_R = 1.5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{Dchapter}
{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7325}%

% latex2html id marker 7325
\setcounter{footnote}{6}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7326}%

% latex2html id marker 7326
\setcounter{footnote}{6}\fnsymbol{footnote}%
\lthtmlpictureZ
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\stepcounter{section}
\stepcounter{Dchapter}
\stepcounter{Dchapter}
\appendix
\stepcounter{Dchapter}
{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7331}%

% latex2html id marker 7331
\setcounter{footnote}{6}\fnsymbol{footnote}%
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{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7332}%

% latex2html id marker 7332
\setcounter{footnote}{6}\fnsymbol{footnote}%
\lthtmlpictureZ
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\stepcounter{section}
{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7334}%

% latex2html id marker 7334
\setcounter{footnote}{6}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7335}%

% latex2html id marker 7335
\setcounter{footnote}{6}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3084}%
$R^d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3086}%
$c_p^d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3088}%
$R$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3092}%
$c_p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7346}%
$\displaystyle p^d$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7348}%
$\displaystyle \rho^{d} R^d T,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7349}%
$\displaystyle p^v$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7351}%
$\displaystyle \rho^{v} R^v T,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3094}%
$\bullet^d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3096}%
$\bullet^v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3098}%
$p=p^d+p^v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7356}%
$\displaystyle p$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7358}%
$\displaystyle (\rho^d R^d + \rho^v R^v) T$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7360}%
$\displaystyle \rho R^d ( 1 + \epsilon_v q ) T,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3100}%
$q=\rho_v/\rho$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3102}%
$\epsilon_v \equiv
1/\epsilon -1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3104}%
$\epsilon \equiv R^d/R^v(=0.622)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2844}%
\begin{displaymath}
      p = \rho R T.
    \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3106}%
$R \equiv R^d ( 1+\epsilon_v q )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3108}%
$T_v \equiv T ( 1 + \epsilon_v q )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2847}%
\begin{displaymath}
      p = \rho R^d T_v.
    \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath2852}%
\begin{displaymath}
        \DP{\rho}{t}
      + \DP{}{x_j}( \rho v_j )
      = 0.
    \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2859}%
\begin{displaymath}
        \DD{\rho}{t}
      + \rho \Ddiv \Dvect{v}
      = 0.
    \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3110}%
$\rho^v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3112}%
$S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2865}%
\begin{displaymath}
     \DP{\rho^v}{t}
      + \DP{}{x_j} ( \rho^v v_j )
      = S.
    \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3114}%
$q=\rho^v/\rho$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2875}%
\begin{displaymath}
      \DD{q}{t} = S_q.
    \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath2880}%
\begin{displaymath}
        \DP{}{t}(\rho v_i)
      + \DP{}{x_j}( \rho v_i v_j )
      + \DP{p}{x_i} 
      - \DP{\sigma_{ij}}{x_j}
      + \rho \DP{\Phi^*}{x_i}
     = F'_i.
    \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3120}%
$\sigma_{ij}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3122}%
$\Phi^*$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3124}%
$F'_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2895}%
\begin{displaymath}
        \rho \DD{v_i}{t}
      + \DP{p}{x_i}
      - \DP{\tau_{ij}}{x_j}
      + \rho \DP{\Phi^*}{x_i}
     = F'_i,
    \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3126}%
$F_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2905}%
\begin{displaymath}
        \rho \DD{\Dvect{v}}{t}
      + \Dgrad p
      + \rho \Dgrad \Phi^*
     = \Dvect{F}.
    \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3128}%
$\Dvect{v}/2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3130}%
$\varepsilon$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2912}%
\begin{displaymath}
            \DP{}{t} 
             \left[ \rho 
                   \left(   \frac{1}{2} \Dvect{v}^2 
                 + \varepsilon + \Phi^* \right) \right]
         + \DP{}{x_j} \left[ 
             \rho 
               \left(   \frac{1}{2} \Dvect{v}^2 
                    + \varepsilon + \Phi^* \right)v_j
                    + p v_j - \sigma_{ij}v_i  
            \right]
      =  \rho Q + F'_i v_i,
    \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3136}%
$v_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3138}%
$\DP{\Phi^*}{t}=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7402}%
$\displaystyle v_i \DP{}{t} ( \rho v_i )
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\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7404}%
$\displaystyle \DP{}{t} ( \rho v_i^2 )
+ \DP{}{x_j} ( \rho v_j v_i^2 )
- \rho \DP{}{t} \left( \frac{1}{2}  v_i^2 \right)
- \rho v_j \DP{}{x_j} \left( \frac{1}{2} v_i^2 \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7406}%
$\displaystyle \DP{}{t} ( \rho v_i^2 )
+ \DP{}{x_j} ( \rho v_j v_i^2 )
- \DP{}{t} \left( \frac{1}{2}  \rho v_i^2 \right)
- \DP{}{x_j} \left( \frac{1}{2} v_i^2 \rho v_j \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7407}%
$\displaystyle + \frac{1}{2} v_i^2 \DP{\rho}{t}
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\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7409}%
$\displaystyle \DP{}{t} \left( \frac{1}{2} \rho v_i^2 \right)
+ \DP{}{x_j} ( \frac{1}{2} \rho v_j v_i^2 )
+ \frac{1}{2} v_i^2
\left\{ \DP{\rho}{t} + \DP{}{x_j} ( \rho v_j ) \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7411}%
$\displaystyle \DP{}{t} \left( \frac{1}{2} \rho v_i^2 \right)
+ \DP{}{x_j} ( \frac{1}{2} \rho v_j v_i^2 ).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7413}%
$\displaystyle v_i \rho \DP{\Phi^*}{x_i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7415}%
$\displaystyle \Phi^* \left\{ \DP{\rho}{t} + \DP{}{x_i}(\rho v_i) \right\}
+ \rho \DP{\Phi^*}{t}
+ v_i \rho \DP{\Phi^*}{x_i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7417}%
$\displaystyle \DP{}{t} ( \rho \Phi^* )
+ \DP{}{x_i} ( \rho \Phi^* v_i ).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3005}%
\begin{displaymath}
      \DP{}{t} \left( \frac{1}{2} \rho v_i^2 + \rho \Phi^* \right) 
    + \DP{}{x_j} \left( \frac{1}{2} \rho v_j \Dvect{v}^2
                        + \rho \Phi^* v_j
                        + p v_j - \sigma_{ij} v_i \right)
 =  p \DP{v_j}{x_j} - \sigma_{ij} \DP{v_i}{x_j} + F'_i v_i,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3025}%
\begin{displaymath}
   \DP{}{t} ( \rho \varepsilon )
     + \DP{}{x_j} ( \rho \varepsilon v_j )
   =  - p \DP{v_j}{x_j} + \sigma_{ij} \DP{v_i}{x_j}
     + \rho Q.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3036}%
\begin{displaymath}
   \rho \DD{\varepsilon}{t} 
  =   \frac{p}{\rho} \left( \DD{\rho}{t} \right)
    + \rho Q.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3140}%
$Q^*$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3142}%
$\varepsilon = c_v T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3144}%
$c_p = c_v + R$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3047}%
\begin{displaymath}
        \DD{c_p  T}{t} = \frac{1}{\rho} \DD{p}{t} + Q^*,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3154}%
$T_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3056}%
\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
\lthtmlpictureA{tex2html_wrap7434}%

