\batchmode


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


\usepackage{Dennou6}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage{html}

%
\providecommand{\Dmodelbase}{dcpam}   % ¥â¥Ç¥ëÌ¾ (¥Ð¡¼¥¸¥ç¥ó¤Ê¤·)%
\providecommand{\Dmodelver}{4}        % ¥â¥Ç¥ë¥Ð¡¼¥¸¥ç¥ó%
\providecommand{\Dmodel}{dcpam4}  % ¥â¥Ç¥ëÌ¾ (¥Ð¡¼¥¸¥ç¥ó¤¢¤ê)


\Dtitle[dcpam4»ÙÇÛÊýÄø¼°·Ï¤È¤½¤ÎÎ¥»¶²½]{dcpam4\\[5mm]
          »ÙÇÛÊýÄø¼°·Ï¤È¤½¤ÎÎ¥»¶²½ \\[70mm]}
  \Dauthor[ÃÏµåÎ®ÂÎÅÅÇ¾¶æ³ÚÉô]{ÃÏµåÎ®ÂÎÅÅÇ¾¶æ³ÚÉô}
  %%
\providecommand{\Dmodelverprint}{20080624-1}%
\providecommand{\Dmodeldateprint}{2008/06/24}%
\providecommand{\DmodeldateprintJ}{2008Ç¯06·î24Æü} 
  \Ddate[2008/06/24]{2008Ç¯06·î24Æü(dcpam4-20080624-1)}
  \Dparskip

%
\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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\providecommand{\selectlanguage}[1]{}%
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\providecommand{\Beta}{\textrm{B}}
\providecommand{\Mu}{\textrm{M}}
\providecommand{\Kappa}{\textrm{K}}
\providecommand{\Rho}{\textrm{R}}
\providecommand{\Epsilon}{\textrm{E}}
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\providecommand{\Iota}{\textrm{J}}
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\providecommand{\Eta}{\textrm{H}}
\providecommand{\Nu}{\textrm{N}}
\providecommand{\Omicron}{\textrm{O}}
\providecommand{\Tau}{\textrm{T}}
\providecommand{\Alpha}{\textrm{A}}


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\begin{align*}\begin{split}  \Delta \sigma_k       &\equiv \sigma_{k-1/2} - \sigma_{k+1/2},     \qquad ( 1 < k < K )   \\\Delta \sigma_{1/2}   &\equiv \sigma_{1/2} - \sigma_{1}                          = 1 -\sigma_{1}, \\\Delta \sigma_{K+1/2} &\equiv \sigma_{K} - \sigma_{K+1/2}                          = \sigma_{K}.  \end{split}\end{align*}%
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\lthtmlinlinemathA{tex2html_wrap_inline6301}%
$ {\displaystyle w_j \equiv
\frac{(2J-1)(1-\sin^2 \varphi_j)}
{\left\{J P_{J-1}(\sin \varphi_j)\right\}^2 }    }$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6304}%
$ A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6306}%
$ (\lambda_i,\varphi_j)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6308}%
$ i=1,2,\cdots,I. \quad j=1,2,\cdots,J$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6310}%
$ A_{ij}=A(\lambda_i,\varphi_j)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6312}%
$ Y_n^m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6314}%
$ m=-M,\cdots,M. \quad n=|m|,\cdots,N(m)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6316}%
$ \tilde{A}_n^m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6319}%
$\displaystyle A_{ij}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6320}%
$\displaystyle \equiv              \sum_{m=-M}^{M} \sum_{n=|m|}^{N}               \tilde{A}_n^m               Y_n^m (\lambda_i,\varphi_j),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6321}%
$\displaystyle \tilde{A}_n^m$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6322}%
$\displaystyle =              \frac{1}{I}              \sum_{i=1}^{I} \sum_{j=1}^{J}                A_{ij} Y_n^{m*} (\lambda_i,  \varphi_j) w_j .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6326}%
$ {\displaystyle 
\left\{\tilde{A}^m_n \exp(im\lambda) \right\}^*
= \tilde{A}^{-m}_n \exp(-im\lambda) }$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6328}%
$ m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6334}%
$ n-m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6336}%
$ \varphi=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6342}%
$ A_{ij}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6344}%
$ A_{ij}^{even}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6346}%
$ A_{ij}^{odd}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6348}%
$ A{i,J-j}=A_{ij}^{even}-A_{ij}^{odd}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6350}%
$ A_n^m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6352}%
$ A_{i,j}+A_{i,J-j}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6354}%
$ A_{i,j}-A_{i,J-j}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6356}%
$ j$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6358}%
$ J/2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6360}%
$ *$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6364}%
$\displaystyle =  \sum_{m=0}^{M} \sum_{n=m}^{N}             \Re \tilde{A}_n^m Y_n^m(\lambda_i, \varphi_j),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6366}%
$\displaystyle =   \left\{        \begin{array}{ll}      {\displaystyle \frac{1}{I}                   \sum_{i=1}^{I} \sum_{j=1}^{J}  }                  A_{ij} Y_n^{m*}(\lambda_i, \varphi_j) w_j ,      &   \  \ \  m=0, \quad m \le n \le N, \\{\displaystyle \frac{2}{I}                   \sum_{i=1}^{I} \sum_{j=1}^{J}  }                  A_{ij} Y_n^{m*}(\lambda_i,\varphi_j) w_j ,      &   \  \ \  1 \le m \le M, \quad m \le n \le N.   \end{array}       \right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6371}%
$ A(\lambda,\varphi)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6378}%
$\displaystyle A(\lambda,\varphi)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6379}%
$\displaystyle \equiv \sum_{m=-M}^{M} \sum_{n=|m|}^{N}                 \tilde{A}_n^m Y_n^m (\lambda, \varphi)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6383}%
$\displaystyle \left( \DP{f}{\lambda} \right)_{ij}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6384}%
$\displaystyle \equiv \sum_{m=-M}^M                      \sum_{n=|m|}^N im \tilde{f}_n^m                  Y_n^m (\lambda_i,\varphi_j) ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6385}%
$\displaystyle \widetilde{ \left( \DP{f}{\lambda} \right) }_n^m$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6386}%
$\displaystyle =   \frac{1}{I} \sum_{i=1}^I \sum_{j=1}^J                     im f_{ij} Y_n^{m*} (\lambda_i, \varphi_j) w_j  .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6389}%
$\displaystyle \left(\DP{f}{\varphi}\right)_{ij}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6390}%
$\displaystyle \equiv  \sum_{m=-M}^M \sum_{n=|m|}^N \tilde{f}_n^m                    \left. \DD{P_n^m}{\varphi} \right|_j                     \exp(im \lambda_i) ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6391}%
$\displaystyle \widetilde{\left(\DP{f}{\varphi}\right)}_n^m$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6392}%
$\displaystyle = - \frac{1}{I} \sum_{i=1}^I \sum_{j=1}^J f_{ij}                     \left. \DD{P_n^m}{\varphi}\right|_j                     \exp(-im \lambda_i) w_j .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{chapter}
\stepcounter{section}
\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6399}%
$\displaystyle \DP{\pi}{t}   + \frac{u}{a \cos \varphi} \DP{\pi}{\lambda}   + \frac{v}{a} \DP{\pi}{\varphi}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6400}%
$\displaystyle =   - D   - \DP{\dot{\sigma}}{\sigma}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6402}%
$\displaystyle \DP{\Phi}{\sigma} = - \frac{RT_v}{\sigma}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6404}%
$\displaystyle \DP{\zeta}{t}       \ $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6405}%
$\displaystyle = \  \Dinv{a \cos \varphi}            \left\{ \DP{v_A}{\lambda} - \DP{(u_A \cos \varphi)}{\varphi} \right\}           + {\cal D}(\zeta),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6406}%
$\displaystyle \DP{D}{t}       \ $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6407}%
$\displaystyle = \  \Dinv{a \cos \varphi}            \left\{ \DP{u_A}{\lambda} + \DP{(v_A \cos \varphi)}{\varphi} \right\}           - \nabla^{2}_{\sigma}            ( \Phi + R \overline{T} \pi +$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6408}%
$\displaystyle )            + {\cal D}(D).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{alignstar6410}%
\begin{align*}\begin{split}   \DP{T}{t}     \  &= \            - \Dinv{a \cos \varphi}              \left\{  \DP{(u T^{\prime})}{\lambda}                     + \DP{(v T^{\prime} \cos \varphi)}{\varphi}              \right\}           + T^{\prime} D \\\  & \  \quad        - \dot{\sigma}                \DP{T}{\sigma}        + \kappa T_v            \left(                    \DP{\pi}{t}                  + \frac{u}{a \cos \varphi} \DP{\pi}{\lambda}                  + \frac{v}{a} \DP{\pi}{\varphi}                  + \frac{ \dot{\sigma} }{ \sigma }             \right)        + \frac{Q}{C_p}        + {\cal D}(T)         + {\cal D}^{\prime}(\Dvect{v}).  \end{split}\end{align*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{alignstar6412}%