% latex2html id marker 7434
\setcounter{footnote}{11}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7435}%

% latex2html id marker 7435
\setcounter{footnote}{11}\fnsymbol{footnote}%
\lthtmlpictureZ
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\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3400}%
$\Dvect{\Omega}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3402}%
$\psi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3216}%
\begin{displaymath}
   \left( \DD{\psi}{t} \right)_{\rm a}
 = \left( \DD{\psi}{t} \right)_{\rm r},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3406}%
$\Dvect{A}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3227}%
\begin{displaymath}
  \left( \DD{\Dvect{A}}{t} \right)_{\rm a}
     = \left( \DD{\Dvect{A}}{t} \right)_{\rm r}
      + \Dvect{\Omega} \times \Dvect{A}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7450}%
$\textstyle \Dvect{A} =$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7451}%
$\displaystyle \Dvect{i} A_x
+ \Dvect{j} A_y
+ \Dvect{k} A_z$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7454}%
$\displaystyle \Dvect{i}' A'_x
+ \Dvect{j}' A'_y
+ \Dvect{k}' A'_z$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7456}%
$\displaystyle \left( \DD{\Dvect{A}}{t} \right)_{\rm a}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7458}%
$\displaystyle \Dvect{i} \left( \DD{A_x}{t} \right)_{\rm a}
+ \Dvect{j} \left( \DD{A_y}{t} \right)_{\rm a}
+ \Dvect{k} \left( \DD{A_z}{t} \right)_{\rm a}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7460}%
$\displaystyle \Dvect{i}' \left( \DD{A'_x}{t} \right)_{\rm a}
+ \Dvect{j}' \left( \DD{A'_y}{t} \right)_{\rm a}
+ \Dvect{k}' \left( \DD{A'_z}{t} \right)_{\rm a}
+ \left( \DD{\Dvect{i}'}{t} \right)_{\rm a} A'_x
+ \left( \DD{\Dvect{j}'}{t} \right)_{\rm a} A'_y
+ \left( \DD{\Dvect{k}'}{t} \right)_{\rm a} A'_z$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7462}%
$\displaystyle \Dvect{i}' \left( \DD{A'_x}{t} \right)_{\rm r}
+ \Dvect{j}' \left( \DD{A'_y}{t} \right)_{\rm r}
+ \Dvect{k}' \left( \DD{A'_z}{t} \right)_{\rm r}
+ \Dvect{\Omega} \times \Dvect{i}' A'_x
+ \Dvect{\Omega} \times \Dvect{j}' A'_y
+ \Dvect{\Omega} \times \Dvect{k}' A'_z$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7464}%
$\displaystyle \left( \DD{\Dvect{A}}{t} \right)_{\rm r}
+ \Dvect{\Omega} \times \Dvect{A}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3410}%
$\Dvect{A}=\Dvect{r}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3412}%
$\Dvect{r}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3414}%
$\Dvect{v}_a \equiv (d\Dvect{r}/dt)_{\rm a}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3416}%
$\Dvect{v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3418}%
$\Dvect{v} \equiv (d\Dvect{r}/dt)_{\rm
r}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3324}%
\begin{displaymath}
  \Dvect{v}_a = \Dvect{v} + \Dvect{\Omega} \times \Dvect{r}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3420}%
$\Dvect{A}=\Dvect{v}_{\rm a}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3334}%
\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{displaymath3348}%
\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_inline3422}%
$\Dvect{g} \equiv \Dgrad \Phi^* - \Dvect{\Omega}
\times ( \Dvect{\Omega} \times \Dvect{v})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3364}%
\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_wrap7479}%

% latex2html id marker 7479
\setcounter{footnote}{13}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7480}%

% latex2html id marker 7480
\setcounter{footnote}{13}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3915}%
$(\xi_1, \xi_2, \xi_3)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3917}%
$\bullet$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3919}%
$\Dvect{A}=(A_1, A_2, A_3)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3921}%
$h_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3923}%
$\Dvect{e}_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3512}%
\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{displaymath3526}%
\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{displaymath3537}%
\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{displaymath3559}%
\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{displaymath3580}%
\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{displaymath3598}%
\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_inline3925}%
$\Dvect{g}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3927}%
$(\xi_1, \xi_2, \xi_3) = (\lambda, \varphi, r)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3929}%
$(x_1, x_2, x_3)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7499}%
$\displaystyle x_1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7501}%
$\displaystyle r \cos \varphi \cos \lambda,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7502}%
$\displaystyle x_2$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7504}%
$\displaystyle r \cos \varphi \sin \lambda,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7505}%
$\displaystyle x_3$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7507}%
$\displaystyle r \sin \varphi,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3933}%
$\varphi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3937}%
$(\Dvect{e}_{\lambda}, \Dvect{e}_{\varphi},
\Dvect{e}_{r})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3939}%
$(u, v, w)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3633}%
\begin{displaymath}
  h_\lambda = r \cos \varphi, \ \ h_\varphi = r, \ \ h_r = 1.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3943}%
$\Dvect{A}=(A_{\lambda}, A_{\varphi}, A_r)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3638}%
\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{displaymath3655}%
\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{displaymath3667}%
\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_indisplay7520}%
$\displaystyle \Drot \Dvect{A}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7522}%
$\displaystyle \Dvect{e}_{\lambda} \frac{1}{r}
\left[ \DP{A_r}{\varphi} - \DP{}{r}(r A_{\varphi})
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7523}%
$\displaystyle + \Dvect{e}_{\varphi} \frac{1}{r \cos \varphi}
\left[ \DP{}{r} (r \cos \varphi A_{\lambda}) -
\DP{A_r}{\lambda} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7524}%
$\displaystyle + \Dvect{e}_r \frac{1}{r \cos \varphi}
\left[ \DP{A_{\varphi}}{\lambda} - \DP{}{\varphi} (\cos
\varphi A_{\lambda}) \right],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3714}%
\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_indisplay7527}%
$\displaystyle \DD{\Dvect{A}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7529}%
$\displaystyle \Dvect{e}_{\lambda} \left[
\DP{A_{\lambda}}{t} + \frac{u}{r \cos \varphi} \DP{A_{\lambda}}{\lambda}
+ \frac{v}{r} \DP{A_{\lambda}}{\varphi} + w \DP{A_{\lambda}}{r}
+ \frac{u}{r} A_r - \frac{u \tan \varphi}{r} A_{\varphi} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7530}%
$\displaystyle + \Dvect{e}_{\varphi} \left[
\DP{A_{\varphi}}{t} + \frac{u}{r \cos \varphi} \DP{A_{\varphi}}{\lambda}
+ \frac{v}{r} \DP{A_{\varphi}}{\varphi} + w \DP{A_{\varphi}}{r}
+ \frac{v}{r} A_r + \frac{u \tan \varphi}{r} A_{\lambda} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7531}%
$\displaystyle + \Dvect{e}_r \left[
\DP{A_r}{t} + \frac{u}{r \cos \varphi} \DP{A_r}{\lambda}
+ \frac{v}{r} \DP{A_r}{\varphi} + w \DP{A_r}{r}
- \frac{v}{r} A_{\varphi} - \frac{u}{r} A_{\lambda} \right].$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7534}%
$\displaystyle 2 \Dvect{\Omega} \times \Dvect{v}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7536}%
$\displaystyle 2 \Omega ( \Dvect{e}_{\varphi} \cos \varphi
+ \Dvect{e}_r \sin \varphi)
\times ( u \Dvect{e}_{\lambda} + v \Dvect{e}_{\varphi}
+ w \Dvect{e}_r)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7538}%
$\displaystyle ( 2 \Omega \cos \varphi w - 2 \Omega \sin \varphi v) \Dvect{e}_{\lambda}
+ 2 \Omega \sin \varphi u \Dvect{e}_{\varphi}
- 2 \Omega \cos \varphi u \Dvect{e}_r.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7540}%
$\displaystyle \DD{u}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7542}%
$\displaystyle - \frac{1}{\rho r \cos \varphi } \DP{p}{\lambda}
+  2 \Omega v \sin \varphi
-  2 \Omega w \cos \varphi
+  \frac{u v}{r} \tan \varphi
-  \frac{u w}{r}
+ F_\lambda,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7543}%
$\displaystyle \DD{v}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7545}%
$\displaystyle - \frac{1}{\rho r} \DP{p}{\varphi}
- 2 \Omega u \sin \varphi
- \frac{u^2}{r} \tan \varphi
- \frac{v w}{r}
+ F_\varphi,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7546}%
$\displaystyle \DD{w}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7548}%
$\displaystyle - \frac{1}{\rho} \DP{p}{r} -g
+ 2 \Omega u \cos \varphi
+ \frac{u^2}{r}
+ \frac{v^2}{r}
+ F_r.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3841}%
\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{displaymath3857}%
\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{displaymath3873}%
\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_wrap7554}%