\begin{align*}\begin{split}  \DP{q}{t}     \  &= \            - \Dinv{a \cos \varphi}              \left\{  \DP{(u q)}{\lambda}                     + \DP{(v q \cos \varphi)}{\varphi}              \right\}           + q D  \\\  & \quad           - \dot{\sigma} \DP{q}{\sigma}           + S_{q}           + {\cal D}(q).  \end{split}\end{align*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6413}%
$\displaystyle \varphi$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6414}%
$\displaystyle : \quad °ÞÅÙ [\mathrm{deg.}],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6415}%
$\displaystyle \lambda$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6416}%
$\displaystyle : \quad ·ÐÅÙ [\mathrm{deg.}],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6417}%
$\displaystyle \sigma$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6418}%
$\displaystyle \equiv p/p_s,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6419}%
$\displaystyle t$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6420}%
$\displaystyle : \quad »þ´Ö [\mathrm{s}].$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6422}%
$ p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6424}%
$ p_s$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6425}%
$\displaystyle \pi\  (\varphi, \lambda)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6426}%
$\displaystyle \equiv \ln p_s,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6427}%
$\displaystyle T\  (\varphi, \lambda, \sigma)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6428}%
$\displaystyle : \quad µ¤²¹ [\mathrm{K}],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6429}%
$\displaystyle q\  (\varphi, \lambda, \sigma)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6430}%
$\displaystyle : \quad Èæ¼¾ [\mathrm{kg}\  \mathrm{kg}^{-1}],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6431}%
$\displaystyle \zeta\  (\varphi, \lambda, \sigma)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6432}%
$\displaystyle \equiv \Dinv{a \cos \varphi}                         \left\{   \DP{v}{\lambda}                                 - \DP{(u \cos \varphi)}{\varphi} \right\}                       : \quad ±²ÅÙ [\mathrm{s}^{-1}],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6433}%
$\displaystyle D\  (\varphi, \lambda, \sigma)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6434}%
$\displaystyle \equiv  \Dinv{a \cos \varphi}                         \left\{   \DP{u}{\lambda}                                 + \DP{(v \cos \varphi)}{\varphi} \right\}                       : \quad È¯»¶ [\mathrm{s}^{-1}].$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6436}%
$ u$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6438}%
$ v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6440}%
$ (\varphi, \lambda, \sigma)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6441}%
$\displaystyle \Phi$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6442}%
$\displaystyle \equiv gz                       : \quad ¥¸¥ª¥Ý¥Æ¥ó¥·¥ã¥ë¹âÅÙ                               [\mathrm{m}^{2}\   \mathrm{s}^{-2}],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6443}%
$\displaystyle \dot{\sigma}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6444}%
$\displaystyle \equiv \DD{\sigma}{t}                       \  \equiv \                            \DP{\sigma}{t}                        + \frac{u}{a \cos \varphi} \DP{\sigma}{\lambda}                        + \frac{v}{a} \DP{\sigma}{\varphi}                        + \DP{\sigma}{\sigma},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6445}%
$\displaystyle \overline{T}\  (\sigma)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6446}%
$\displaystyle : \quad ¿åÊ¿Ê¿¶Ñµ¤²¹ [\mathrm{K}],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6447}%
$\displaystyle T^{\prime}\  (\varphi, \lambda, \sigma)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6448}%
$\displaystyle \equiv T - \overline{T},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6449}%
$\displaystyle T_v\  (\varphi, \lambda, \sigma)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6450}%
$\displaystyle \equiv T                           \left\{                             1 + \left(\epsilon_v^{-1} - 1\right) q                           \right\},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6451}%
$\displaystyle T_v^{\prime}\  (\varphi, \lambda, \sigma)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6452}%
$\displaystyle \equiv T_v - \overline{T},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6453}%
$\displaystyle u_A\  (\varphi, \lambda, \sigma)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6454}%
$\displaystyle \equiv                           ( \zeta + f ) v                          - \dot{\sigma} \DP{u}{\sigma}                          - \frac{R T_v^{\prime}}{a \cos \varphi} \DP{\pi}{\lambda}                          + {\cal F}_{\lambda},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6455}%
$\displaystyle v_A\  (\varphi, \lambda, \sigma)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6456}%
$\displaystyle \equiv                         - ( \zeta + f ) u                          - \dot{\sigma} \DP{v}{\sigma}                          - \frac{R T_v^{\prime}}{a} \DP{\pi}{\varphi}                          + {\cal F}_{\varphi},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6457}%
$\displaystyle \nabla^{2}_{\sigma}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6458}%
$\displaystyle \equiv                 \frac{1}{a^{2} \cos^2 \varphi} \DP[2]{}{\lambda}               + \frac{1}{a^{2} \cos \varphi}                 \DP{}{\varphi}                   \left( \cos \varphi \DP{}{\varphi} \right),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6459}%
$\displaystyle \  (\varphi, \lambda, \sigma)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6460}%
$\displaystyle \equiv  \frac{u^{2}+v^{2}}{2 }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6461}%
$\displaystyle {\cal D}(\zeta)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6462}%
$\displaystyle : \qquad ±²ÅÙ¿åÊ¿³È»¶,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6463}%
$\displaystyle {\cal D}(D)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6464}%
$\displaystyle : \qquad È¯»¶¿åÊ¿³È»¶,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6465}%
$\displaystyle {\cal D}(T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6466}%
$\displaystyle : \qquad ²¹ÅÙ¿åÊ¿³È»¶,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6467}%
$\displaystyle {\cal D}(q)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6468}%
$\displaystyle : \qquad Èæ¼¾¿åÊ¿³È»¶,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6469}%
$\displaystyle {\cal F}_\lambda \  (\varphi, \lambda, \sigma)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6470}%
$\displaystyle : \qquad ¾®µ¬ÌÏ±¿Æ°²áÄø (·ÐÅÙÊý¸þ),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6471}%
$\displaystyle {\cal F}_\varphi \  (\varphi, \lambda, \sigma)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6472}%
$\displaystyle : \qquad ¾®µ¬ÌÏ±¿Æ°²áÄø (°ÞÅÙÊý¸þ),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6473}%
$\displaystyle Q \  (\varphi, \lambda, \sigma)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6474}%
$\displaystyle : \qquad Êü¼Í, ¶Å·ë, ¾®µ¬ÌÏ±¿Æ°²áÄøÅù¤Ë¤è¤ë²ÃÇ®¡¦²¹ÅÙÊÑ²½,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6475}%
$\displaystyle S_q \  (\varphi, \lambda, \sigma)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6476}%
$\displaystyle : \qquad ¶Å·ë, ¾®µ¬ÌÏ±¿Æ°²áÄøÅù¤Ë¤è¤ë¿å¾øµ¤¥½¡¼¥¹,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6477}%
$\displaystyle {\cal D}' \  (\Dvect{v})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6478}%
$\displaystyle : \qquad Ëà»¤Ç®.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6479}%
$\displaystyle a$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6480}%
$\displaystyle : \quad ÏÇÀ±È¾·Â [\mathrm{m}],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6481}%
$\displaystyle R$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6482}%
$\displaystyle : \quad ´¥ÁçÂçµ¤¤Îµ¤ÂÎÄê¿ô [\mathrm{J\   kg}^{-1}\   \mathrm{K}^{-1}],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6483}%
$\displaystyle C_p$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6484}%
$\displaystyle : \quad ´¥ÁçÂçµ¤¤ÎÂçµ¤Äê°µÈæÇ® [\mathrm{J\  kg}^{-1}\  \mathrm{K}^{-1}],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6485}%
$\displaystyle f$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6486}%