% latex2html id marker 7554
\setcounter{footnote}{13}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7555}%

% latex2html id marker 7555
\setcounter{footnote}{13}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7556}%

% latex2html id marker 7556
\setcounter{footnote}{13}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath3978}%
\begin{displaymath}
0  =  - \frac{1}{\rho} \DP{p}{z} - g.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4173}%
$u,
v, w$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7563}%
$\displaystyle \DD{}{t} \left( \frac{1}{2} \Dvect{v}^2 \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7565}%
$\displaystyle u \DD{u}{t} + v \DD{v}{t} + w \DD{w}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7567}%
$\displaystyle u \biggl\{
- \frac{1}{\rho r \cos \varphi } \DP{p}{\lambda}
+  \underbrace{ 2 v \Omega \sin \varphi }_{(1)}
-  \underbrace{ 2 w \Omega \cos \varphi }_{(2)}
+  \underbrace{ \frac{u v}{r} \tan \varphi }_{(3)}
-  \underbrace{ \frac{u w}{r} }_{(4)}
+ F_\lambda \biggl\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7568}%
$\displaystyle + v \biggl\{ - \frac{1}{\rho r} \DP{p}{\varphi}
- \underbrace{ 2 \Omega u \sin \varphi }_{(1)}
- \underbrace{ \frac{u^2}{r} \tan \varphi }_{(3)}
- \underbrace{ \frac{v w}{r} }_{(5)}
+ F_\varphi \biggl\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7569}%
$\displaystyle + w \biggl\{ - \frac{1}{\rho} \DP{p}{r} -g
+ \underbrace{ 2 \Omega u \cos \varphi }_{(2)}
+ \underbrace{ \frac{u^2}{r} }_{(4)}
+ \underbrace{ \frac{v^2}{r} }_{(5)}
+ F_r \biggl\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7571}%
$\displaystyle - \frac{1}{\rho} \Dvect{v} \Dgrad{p} - g w
- \Dvect{v} \cdot \Dvect{F}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7577}%
$\displaystyle \frac{uv \tan \varphi}{r}
+ fv - \frac{1}{\rho r \cos \varphi} \DP{p}{\lambda}
+ F_{\lambda}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7580}%
$\displaystyle - \frac{u^2 \tan \varphi}{a}
- fu - \frac{1}{\rho r } \DP{p}{\varphi}
+ F_{\varphi}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4175}%
$f$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4177}%
$f \equiv 2\Omega \sin \varphi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4181}%
$a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4063}%
\begin{displaymath}
      \DD{\rho}{t} = - \rho \Ddiv \Dvect{v},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4068}%
\begin{displaymath}
      \DD{q}{t}  = S_q,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4072}%
\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{displaymath4083}%
\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{displaymath4094}%
\begin{displaymath}
0  =  - \frac{1}{\rho} \DP{p}{z} - g,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4100}%
\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{displaymath4113}%
\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{displaymath4129}%
\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_wrap7597}%