$\displaystyle : \quad ¥³¥ê¥ª¥ê¥Ñ¥é¥á¡¼¥¿ [\mathrm{s}^{-1}],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6487}%
$\displaystyle \kappa$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6488}%
$\displaystyle \equiv R/C_p,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6489}%
$\displaystyle \epsilon_v$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6490}%
$\displaystyle : \quad ¿å¾øµ¤Ê¬»ÒÎÌÈæ.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6492}%
$\displaystyle \dot{\sigma} = 0  \  \ \  at \  \ \sigma = 0 , \  1 .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6496}%
$ \dot{\sigma}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6497}%
$\displaystyle \DP{\pi}{t}    = - \int_{0}^{1} \Dvect{v}_{H} \cdot \nabla_{\sigma} \pi d \sigma      - \int_{0}^{1} D  d \sigma ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6498}%
$\displaystyle \dot{\sigma}     = - \sigma       \DP{\pi}{t}      - \int_{0}^{\sigma} D d \sigma      - \int_{0}^{\sigma}           \Dvect{v}_{H} \cdot \nabla_{\sigma} \pi d \sigma ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6501}%
$ \nabla^{N_D}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6503}%
$\displaystyle {\cal D}(\zeta) = - K_{HD}                        \left[ (-1)^{N_D/2} \nabla^{N_D}                               - \left( \frac{2}{a^2} \right)^{N_D/2}                        \right]                     \zeta ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6505}%
$\displaystyle {\cal D}(D) = - K_{HD}                        \left[ (-1)^{N_D/2} \nabla^{N_D}                               - \left( \frac{2}{a^2} \right)^{N_D/2}                        \right]                     D ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6507}%
$\displaystyle {\cal D}(T) = - (-1)^{N_D/2} K_{HD} \nabla^{N_D} T ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6509}%
$\displaystyle {\cal D}(q) = - (-1)^{N_D/2} K_{HD} \nabla^{N_D} q .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6511}%
$ N_D$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6513}%
$ \sim$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6516}%
$\displaystyle \DP{\pi}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6517}%
$\displaystyle = - \sum_{k=1}^{K} ( D_k + \Dvect{v}_k \cdot \nabla \pi )         \Delta  \sigma_k,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6518}%
$\displaystyle \dot{\sigma}_{k-1/2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6519}%
$\displaystyle = - \sigma_{k-1/2} \DP{\pi}{t}    - \sum_{l=k}^{K} ( D_l + \Dvect{v}_l \cdot \nabla \pi )                  \Delta  \sigma_l,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6520}%
$\displaystyle \dot{\sigma}_{1/2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6521}%
$\displaystyle = \dot{\sigma}_{K+1/2} = 0.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6522}%
$\displaystyle \Dvect{v} \cdot \nabla \pi =   \frac{u}{a \cos \varphi} \DP{\pi}{\lambda}   + \frac{v}{a} \DP{\pi}{\varphi}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{alignstar6524}%
\begin{align*}\begin{split}   \Phi_{1} & = \Phi_{s} + C_{p} ( \sigma_{1}^{-\kappa} - 1  ) T_{v,1} \\& = \Phi_{s} + C_{p} \alpha_{1} T_{v,1}.  \end{split}\end{align*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{alignstar6525}%
\begin{align*}\begin{split}   \Phi_k - \Phi_{k-1}      & = C_{p}       \left[ \left( \frac{ \sigma_{k-1/2} }{ \sigma_k } \right)^{\kappa}              - 1       \right] T_{v,k}        + C_{p}       \left[ 1-           \left( \frac{ \sigma_{k-1/2} }{ \sigma_{k-1} } \right)^{\kappa}       \right] T_{v,k-1} \\& = C_{p} \alpha_k T_{v,k} + C_{p} \beta_{k-1} T_{v,k-1}.  \end{split}\end{align*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6526}%
$\displaystyle \alpha_k$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6527}%
$\displaystyle = \left( \frac{ \sigma_{k-1/2} }                                { \sigma_k } \right)^{\kappa} -1 ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6528}%
$\displaystyle \beta_k$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6529}%
$\displaystyle = 1- \left( \frac{ \sigma_{k+1/2} }                                { \sigma_k } \right)^{\kappa} .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6531}%
$\displaystyle \DP{\zeta_k}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6532}%
$\displaystyle =   \Dinv{a \cos \varphi}           \left\{               \DP{{v_A}_{,k}}{\lambda}             - \DP{({u_A}_{,k} \cos \varphi)}{\varphi}           \right\}         + {\cal D}(\zeta_k),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6534}%
$\displaystyle =   \Dinv{a \cos \varphi}           \left\{               \DP{{u_A}_{,k}}{\lambda}             + \DP{({v_A}_{,k} \cos \varphi)}{\varphi}           \right\}         - \nabla^{2}_{\sigma}          ( \Phi_k + C_{p} \hat{\kappa}_k \overline{T}_k \pi             + ($%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6535}%
$\displaystyle )_k )         + {\cal D}(D_k).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{alignstar6536}%
\begin{align*}\begin{split}   {u_A}_{,k}     & =   ( \zeta_k + f ) v_k          - \frac{1}{2 \Delta \sigma_k}               [   \dot{\sigma}_{k-1/2} ( u_{k-1} - u_k   )                + \dot{\sigma}_{k+1/2} ( u_k     - u_{k+1} ) ] \\& \quad         - \frac{C_{p} \hat{\kappa}_k T_{v,k}^{\prime}}{a \cos \varphi}              \DP{\pi}{\lambda}          + {\cal F}_{\lambda, k},   \end{split}\end{align*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{alignstar6537}%
\begin{align*}\begin{split}   {v_A}_{,k}       & = - ( \zeta_k + f ) u_k          - \frac{1}{2 \Delta \sigma_k}               [   \dot{\sigma}_{k-1/2} ( v_{k-1} - v_k   )                + \dot{\sigma}_{k+1/2} ( v_k   - v_{k+1} ) ] \\& \quad         - \frac{C_{p} \hat{\kappa}_k T_{v,k}'}{a}               \DP{\pi}{\mu}          + {\cal F}_{\varphi, k},   \end{split}\end{align*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{alignstar6538}%
\begin{align*}\begin{split}   \hat{\kappa}_k       & = \frac{  \sigma_{k-1/2}(   \sigma^{\kappa}_{k-1/2}                                   - \sigma^{\kappa}_k      )                 + \sigma_{k+1/2}(   \sigma^{\kappa}_k                                   - \sigma^{\kappa}_{k+1/2}  ) }               { \sigma^{\kappa}_k ( \sigma_{k-1/2} - \sigma_{k+1/2} ) } \\& = \frac{ \sigma_{k-1/2} \alpha_k + \sigma_{k+1/2} \beta_k }               { \Delta \sigma_k                                  },    \end{split}\end{align*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6539}%
$\displaystyle %
T_{v,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6540}%
$\displaystyle = T_k - \overline{T}_k,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6541}%
$\displaystyle %
($%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6542}%
$\displaystyle )_k$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6543}%
$\displaystyle = \frac{v^{2}_k + v^{2}_k}{2}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{alignstar6545}%
\begin{align*}\begin{split}   \DP{T_k}{t}     & = - \Dinv{a \cos \varphi}             \left\{   \DP{(u_k T^{\prime}_k)}{\lambda}                     + \DP{(v_k T^{\prime}_k \cos \varphi)}{\varphi}             \right\}         + \hat{H}_k  \\& \quad         + \frac{Q_k}{C_{p}}         + {\cal D}(T_k)          + {\cal D}'(\Dvect{v}).  \end{split}\end{align*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{alignstar6546}%
\begin{align*}\begin{split}    \hat{H}_k      & \equiv            T_k' D_k          - \frac{1}{\Delta \sigma_k}               [   \dot{\sigma}_{k-1/2} ( \hat{T}_{k-1/2} - T_k   )                + \dot{\sigma}_{k+1/2} ( T_k   - \hat{T}_{k+1/2} ) ]                \\& \quad          + \left\{ \alpha_k                     \left[   \sigma_{k-1/2} \Dvect{v}_k \cdot \nabla \pi                            - \sum_{l=k}^{K}                                 ( D_l + \Dvect{v}_l \cdot \nabla \pi )                                  \Delta  \sigma_l                     \right]            \right.                \\& \quad          + \quad            \left. \beta_k                    \left[   \sigma_{k+1/2} \Dvect{v}_k \cdot \nabla \pi                           - \sum_{l=k+1}^{K}                                ( D_l + \Dvect{v}_l \cdot \nabla \pi )                                 \Delta  \sigma_l                    \right]            \right\}               \frac{1}{\Delta \sigma_k} T_{v,k} \\& =    T_k' D_k           - \frac{1}{\Delta \sigma_k}               [   \dot{\sigma}_{k-1/2} ( \hat{T}_{k-1/2} - T_k   )                + \dot{\sigma}_{k+1/2} ( T_k   - \hat{T}_{k+1/2} ) ]                \\& \quad          + \hat{\kappa}_k \Dvect{v}_k \cdot \nabla \pi T_{v,k}                 \\& \quad          - \alpha_k \sum_{l=k}^{K}                        ( D_l + \Dvect{v}_l \cdot \nabla \pi )                         \Delta  \sigma_l                            \frac{T_{v,k}}{\Delta \sigma_k}                 \\& \quad          - \beta_k \sum_{l=k+1}^{K}                       ( D_l + \Dvect{v}_l \cdot \nabla \pi )                        \Delta  \sigma_l                           \frac{T_{v,k}}{\Delta \sigma_k},   \end{split}\end{align*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{alignstar6547}%