% latex2html id marker 7597
\setcounter{footnote}{14}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7598}%

% latex2html id marker 7598
\setcounter{footnote}{14}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath4221}%
\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{displaymath4231}%
\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_inline5005}%
$u$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5007}%
$\frac{1}{a \cos \varphi} \DP{}{\varphi} \cos
\varphi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5009}%
$v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5011}%
$\frac{1}{a \cos \varphi} \DP{}{\lambda}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7609}%
$\displaystyle \DP{\zeta}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7611}%
$\displaystyle - \frac{1}{a \cos \varphi} \DP{}{\varphi}
( \zeta v \cos  \varphi )
-  \frac{1}{a \cos \varphi} \DP{}{\lambda}
( \zeta u )$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7612}%
$\displaystyle - \frac{1}{a \cos \varphi} \DP{}{\lambda}
\left[   \dot{\sigma} \DP{v}{\sigma}
+ \frac{R^d T_v}{a p_s} \DP{p_s}{\varphi}
- F_{\varphi} + f u \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7613}%
$\displaystyle - \frac{1}{a \cos \varphi} \DP{}{\varphi}
\left[   - \cos \varphi \dot{\sigma} \DP{u}{\sigma}
- \frac{R^d T_v}{a p_s} \DP{p_s}{\lambda}
+ F_{\lambda} \cos \varphi + f v \cos \varphi \right].$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7620}%
$\displaystyle \DP{D}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7622}%
$\displaystyle \frac{1}{a \cos \varphi} \DP{}{\lambda}
( \zeta v )
-  \frac{1}{a \cos \varphi} \DP{}{\varphi}
( \zeta u \cos \varphi)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7623}%
$\displaystyle - \frac{1}{a \cos \varphi} \DP{}{\lambda}
\left[   \dot{\sigma} \DP{u}{\sigma}
+ \frac{R^d T_v}{a \cos \varphi p_s} \DP{p_s}{\lambda}
- F_{\lambda} - f v \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7624}%
$\displaystyle - \frac{1}{a \cos \varphi} \DP{}{\varphi}
\left[    \cos \varphi \dot{\sigma} \DP{v}{\sigma}
+ \frac{R^d T_v}{a p_s} \DP{p_s}{\varphi} \cos \varphi
- F_{\varphi} \cos \varphi + f u \cos \varphi \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7625}%
$\displaystyle - \nabla^2_{\sigma} ( \Phi + KE).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7627}%
$\displaystyle \nabla^2_{\sigma}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7629}%
$\displaystyle \frac{1}{a^2 \cos^2 \varphi} \DP[2]{}{\lambda}
+ \frac{1}{a^2 \cos \varphi} \DP{}{\varphi} ( \cos
\varphi \DP{}{\varphi} ),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7630}%
$\displaystyle KE$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7632}%
$\displaystyle \frac{u^2 + v^2}{2}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5021}%
$\mu \equiv \sin \varphi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5023}%
$u, v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5025}%
$U \equiv u
\cos \phi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5027}%
$V \equiv \cos \phi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5033}%
$D$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7648}%
$\displaystyle \frac{1}{a \cos \varphi} \DP{v}{\lambda}
- \frac{1}{a \cos \varphi} \DP{}{\varphi} ( u \cos \varphi)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7650}%
$\displaystyle \frac{1}{a \cos^2 \varphi} \DP{v \cos \phi}{\lambda}
- \frac{1}{a \cos \varphi} \DP{}{\varphi} ( u \cos \varphi)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7652}%
$\displaystyle \frac{1}{a ( 1- \mu^2 )} \DP{V}{\lambda}
- \frac{1}{a} \DP{U}{\mu},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7656}%
$\displaystyle \frac{1}{a \cos \varphi} \DP{u}{\lambda}
+ \frac{1}{a \cos \varphi} \DP{}{\varphi} ( v \cos \varphi)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7658}%
$\displaystyle \frac{1}{a \cos^2 \varphi} \DP{u \cos \phi}{\lambda}
+ \frac{1}{a \cos \varphi} \DP{}{\varphi} ( v \cos \varphi)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7660}%
$\displaystyle \frac{1}{a ( 1-\mu^2)} \DP{U}{\lambda}
+ \frac{1}{a} \DP{V}{\mu}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7662}%
$\displaystyle \frac{u}{a \cos\phi}\DP{\bullet}{\lambda}
+ \frac{v}{a} \DP{\bullet}{\phi}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7664}%
$\displaystyle \frac{1}{a \cos^2 \phi}
\left\{ \DP{}{\lambda} (u \cos \phi \bullet)
- \bullet \DP{}{\lambda} ( u \cos \phi ) \right\}
\frac{1}{a \cos \phi}
\left\{ \DP{}{\phi} (v \cos \phi \bullet)
- \bullet \DP{}{\phi} ( v \cos \phi ) \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7666}%
$\displaystyle \frac{1}{a (1-\mu^2)} \DP{}{\lambda} (U\bullet)
-\frac{\bullet}{a (1-\mu^2)} \DP{U}{\lambda}
+\frac{1}{a \mu} \DP{}{\phi} (V\bullet)
-\frac{\bullet}{a} \DP{V}{\mu}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7668}%
$\displaystyle \frac{1}{a (1-\mu^2)} \DP{}{\lambda} (U\bullet)
+\frac{1}{a \mu} \DP{}{\phi} (V\bullet)
+\bullet D.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7672}%
$\displaystyle + \frac{u \cos \phi }{a \cos^2 \phi}\DP{\bullet}{\lambda}
+ \frac{v \cos \phi }{a \cos \phi } \DP{\bullet}{\phi}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7674}%
$\displaystyle + \frac{U}{a (1-\mu^2)} \DP{\bullet}{\lambda}
+ \frac{V}{a} \DP{\bullet}{\mu}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7676}%
$\displaystyle \Dvect{v}_H \cdot \Dgrad_{\sigma} \bullet.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4476}%
\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_indisplay7684}%
$\displaystyle -\frac{1}{a}\DP{}{\mu} ( \zeta V )
-\frac{1}{a (1-\mu^2)} \DP{}{\lambda} ( \zeta U )$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7685}%
$\displaystyle - \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[   \dot{\sigma} \DP{V}{\sigma}
+ \frac{R^d T_v}{a} (1-\mu^2) \DP{\pi}{\mu}
- F_{\varphi} \cos \varphi + f U \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7686}%
$\displaystyle - \frac{1}{a} \DP{}{\mu}
\left[   - \dot{\sigma} \DP{U}{\sigma}
- \frac{R^d T_v}{a} \DP{\pi}{\lambda}
+ F_{\lambda} \cos \varphi + fV \right].$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7690}%
$\displaystyle \frac{1}{a (1-\mu^2)} \DP{}{\lambda} ( \zeta V )
-  \frac{1}{a} \DP{}{\mu}
( \zeta U )$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7691}%
$\displaystyle - \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[   \dot{\sigma} \DP{U}{\sigma}
+ \frac{R^d T_v}{a} \DP{\pi}{\lambda}
- F_{\lambda} \cos \varphi - f V \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7692}%
$\displaystyle - \frac{1}{a} \DP{}{\mu}
\left[ \dot{\sigma} \DP{V}{\sigma}
+ \frac{R^d T_v}{a} ( 1-\mu^2 ) \DP{\pi}{\mu}
- F_{\varphi} \cos \varphi + f U \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7695}%
$\displaystyle \DP{T}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7697}%
$\displaystyle - \frac{1}{a(1-\mu^{2})} \DP{UT}{\lambda}
- \frac{1}{a}
\DP{VT}{\mu}
+ T D$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7698}%
$\displaystyle - \dot{\sigma}
\DP{T}{\sigma}
+ \kappa T \left( \DP{\pi}{t}
+ \Dvect{v}_{H} \cdot \nabla_{\sigma} \pi
+ \frac{ \dot{\sigma} }{ \sigma }
\right)
+ \frac{Q^*}{C_{p}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7700}%
$\displaystyle \DP{q}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7702}%
$\displaystyle - \frac{1}{a(1-\mu^{2})}
\DP{Uq}{\lambda}
- \frac{1}{a}
\DP{Vq}{\mu}
+ q D$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7703}%
$\displaystyle - \dot{\sigma} \frac{\partial q }{\partial \sigma}
+ S_{q}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5045}%
$\bar{T}_v(\sigma)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5047}%
$T'_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7710}%
$\displaystyle - \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ + \frac{R^d T_v}{a} (1-\mu^2) \DP{\pi}{\mu} \right]
- \frac{1}{a} \DP{}{\mu}
\left[ - \frac{R^d T_v}{a} \DP{\pi}{\lambda} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7712}%
$\displaystyle - \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ + \frac{R^d \bar{T}_v}{a} (1-\mu^2) \DP{\pi}{\mu} \right]
- \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ + \frac{R^d T'_v}{a} (1-\mu^2) \DP{\pi}{\mu} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7713}%
$\displaystyle - \frac{1}{a} \DP{}{\mu}
\left[ - \frac{R^d \bar{T}_v}{a} \DP{\pi}{\lambda} \right]
- \frac{1}{a} \DP{}{\mu}
\left[ - \frac{R^d T'_v}{a} \DP{\pi}{\lambda} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7715}%
$\displaystyle - \frac{1}{a} \frac{R^d \bar{T}_v}{a}
\frac{\partial^2 \pi}{\partial \lambda \partial \mu}
- \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ + \frac{R^d T'_v}{a} (1-\mu^2) \DP{\pi}{\mu} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7716}%
$\displaystyle + \frac{1}{a} \frac{R^d \bar{T}_v}{a}
\frac{\partial^2 \pi}{\partial \mu \partial \lambda}