\begin{align*}\begin{split}   \hat{T}_{k-1/2}     & = \frac{           \left[             \left( \displaystyle                 \frac{ \sigma_{k-1/2} }{ \sigma_k } \right)^{\kappa}               - 1             \right] \sigma_{k-1}^{\kappa} T_k          + \left[               1             - \left( \displaystyle                   \frac{ \sigma_{k-1/2} }{ \sigma_{k-1} }               \right)^{\kappa}           \right] \sigma_k^{\kappa} T_{k-1}                   }         { \sigma_{k-1}^{\kappa} - \sigma_k^{\kappa}           }         \\& = a_k T_k + b_{k-1} T_{k-1},   \end{split}\end{align*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6548}%
$\displaystyle a_k$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6549}%
$\displaystyle = \alpha_k              \left[ 1- \left( \frac{ \sigma_k }{ \sigma_{k-1} }                         \right)^{\kappa} \right]^{-1},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6550}%
$\displaystyle b_k$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6551}%
$\displaystyle = \beta_k              \left[ \left( \frac{ \sigma_k }{ \sigma_{k+1} }                       \right)^{\kappa} - 1 \right]^{-1} .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6553}%
$\displaystyle \DP{q_k}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6554}%
$\displaystyle =   - \Dinv{a \cos \varphi}               \left\{   \DP{(u_k q_k)}{\lambda}                       + \DP{(v_k q_k \cos \varphi)}{\varphi}               \right\}           + R_k            + S_{q,k}           + {\cal D}(q_k).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6555}%
$\displaystyle R_k  =    q_k D_k           - \frac{1}{2 \Delta \sigma_k}               \left[   \dot{\sigma}_{k-1/2} ( q_{k-1} - q_k   )                     + \dot{\sigma}_{k+1/2} ( q_k   - q_{k+1} ) \right].$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6558}%
$\displaystyle \DP{\tilde{\pi}_n^m}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6559}%
$\displaystyle = - \sum_{k=1}^{K} (\tilde{D}_n^m)_k \Delta  \sigma_k         + \frac{1}{I} \sum_{i=1}^{I} \sum_{j=1}^{J}                  Z_{ij} Y_n^{m *} ( \lambda_i, \mu_j ) w_j.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6560}%
$\displaystyle Z \equiv - \sum_{k=1}^{K} \Dvect{v}_k \cdot \nabla \pi.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{alignstar6562}%
\begin{align*}\begin{split}    \DP{\tilde{\zeta}_n^m}{t}       & = \frac{1}{I} \sum_{i=1}^{I} \sum_{j=1}^{J}              im (v_A)_{ij}            Y_n^{m *} ( \lambda_i, \varphi_j )           \frac{w_j}{a \cos \varphi_j}            \\& \quad +             \frac{1}{I} \sum_{i=1}^{I} \sum_{j=1}^{J}              (u_A)_{ij} \cos \varphi_j            \DP{}{\varphi}  Y_n^{m *} ( \lambda_i, \varphi_j )            \frac{w_j}{a \cos \varphi_j}            \\& \quad +           \tilde{\cal D}_{M,n}^m \tilde{\zeta}_n^m  ,  \end{split}\end{align*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{alignstar6563}%
\begin{align*}\begin{split}    \DP{\tilde{D}_n^m}{t}       & = \frac{1}{I} \sum_{i=1}^{I} \sum_{j=1}^{J}              im (u_A)_{ij}            Y_n^{m *} ( \lambda_i, \varphi_j )           \frac{w_j}{a \cos \varphi_j}            \\& \quad -            \frac{1}{I} \sum_{i=1}^{I} \sum_{j=1}^{J}              (v_A)_{ij}            \cos \varphi_j             \DP{}{\varphi}  Y_n^{m *} ( \lambda_i, \varphi_j )            \frac{w_j}{a \cos \varphi_j}            \\& \quad -           \frac{n(n+1)}{a^{2}}            \frac{1}{I} \sum_{i=1}^{I} \sum_{j=1}^{J}              (\mbox{\sl KE})_{ij}            Y_n^{m *} ( \lambda_i, \varphi_j )            w_j           \\& \quad +            \frac{n(n+1)}{a^{2}}             ( \Phi_n^m + C_{p} \hat{\kappa}_k \bar{T}_k \pi_n^m )             +  \tilde{\cal D}_{M,n}^m \tilde{D}_n^m .  \end{split}\end{align*}%
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\lthtmlinlinemathA{tex2html_wrap_indisplay6564}%
$\displaystyle \tilde{\cal D}_{M,n}^m = - K_{HD} \left[                              \left( \frac{-n(n+1)}{a^{2}} \right)^{N_D/2}                             - \left( \frac{2}{a} \right)^{N_D}                             \right]  .$%
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\lthtmldisplayA{alignstar6566}%
\begin{align*}\begin{split}    \DP{\tilde{T}_n^m}{t}   & = - \frac{1}{I} \sum_{i=1}^{I} \sum_{j=1}^{J}            im u_{ij} T'_{ij}          Y_n^{m *} ( \lambda_i, \varphi_j )         \frac{w_j}{a \cos \varphi_j}          \\& \quad       + \frac{1}{I} \sum_{i=1}^{I} \sum_{j=1}^{J}            v_{ij} T'_{ij}          \cos \varphi_j           \DP{}{\varphi}  Y_n^{m *} ( \lambda_i, \varphi_j )          \frac{w_j}{a \cos \varphi_j}          \\& \quad       + \frac{1}{I} \sum_{i=1}^{I} \sum_{j=1}^{J}            \left( \hat{H}_{ij} + \frac{Q_{ij}}{C_{p}} \right)          Y_n^{m *} ( \lambda_i, \varphi_j )          w_j         \\& \quad       + \tilde{\cal D}_{H,n}^m \tilde{T}_n^m         \\& \quad       + \frac{1}{I} \sum_{i=1}^{I} \sum_{j=1}^{J}            {\cal D}'_{ij}(\Dvect{v})          Y_n^{m *} ( \lambda_i, \varphi_j )          w_j .  \end{split}\end{align*}%
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$\displaystyle \tilde{\cal D}_{H,n}^m     = - K_{HD} \left( \frac{-n(n+1)}{a^{2}} \right)^{N_D/2} .$%
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\lthtmldisplayA{alignstar6569}%
\begin{align*}\begin{split}    \DP{\tilde{q}_n^m}{t}   & = - \frac{1}{I} \sum_{i=1}^{I} \sum_{j=1}^{J}           im u_{ij} q_{ij}         Y_n^{m *} ( \lambda_i, \varphi_j )        \frac{w_j}{a \cos \varphi_j}         \\& \quad       + \frac{1}{I} \sum_{i=1}^{I} \sum_{j=1}^{J}           v_{ij} q_{ij}         \cos \varphi_j          \DP{}{\varphi}  Y_n^{m *} ( \lambda_i, \varphi_j )         \frac{w_j}{a \cos \varphi_j}         \\& \quad       + \frac{1}{I} \sum_{i=1}^{I} \sum_{j=1}^{J}           \left( \hat{R}_{ij} + S_{q,ij} \right)         Y_n^{m *} ( \lambda_i, \varphi_j )         w_j        \\& \quad       + \tilde{\cal D}_{H,n}^m \tilde{q}_n^m .  \end{split}\end{align*}%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6572}%
$ \Delta t$%
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\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6575}%
$ 2 \Delta t$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6577}%
$ {\cal F}_\lambda, {\cal F}_\varphi, Q, S_q$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6581}%
$ {\cal A}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6582}%
$\displaystyle \hat{\cal A}^{t+\Delta t}      =  \bar{\cal A}^{t-\Delta t}     + 2 \Delta t        \dot{\cal A}_{adv}\left( {\cal A}^{t} \right)     + 2 \Delta t        \dot{\cal A}_{dif}\left( \hat{\cal A}^{t+\Delta t} \right)     + 2 \Delta t        \dot{\cal A}_{phy}\left( \bar{\cal A}^{t-\Delta t} \right) .$%
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$ \dot{\cal A}_{adv} $%
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{\newpage\clearpage
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$ \dot{\cal A}_{dif} $%
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{\newpage\clearpage
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$ \dot{\cal A}_{phy} $%
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{\newpage\clearpage
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$ \hat{\cal A}^{t+\Delta t} $%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6592}%
$ \dot{\cal A}_{dis} $%
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{\newpage\clearpage
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$ \dot{\cal A}_{cnd} $%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6596}%
$ {\cal A}^{t+\Delta t} $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6597}%
$\displaystyle {\cal A}^{t+\Delta t}      =  \hat{\cal A}^{t+\Delta t}     + 2 \Delta t        \dot{\cal A}_{dis}\left( \hat{\cal A}^{t+\Delta t} \right)     + 2 \Delta t        \dot{\cal A}_{cnd}\left( \hat{\cal A}^{t+\Delta t} \right) .$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6598}%
$\displaystyle \bar{\cal A}^{t}     = ( 1-2 \epsilon_f ) {\cal A}^{t}     +  \epsilon_f          \left( \bar{\cal A}^{t-\Delta t} + {\cal A}^{t+\Delta t} \right)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6600}%
$ \bar{\cal A}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6602}%
$ \epsilon_f$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6605}%
$ T=\overline{T}_k$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6607}%
$ \Dvect{D}=\{ D_{k} \}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6609}%
$ \Dvect{T}=\{ T_{k} \}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6610}%
$\displaystyle \DP{\pi}{t} =           \left( \frac{\partial \pi}{\partial t} \right)_{\rm NG}      - \Dvect{C} \cdot \Dvect{D}  ,$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6611}%
$\displaystyle \frac{\partial \Dvect{D}}{\partial t} =            \left( \DP{\Dvect{D}}{t} \right)_{\rm NG}             - \nabla^{2}_{\sigma} ( \Dvect{\Phi}_{S}                                    + \underline{W} \Dvect{T}                                   + \Dvect{G} \pi )             + {\cal D}_M \Dvect{D} ,$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6612}%
$\displaystyle \DP{\Dvect{T}}{t}$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6613}%
$\displaystyle =   \left( \DP{\Dvect{T}}{t}       \right)_{\rm NG}            - \underline{h} \Dvect{D}          + {\cal D}_H \Dvect{T} .$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6614}%
$\displaystyle \left( \DP{\pi}{t} \right)^{\rm NG}    =   - \sum_{k=1}^{K} \Dvect{v}_{k} \cdot \nabla \pi          \Delta  \sigma_{k}     =   Z_{k} ,$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6615}%
$\displaystyle \dot{\sigma}^{\rm NG}_{k-1/2}  = - \sigma_{k-1/2} \left( \DP{\pi}{t} \right)^{\rm NG}    - \sum_{l=k}^{K} \Dvect{v}_{l} \cdot \nabla \pi        \Delta  \sigma_{l} ,$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6616}%
$\displaystyle \left( \DP{D}{t} \right)^{\rm NG}    =             \Dinv{a \cos \varphi}             \left\{                 \DP{{u_A}_{,k}}{\lambda}               + \DP{({v_A}_{,k} \cos \varphi)}{\varphi}             \right\}           - \nabla^{2}_{\sigma} ($%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6617}%
$\displaystyle )_{k}            - \nabla^{2}_{\sigma} \sum_{k=1}^{K} W_{kl} ( T_{v,l}-T_{l} )           + {\cal D}(D_{k}) ,$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6618}%
$\displaystyle \left( \DP{T_{k}}{t} \right)^{\rm NG}        =   - \frac{1}{a(1-\mu^{2})}                 \DP{U_k T'_k}{\lambda}           - \frac{1}{a}                \DP{V_k T'_k}{\mu}           + H_{k}            + {\cal D}(T_{k})            + {\cal D}^{\prime}(\Dvect{v}) ,$%
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{\newpage\clearpage
\lthtmldisplayA{alignstar6619}%
\begin{align*}\begin{split}   H_k & =     T_{k}^{\prime} D_{k}  \\& \quad            - \frac{1}{\Delta \sigma_{k}}               [   \dot{\sigma}_{k-1/2} ( \hat{T^{\prime}}_{k-1/2}                                           - T^{\prime}_{k}   )                + \dot{\sigma}_{k+1/2} ( T^{\prime}_{k}                                            - \hat{T^{\prime}}_{k+1/2} ) ]                 \\& \quad            - \frac{1}{\Delta \sigma_{k}}               [   \dot{\sigma}^{\rm NG}_{k-1/2} ( \hat{\overline{T}}_{k-1/2}                                           - \overline{T}_{k}   )                + \dot{\sigma}^{\rm NG}_{k+1/2} ( \overline{T}_{k}                                            - \hat{\overline{T}}_{k+1/2} ) ]                 \\& \quad            + \hat{\kappa}_{k} T_{v,k} \Dvect{v}_{k} \cdot \nabla \pi                 \\& \quad            - \frac{\alpha_{k}}{\Delta \sigma_{k} } T_{v,k}              \sum_{l=k}^{K} \Dvect{v}_{l} \cdot \nabla \pi                 \Delta \sigma_{l}            - \frac{\beta_{k}}{\Delta \sigma_{k} } T_{v,k}              \sum_{l=k+1}^{K} \Dvect{v}_{l} \cdot \nabla \pi                 \Delta \sigma_{l}                 \\& \quad            - \frac{\alpha_{k}}{\Delta \sigma_{k} } T'_{v,k}              \sum_{l=k}^{K} D_l  \Delta \sigma_{l}            - \frac{\beta_{k}}{\Delta \sigma_{k} } T'_{v,k}              \sum_{l=k+1}^{K} D_l  \Delta \sigma_{l} .  \end{split}\end{align*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6620}%
$\displaystyle C_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6621}%
$\displaystyle = \Delta \sigma_{k} ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6622}%
$\displaystyle W_{kl}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6623}%
$\displaystyle = C_{p} \alpha_{l} \delta_{k \geq l}           + C_{p} \beta_{l} \delta_{k-1 \geq l} ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6624}%
$\displaystyle G_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6625}%
$\displaystyle = \hat{\kappa}_{k} C_{p} \overline{T}_{k} ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6626}%
$\displaystyle \underline{h}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6627}%
$\displaystyle = \underline{Q}\underline{S} - \underline{R} ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6628}%
$\displaystyle Q_{kl}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6629}%
$\displaystyle =            \frac{1}{\Delta \sigma_{k}}               ( \hat{\overline{T}}_{k-1/2} - \overline{T}_{k} ) \delta_{k=l}           + \frac{1}{\Delta \sigma_{k}}               ( \overline{T}_{k} - \hat{\overline{T}}_{k+1/2}  )  \delta_{k+1=l}  ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6630}%
$\displaystyle S_{kl}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6631}%
$\displaystyle =  \sigma_{k-1/2} \Delta \sigma_{l}             - \Delta \sigma_{l} \delta_{k \leq l }  ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6632}%
$\displaystyle R_{kl}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6633}%
$\displaystyle = - \left(  \frac{ \alpha_{k} }{ \Delta \sigma_{k} }                        \Delta \sigma_{l} \delta_{k \leq l}                      + \frac{ \beta_{k} }{ \Delta \sigma_{k} }                        \Delta \sigma_{l} \delta_{k+1 \leq l}                 \right) \overline{T}_{k} .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6635}%
$ \delta_{k \leq l}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6637}%
$ k \leq l$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6638}%
$\displaystyle \delta_{t} {\cal A}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6639}%
$\displaystyle \equiv         \frac{1}{2 \Delta t}            \left( {\cal A}^{t+\Delta t} - {\cal A}^{t-\Delta t} \right) ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6640}%
$\displaystyle \overline{\cal A}^{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6641}%
$\displaystyle \equiv \frac{1}{2} \left(   {\cal A}^{t+\Delta t}                                   + {\cal A}^{t-\Delta t} \right)       =      {\cal A}^{t-\Delta t} + \delta_{t} {\cal A} \Delta t .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6642}%
$\displaystyle \delta_{t} \pi =           \left( \DP{\pi}{t} \right)_{\rm NG}        - \Dvect{C} \cdot \overline{ \Dvect{D} }^{t} ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6643}%
$\displaystyle \delta_{t} \Dvect{D} =           \left( \DP{\Dvect{D}}{t} \right)_{\rm NG}             - \nabla^{2}_{\sigma} ( \Dvect{\Phi}_{S}                                    + \underline{W}                                       \overline{ \Dvect{T} }^{t}                                   + \Dvect{G}                                   \overline{\pi}^{t} )            + {\cal D}_M ( \Dvect{D}^{t-\Delta t}                           + 2 \Delta t \delta_{t} \Dvect{D} ) ,$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6644}%
$\displaystyle \delta_{t} \Dvect{T} =         \left( \DP{\Dvect{T}}{t} \right)_{\rm NG}            - \underline{h} \overline{ \Dvect{D} }^{t}           + {\cal D}_H ( \Dvect{T}^{t-\Delta t}                         + 2 \Delta t \delta_{t} \Dvect{T} ) .$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{alignstar6645}%