- \frac{1}{a} \DP{}{\mu}
\left[ - \frac{R^d T'_v}{a} \DP{\pi}{\lambda} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7718}%
$\displaystyle - \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ + \frac{R^d T'_v}{a} (1-\mu^2) \DP{\pi}{\mu} \right]
- \frac{1}{a} \DP{}{\mu}
\left[ - \frac{R^d T'_v}{a} \DP{\pi}{\lambda} \right].$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7721}%
$\displaystyle - \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ \frac{R^d T_v}{a} \DP{\pi}{\lambda} \right]
- \frac{1}{a} \DP{}{\mu}
\left[ \frac{R^d T_v}{a} ( 1-\mu^2 ) \DP{\pi}{\mu} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7723}%
$\displaystyle - \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ \frac{R^d \bar{T}_v}{a} \DP{\pi}{\lambda} \right]
- \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ \frac{R^d T'_v}{a} \DP{\pi}{\lambda} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7724}%
$\displaystyle - \frac{1}{a} \DP{}{\mu}
\left[ \frac{R^d \bar{T}_v}{a} ( 1-\mu^2 ) \DP{\pi}{\mu} \right]
- \frac{1}{a} \DP{}{\mu}
\left[ \frac{R^d T'_v}{a} ( 1-\mu^2 ) \DP{\pi}{\mu} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7726}%
$\displaystyle - \frac{1}{a^2 (1-\mu^2)} \DP[2]{}{\lambda}
( R^d \bar{T}_v \pi )
- \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ \frac{R^d T'_v}{a} \DP{\pi}{\lambda} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7727}%
$\displaystyle - \frac{1}{a^2} \DP{}{\mu}
\left[ (1-\mu^2) \DP{}{\mu} ( R^d \bar{T}_v \pi ) \right]
- \frac{1}{a} \DP{}{\mu}
\left[ \frac{R^d T'_v}{a} ( 1-\mu^2 ) \DP{\pi}{\mu} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7729}%
$\displaystyle - \Dgrad^2_{\sigma} ( R^d \bar{T}_v \pi )
- \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ \frac{R^d T'_v}{a} \DP{\pi}{\lambda} \right]
- \frac{1}{a} \DP{}{\mu}
\left[ \frac{R^d T'_v}{a} ( 1-\mu^2 ) \DP{\pi}{\mu} \right].$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7733}%
$\displaystyle - \frac{1}{a(1-\mu^{2})} \DP{U \bar{T}}{\lambda}
- \frac{1}{a(1-\mu^{2})} \DP{UT'}{\lambda}
- \frac{1}{a} \DP{V \bar{T}}{\mu}
- \frac{1}{a} \DP{VT'}{\mu}
+ \bar{T} D
+ T' D$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7735}%
$\displaystyle - \frac{\bar{T}}{a(1-\mu^{2})} \DP{U}{\lambda}
- \frac{1}{a(1-\mu^{2})} \DP{UT'}{\lambda}
- \frac{\bar{T}}{a} \DP{V}{\mu}
- \frac{1}{a} \DP{VT'}{\mu}
+ \bar{T} \left[ \frac{1}{a(1-\mu^{2})} \DP{U}{\lambda}
+ \frac{\bar{1}}{a} \DP{V}{\mu}         \right]
+ T' D$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7737}%
$\displaystyle - \frac{1}{a(1-\mu^{2})} \DP{UT'}{\lambda}
- \frac{1}{a} \DP{VT'}{\mu}
+ T' D.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4860}%
\begin{displaymath}
  \DP{\Phi}{\sigma} = - \frac{R^d T_v}{\sigma}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4867}%
\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{displaymath4879}%
\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_indisplay7747}%
$\displaystyle UA$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7749}%
$\displaystyle ( \zeta + f ) V
- \dot{\sigma} \DP{U}{\sigma}
- \frac{RT'}{a}
\DP{\pi}{\lambda}
+ F_{\lambda} \cos \varphi$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7750}%
$\displaystyle VA$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7752}%
$\displaystyle - ( \zeta + f ) U
- \dot{\sigma} \DP{V}{\sigma}
- \frac{RT'}{a} ( 1 - \mu^{2} )
\DP{\pi}{\mu}
+ F_{\varphi} \cos \varphi.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7756}%
$\displaystyle - \frac{1}{a(1-\mu^{2})} \DP{UT'}{\lambda}
- \frac{1}{a} \DP{VT'}{\mu}
+ T' D
- \dot{\sigma}
\DP{T}{\sigma}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7757}%
$\displaystyle \qquad
+ \kappa T \left( \DP{\pi}{t}
+ \Dvect{v}_{H} \cdot \nabla_{\sigma} \pi
+ \frac{ \dot{\sigma} }{ \sigma }
\right)
+ \frac{Q^*}{C_p^d}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4936}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5059}%
$c_p \mathcal{D}(\Dvect{v})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5061}%
$Q^*=Q+c_p \mathcal{D}(\Dvect{v})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5063}%
$\mathcal{D}(\zeta)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5065}%
$\mathcal{D}(D)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5067}%
$\mathcal{D}(T)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5069}%
$\mathcal{D}(q)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{Dchapter}
{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7772}%