\begin{align*}\begin{split}  &   \left\{   ( 1-2\Delta t {\cal D}_H )( 1-2\Delta t {\cal D}_M )                  \underline{I}                - ( \Delta t )^{2}                  (   \underline{W} \  \underline{h}                     + \Dvect{G} \Dvect{C}^{T} ) \nabla^{2}_{\sigma}      \right\}       \overline{ \Dvect{D} }^{t}         \\& \qquad      =   ( 1-2\Delta t {\cal D}_H )( 1-\Delta t {\cal D}_M )             \Dvect{D}^{t-\Delta t}        + ( 1-2\Delta t {\cal D}_H ) \Delta t             \left( \DP{\Dvect{D}}{t} \right)_{\rm NG}     \\& \qquad \quad        -  \Delta t \nabla^{2}_{\sigma}                         \left\{ \quad                             ( 1-2\Delta t {\cal D}_H ) \Dvect{\Phi}_{S}                            + \underline{W}                              \left[ ( 1-2\Delta t {\cal D}_H )                                      \Dvect{T}^{t-\Delta t}                                   + \Delta t                                        \left( \DP{\Dvect{T}}{t}                                            \right)_{\rm NG} \right]                    \right.   \\& \qquad                    \left.  \hspace*{20mm}                            + ( 1-2\Delta t {\cal D}_H ) \Dvect{G}                              \left[ \pi^{t-\Delta t}                                    + \Delta t                                      \left( \DP{\pi}{t} \right)_{\rm NG}                               \right]                    \right\} .   \end{split}\end{align*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6646}%
$\displaystyle \nabla^{2}_{\sigma} = - \frac{n(n+1)}{a^{2}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6648}%
$ \overline{ \Dvect{D}_n^m }^{t}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6649}%
$\displaystyle D^{t+\Delta t} = 2\overline{ \Dvect{D} }^{t} - D^{t-\Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6651}%
$ t+\Delta t$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{chapter}
\stepcounter{section}
\stepcounter{section}
\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6669}%
$ S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6670}%
$\displaystyle \DD{S}{z} < 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6671}%
$\displaystyle \DP{T}{z} - \frac{RT}{C_p p} \DP{p}{z} + \frac{L}{C_p} \DP{q^*}{z} < 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6675}%
$ L$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6677}%
$ q^{*}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6682}%
$ (\hat{q}, \hat{T})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6684}%
$ (q, T)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6685}%
$\displaystyle q_{k-1}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6686}%
$\displaystyle = q^* (T_{k-1}, p_{k-1}),$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6687}%
$\displaystyle q_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6688}%
$\displaystyle = q^{*} (T_{k}, p_{k}),$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6689}%
$\displaystyle T_{k-1} - T_{k}     + \frac{L}{C_p}         \left\{ q^{*} (T_{k-1}, p_{k-1})  - q^{*} (T_{k}, p_{k}) \right\}    - \frac{R}{C_p} \frac{\Delta p_{k-1/2}}{p_{k-1/2}}        \frac{T_{k-1} + T_{k}}{2}  = 0,$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6690}%
$\displaystyle (C_p T_{k} + L q_{k}) \Delta p_{k}   + (C_p T_{k-1} + L q_{k-1}) \Delta p_{k-1} =   (C_p \hat{T}_{k} + L \hat{q}_{k}) \Delta p_{k}   + (C_p \hat{T}_{k-1} + L \hat{q}_{k-1}) \Delta p_{k-1}.$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6692}%
$ q_{k}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6694}%
$ q_{k-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6696}%
$ q \ll 1$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6698}%
$\displaystyle = q^{*} (\hat{T}_{k},p_{k})    + \left. \DP{q^{*}}{T} \right|_{\hat{T}_{k}}     \Delta T_{k},$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6700}%
$\displaystyle = q^{*} (\hat{T}_{k-1},p_{k-1})    + \left. \DP{q^{*}}{T} \right|_{\hat{T}_{k-1}}     \Delta T_{k-1}.$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6701}%
$\displaystyle \Delta T_{k}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6702}%
$\displaystyle = T_{k}   - \hat{T}_{k}   ,$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6703}%
$\displaystyle \Delta T_{k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6704}%
$\displaystyle = T_{k-1} - \hat{T}_{k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6706}%
$ \Delta T_{k-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6709}%
$\displaystyle (C_p T_{k-1} + L q_{k-1}) \Delta p_{k-1}     - (C_p \hat{T}_{k-1} + L \hat{q}_{k-1}) \Delta p_{k-1}$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6710}%
$\displaystyle = - (C_p T_{k} + L q_{k}) \Delta p_{k}     + (C_p \hat{T}_{k} + L \hat{q}_{k}) \Delta p_{k},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6711}%
$\displaystyle \left\{ \Delta T_{k-1}        + \frac{L}{C_p} (q_{k-1} - \hat{q}_{k-1} ) \right\}     \Delta p_{k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6712}%
$\displaystyle = - \left\{ \Delta T_{k} + \frac{L}{C_p} (q_{k} - \hat{q}_{k}) \right\}     \Delta p_{k},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6713}%
$\displaystyle \left[   \Delta T_{k-1}             + \frac{L}{C_p}               \left\{   q^{*} (\hat{T}_{k-1} )                       + \left. \DP{q^{*}}{T} \right|_{k-1}                        \Delta T_{k-1}                      - \hat{q}_{k-1}                         \right\}     \right] \Delta p_{k-1} \hspace{-7em}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6714}%
$\displaystyle \hspace{-7em}     = - \left[   \Delta T_{k}             + \frac{L}{C_p}               \left\{   q^{*} (T_{k})                       + \left. \DP{q^{*}}{T} \right|_{k}                        \Delta T_{k}                      - \hat{q}_{k}              \right\}     \right] \Delta p_{k},$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6715}%
$\displaystyle \left\{  1+                      \frac{L}{C_p}   \left. \DP{q^{*}}{T} \right|_{k-1}        \right\}         \Delta T_{k-1} \Delta p_{k-1}      + \frac{L}{C_p}               \left\{   q^{*} (\hat{T}_{k-1} )                       - \hat{q}_{k-1}                         \right\}        \Delta p_{k-1}       \hspace{-7em}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6716}%
$\displaystyle \hspace{-7em}    = - \left[   1            + \frac{L}{C_p}               \left. \DP{q^{*}}{T} \right|_{k}        \right] \Delta T_{k}  \Delta p_{k}      - \frac{L}{C_p}        \left\{  q^{*} (\hat{T}_{k})                       - \hat{q}_{k}        \right\}        \Delta p_{k}$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6717}%
$\displaystyle \gamma_{k} \equiv \frac{L}{C_p} \left. \DP{q^{*}}{T} \right|_{k}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6718}%
$\displaystyle \left\{  1 + \gamma_{k-1} \right\}      \Delta T_{k-1} \Delta p_{k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6719}%
$\displaystyle \hspace{3em} =       - \left(  1            + \gamma_{k}        \right) \Delta T_{k}  \Delta p_{k}      + \frac{L}{C_p}         \left[            \left\{ \hat{q}_{k-1} - q^{*} (\hat{T}_{k-1} ) \right\}             \Delta p_{k-1}          + \left\{ \hat{q}_{k} - q^{*} (\hat{T}_{k}) \right\}            \Delta p_{k}        \right]$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6720}%
$\displaystyle \Delta \hat{Q} \equiv             \left\{ \hat{q}_{k-1} - q^{*} (\hat{T}_{k-1} ) \right\}             \Delta p_{k-1}          + \left\{ \hat{q}_{k} - q^{*} (\hat{T}_{k}) \right\}            \Delta p_{k}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6724}%
$\displaystyle =       - \left(  1            + \gamma_{k}        \right) \Delta T_{k}  \Delta p_{k}      + \frac{L}{C_p} \Delta \hat{Q},$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6726}%
$\displaystyle =       - \frac{ 1 + \gamma_{k} }{ 1 + \gamma_{k-1}}        \frac{\Delta p_{k}}{\Delta p_{k-1}}        \Delta T_{k}      + \frac{1}{ 1 + \gamma_{k-1}}        \frac{L}{C_p} \Delta \hat{Q} \frac{1}{\Delta p_{k-1}}$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6728}%
$ \Delta T_{k}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6732}%
$\displaystyle \hat{T}_{k-1} + \Delta T_{k-1}   - \left( \hat{T}_{k}  + \Delta T_{k} \right)  + \frac{L}{C_p}    \left\{   q^{*} (\hat{T}_{k-1})              + \left. \DP{q^{*}}{T} \right|_{k-1} \Delta T_{k-1}            - q^{*} (\hat{T}_{k})              - \left. \DP{q^{*}}{T} \right|_{k} \Delta T_{k}     \right\}$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6733}%
$\displaystyle \qquad  - \frac{R}{C_p}    \frac{\Delta p_{k-1/2}}{p_{k-1/2}}    \frac{\hat{T}_{k-1} + \Delta T_{k-1} + \hat{T}_{k} + \Delta T_{k}}{2} = 0,$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6734}%
$\displaystyle \hat{T}_{k-1} - \hat{T}_{k}  + \frac{L}{C_p}    \left\{   q^{*} (\hat{T}_{k-1})              - q^{*} (\hat{T}_{k})       \right\}  - \frac{R}{C_p}    \frac{\Delta p_{k-1/2}}{p_{k-1/2}}    \frac{\hat{T}_{k-1} + \hat{T}_{k} }{2}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6735}%
$\displaystyle \qquad  + \Delta T_{k-1} - \Delta T_{k}  +  \frac{L}{C_p} \left. \DP{q^{*}}{T} \right|_{k-1} \Delta T_{k-1}  - \frac{L}{C_p} \left. \DP{q^{*}}{T} \right|_{k} \Delta T_{k}  - \frac{R}{C_p}    \frac{\Delta p_{k-1/2}}{p_{k-1/2}}    \frac{\Delta T_{k-1} + \Delta T_{k}}{2} = 0.$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6736}%
$\displaystyle S_{k-1/2} \equiv     \hat{T}_{k-1} - \hat{T}_{k}  + \frac{L}{C_p}    \left\{   q^{*} (\hat{T}_{k-1})              - q^{*} (\hat{T}_{k})       \right\}  - \frac{R}{C_p}    \frac{\Delta p_{k-1/2}}{p_{k-1/2}}    \frac{\hat{T}_{k-1} + \hat{T}_{k} }{2}$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6737}%
$\displaystyle S_{k-1/2} > 0$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6738}%
$\displaystyle \Delta T_{k-1} - \Delta T_{k}  + \gamma_{k-1} \Delta T_{k-1}  - \gamma_{k} \Delta T_{k}  - \frac{R}{C_p}    \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}    \Delta T_{k-1}   - \frac{R}{C_p}    \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}    \Delta T_{k} = - S_{k-1/2},$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6739}%
$\displaystyle \left( - 1 - \gamma_{k}            - \frac{R}{C_p}            \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}   \right)   \Delta T_{k}  + \left(        1 + \gamma_{k-1}      - \frac{R}{C_p}        \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}    \right)    \Delta T_{k-1}  = - S_{k-1/2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6740}%
$\displaystyle \left( - 1 - \gamma_{k}            - \frac{R}{C_p}            \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}   \right)   \Delta T_{k}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6741}%
$\displaystyle \hspace{2em}  + \left(        1 + \gamma_{k-1}      - \frac{R}{C_p}        \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}    \right) \left(       - \frac{ 1 + \gamma_{k} }{ 1 + \gamma_{k-1}}        \frac{\Delta p_{k}}{\Delta p_{k-1}}        \Delta T_{k}      + \frac{1}{ 1 + \gamma_{k-1}}        \frac{L}{C_p} \Delta \hat{Q} \frac{1}{\Delta p_{k-1}} \right)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6742}%
$\displaystyle \hspace{4em} = - S_{k-1/2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6744}%
$ \kappa = R/C_p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6748}%
$ \kappa$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6749}%
$\displaystyle \left( - 1 - \gamma_{k}            - \kappa            \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}   \right)   \Delta T_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6750}%
$\displaystyle \hspace{2em}  + \left(        1 + \gamma_{k-1}      - \kappa        \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}    \right) \left(       - \frac{ 1 + \gamma_{k} }{ 1 + \gamma_{k-1}}        \frac{\Delta p_{k}}{\Delta p_{k-1}}        \Delta T_{k}      + \frac{1}{ 1 + \gamma_{k-1}}        \frac{L}{C_p} \Delta \hat{Q} \frac{1}{\Delta p_{k-1}} \right)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6754}%
$\displaystyle \left[       \left( - 1 - \gamma_{k}  \right)          - \kappa            \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}      +         \left(             1 + \gamma_{k-1}           - \kappa             \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}        \right)        \left( - \frac{ 1 + \gamma_{k} }{ 1 + \gamma_{k-1}}         \frac{\Delta p_{k}}{\Delta p_{k-1}}        \right)     \right]    \Delta T_{k}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6755}%
$\displaystyle \hspace{2em} = - S_{k-1/2}    - \left(             1 + \gamma_{k-1}           - \kappa             \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}        \right)        \frac{1}{ 1 + \gamma_{k-1}}        \frac{L}{C_p} \Delta \hat{Q} \frac{1}{\Delta p_{k-1}}$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6759}%
$\displaystyle = \frac{ \displaystyle   - S_{k-1/2}    - \left(             1 + \gamma_{k-1}           - \kappa             \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}        \right)        \frac{1}{ 1 + \gamma_{k-1}}        \frac{L}{C_p} \Delta \hat{Q} \frac{1}{\Delta p_{k-1}}   }{ \displaystyle       \left( - 1 - \gamma_{k}  \right)          - \kappa            \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}      +         \left(             1 + \gamma_{k-1}           - \kappa             \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}        \right)        \left( - \frac{ 1 + \gamma_{k} }{ 1 + \gamma_{k-1}}         \frac{\Delta p_{k}}{\Delta p_{k-1}}        \right)    }$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6760}%
$\displaystyle = \frac{ \displaystyle    S_{k-1/2}    + \left(             1 + \gamma_{k-1}           - \kappa             \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}        \right)        \frac{1}{ 1 + \gamma_{k-1}}        \frac{L}{C_p} \Delta \hat{Q} \frac{1}{\Delta p_{k-1}}   }{ \displaystyle        \left( 1 + \gamma_{k}  \right)      + \kappa        \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}      +         \left(             1 + \gamma_{k-1}           - \kappa             \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}        \right)        \frac{ 1 + \gamma_{k} }{ 1 + \gamma_{k-1}}         \frac{\Delta p_{k}}{\Delta p_{k-1}}   }$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6761}%
$\displaystyle = \frac{ \displaystyle     (1 + \gamma_{k-1}) \Delta p_{k-1} S_{k-1/2}    + \left(             1 + \gamma_{k-1}           - \kappa             \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}        \right)        \frac{L}{C_p} \Delta \hat{Q}    }{ \displaystyle        \left( 1 + \gamma_{k}  \right) (1 + \gamma_{k-1}) \Delta p_{k-1}      + \kappa        \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}        (1 + \gamma_{k-1}) \Delta p_{k-1}      +         \left(             1 + \gamma_{k-1}           - \kappa             \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}        \right)        (1 + \gamma_{k})        \Delta p_{k}   }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6762}%
$\displaystyle = \frac{ \displaystyle     (1 + \gamma_{k-1}) \Delta p_{k-1} S_{k-1/2}    + \left(             1 + \gamma_{k-1}           - \kappa             \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}        \right)        \frac{L}{C_p} \Delta \hat{Q}    }{ \displaystyle        \left( 1 + \gamma_{k}  \right) (1 + \gamma_{k-1})         (\Delta p_{k-1} + \Delta p_{k})      + \kappa        \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}        \left\{           (1 + \gamma_{k-1}) \Delta p_{k-1}         -  (1 + \gamma_{k}) \Delta p_{k}        \right\}   }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6765}%
$ k_B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6767}%
$ k_T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6769}%
$\displaystyle T_k = \hat{T}_k      +  \frac{L}{C_p} (1-b) I                     \frac{( T^c_k - T_k )}                         {\displaystyle \sum_{k=k_B}^{k_T}                           ( T^c_k - T_k ) \frac{\Delta p_k}{g}  }$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6771}%
$\displaystyle q_k = \bar{q}_k^{t-\Delta t}      +  b I         \frac{( q^c_k - q_k )}                         {\displaystyle \sum_{k=k_B}^{k_T}                           ( q^c_k - q_k ) \frac{\Delta p_k}{g}  }$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6775}%
$ t-\Delta t$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6779}%
$\displaystyle I = \sum_{k=k_B}^{k_T}       ( \hat{q}_k - \bar{q}_k^{t-\Delta t} ) \frac{\Delta p_k}{g}  .$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6781}%
$ T^c_k, q^c_k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6783}%
$\displaystyle b = \left\{           \begin{array}{ll}            \left( \frac{1-\langle \mbox{RH}\rangle}                        {1-\mbox{RH}_c} \right)^n              & \langle \mbox{RH}\rangle \ge \mbox{RH}_c \\1              & \langle \mbox{RH}\rangle < \mbox{RH}_c \\\end{array}      \right.$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6785}%
$ \equiv \hat{q}/q^*(\hat{T},p)$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6787}%
$\displaystyle \langle$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6788}%
$\displaystyle \rangle    = \frac{\displaystyle \sum_{k=k_B}^{k_T} \hat{q}                                             \frac{\Delta p_k}{g}  }           {\displaystyle \sum_{k=k_B}^{k_T} q^*(\hat{T},p)                                             \frac{\Delta p_k}{g}  }  .$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6792}%