% latex2html id marker 7772
\setcounter{footnote}{17}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5215}%
$q^*(T,p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5217}%
$e^*(T)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5134}%
\begin{displaymath}
q^*(T,p) = \frac{\epsilon e^*(T)}{p} .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5219}%
$\epsilon=0.622$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5138}%
\begin{displaymath}
\frac{1}{e^*_v} \DP{e^*_v}{T} = \frac{L}{R_v T^2}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5223}%
$R_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5147}%
\begin{displaymath}
  e^*(T) = e^*(T=273\mbox{K}) 
                      \exp \left[ \frac{L}{R_v} 
                            \left( \frac{1}{273} - \frac{1}{T} \right)
                       \right] ,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5225}%
$e^*(T=273\mbox{K}) = 611$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5157}%
\begin{displaymath}
  q^*(T,p) = \epsilon 
           e^*(T=273\mbox{K}) 
                      \exp \left[ \frac{L}{R_v} 
                            \left( \frac{1}{273} - \frac{1}{T} \right)
                       \right]
           \frac{1}{p}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5169}%
\begin{displaymath}
  \DP{q^*}{T} (T,p) 
= \frac{L}{R_v T^2} 
  \epsilon 
           e^*(T=273\mbox{K}) 
                      \exp \left[ \frac{L}{R_v} 
                            \left( \frac{1}{273} - \frac{1}{T} \right)
                       \right]
           \frac{1}{p}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7788}%
$\displaystyle e^{*}(T) = p^{*}_{0} \exp \left( - \frac{L}{RT} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5227}%
$p^{*}_{0} = 1.4 \times 10^{11}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7791}%
$\displaystyle q*(T, p) = p^{*}_{0} \exp \left( - \frac{L}{RT} \right) \frac{1}{p}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7793}%

% latex2html id marker 7793
\setcounter{footnote}{17}\fnsymbol{footnote}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5296}%
$\times 10^6$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5298}%
$g$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5300}%
$^{-2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5302}%
$C_p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5304}%
$^{-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5320}%
$C_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5332}%
$d_{H_2O}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5338}%
$^{\circ}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5340}%
$e^*$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5342}%
$\sigma_{SB}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5346}%
$^{-4}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5348}%
$\times 10^{-8}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5350}%
$k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5352}%
$\epsilon_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5354}%
$\delta_v = \epsilon_v^{-1} - 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5356}%
$\kappa = R/C_p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{Dchapter}
\stepcounter{section}

\end{document}