$ k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6794}%
$ (T^a_k, q^a_k)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6796}%
$ k+1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6798}%
$ (T^a_{k+1}, q^a_{k+1})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6800}%
$\displaystyle T^a_{k+1} = T^a_k \left( \frac{p_{k+1}}{p_k} \right)^{\kappa}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6802}%
$\displaystyle q^a_{k+1} = q^a_k$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6804}%
$\displaystyle q^a_{k+1} > q^*( T^a_{k+1}, p_{k+1} )$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6806}%
$\displaystyle T^a_{k+1} \leftarrow         T^a_{k+1}         + \frac{L}{C_p} \frac{ q^a_{k+1} - q^*( T^a_{k+1},p_{k+1}) }                              {\displaystyle                                     1 + \frac{L}{C_p} \DP{q^*}{T} }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6808}%
$\displaystyle q^a_{k+1} \leftarrow         q^a_{k+1}        - \frac{L}{C_p} \DP{q^*}{T}                         \frac{ q^a_{k+1} - q^*( T^a_{k+1},p_{k+1}) }                              {\displaystyle                                     1 + \frac{L}{C_p} \DP{q^*}{T} } ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6810}%
$ T^a_1=\hat{T}_1, q^a_1=\hat{q}_1 $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6812}%
$ T^a_k = \hat{T}_k, q^a_k = q^*( \hat{T}_k, p_k ) $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6814}%
$ T^a_{k+1}, q^a_{k+1} $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6816}%
$\displaystyle T^a_{k+1} > \hat{T}_{k+1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6822}%
$ T^a_{k_B} = \hat{T}_{k_B}, 
q^a_{k_B} = q^*( \hat{T}_{k_B}, p_{k_B} ) $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6824}%
$ T^c_k = T^a_k, q^c_k = q^a_k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6826}%
$ q^c_k = q^*( T^c_k, p_k ) $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6830}%
$\displaystyle T^c_k < \hat{T}_k$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6832}%
$ P$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6834}%
$\displaystyle P = (1-b) I .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
\stepcounter{chapter}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6844}%
$\displaystyle \hat{q} > q^*(\hat{T},p)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6846}%
$ \hat{T}, \hat{q}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6848}%
$\displaystyle q = q^*( T,p )$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6850}%
$\displaystyle C_p T + L q = C_p \hat{T} + L \hat{q}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6852}%
$\displaystyle T = \hat{T} + \frac{L}{C_p} \frac{ \hat{q} - q^*(\hat{T},p)        }                                  {\displaystyle                                     1 + \frac{L}{C_p} \DP{q^*}{T} }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6854}%
$\displaystyle q = \hat{q} - \frac{L}{C_p} \DP{q^*}{T}                             \frac{ \hat{q} - q^*(\hat{T},p)        }                                  {\displaystyle                                     1 + \frac{L}{C_p} \DP{q^*}{T} } .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6858}%
$\displaystyle P = \frac{\Delta p}{g} ( \hat{q} - q ) .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6860}%
$ T,q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
\stepcounter{section}
\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6868}%
$ F_S^I$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6870}%
$ S_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6872}%
$ r_S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6874}%
$ \zeta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6876}%
$\displaystyle F_S^I (\lambda, \varphi)= - S_0 r_S^{-2} \cos \zeta .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6880}%
$\displaystyle \cos \zeta = \cos \varphi \cos \delta_S \cos H            + \sin \varphi \sin \delta_S$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6882}%
$ \delta_S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6884}%
$ H$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6886}%
$ \pi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6889}%
$\displaystyle \overline{F_S^I} (\varphi)   \simeq - S_0 ( A_{ins} + B_{ins} \cos^2 \varphi ) ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6891}%
$\displaystyle \overline{\cos \zeta} \simeq A_{\zeta} + B_{\zeta} \cos^2 \varphi .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6893}%
$ \mathcal{A}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6895}%
$\displaystyle \overline{F_S^I} (\varphi)   \simeq - S_0 (1 - \mathcal{A})( A_{ins} + B_{ins} \cos^2 \varphi )$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6897}%
$ \overline{\cos \zeta}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6899}%
$ \overline{\sec \zeta}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6906}%
$\displaystyle \overline{\sec \zeta} \simeq \frac{1}{A_{\zeta} + B_{\zeta} \cos^2 \varphi} .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6954}%
$ \delta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6956}%
$ \lambda_{subsolar}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6959}%
$\displaystyle H  = \lambda - \lambda_{subsolar} * \frac{180}{\pi}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6962}%
$\displaystyle \cos \zeta = \sin \varphi  \sin \delta
+ \cos \varphi \cdot \sqrt{1 - \sin^2 \delta} \cdot
\cos H$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6965}%
$\displaystyle F_S^I (\lambda, \varphi) = - S_0 (1 - \mathcal{A}) \cos \zeta$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6969}%
$ N_S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6971}%
$ F_S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6974}%
$\displaystyle F_S(z)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6976}%
$\displaystyle =$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6978}%
$\displaystyle \sum_i^{N_S} a_i
\left[
(1-\alpha_A) F_S^I
\exp \left( - \tau_{S,i}(z) \sec \zeta \right)
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6980}%
$\displaystyle \left. - \alpha_g (1-\alpha_A) F_S^I
\exp \left( - \tau_{S,i}(0) \sec \zeta \right)
\exp \left( - ( \tau_{S,i}(0)-\tau_i(z) ) \sec \zeta_0 \right)
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6986}%
$ \zeta_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6988}%
$ \sec \zeta_0 = 1.66$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6990}%
$ \alpha_A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6992}%
$ \alpha_g$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6994}%
$ \tau_{S,i}(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6996}%
$\displaystyle \tau_{S,i}(z) = \int_z^\infty k_{S,i} \rho q dz            + \int_z^\infty \bar{k}_{S,i} \rho dz$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6998}%
$ k_{S,i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7000}%
$ i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7002}%
$ \bar{k}_{S,i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7006}%
$ z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7008}%
$ a_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7012}%
$\displaystyle F_S(0) = \sum_i^{N_S} a_i           (1-\alpha_g) (1-\alpha_A) F_S^I            \exp ( - \tau_{S,i}(0)\sec \zeta ) ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7015}%
$ N_R$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7017}%
$ F_R$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7019}%
$\displaystyle F_R(z) =   \left( \pi B(T_g) - \pi B(T_s) \right) {\cal T}^f(z,0)           +        \pi B(T(z_T))                  {\cal T}^f(z,z_T)           - \int_0^{z_T} \DD{\pi B}{\xi} {\cal T}^f(z,\xi) d \xi$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7021}%
$ {\cal T}^f(z_1,z_2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7023}%
$ z=z_1,z_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7025}%
$ \pi B \equiv \sigma_{SB} T^4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7029}%
$\displaystyle {\cal T}^f(z_1,z_2)     = \sum_{i=1}^{N_R} b_i         \exp \left( - \delta_R | \tau_{R,i}(z_1) - \tau_{R,i}(z_2) |              \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7031}%
$ \tau_i(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7033}%
$\displaystyle \tau_{R,i}(z) = \int_z^\infty k_{R,i} \rho q dz                + \int_z^\infty \bar{k}_{R,i} \rho dz$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7035}%
$ k_{R,i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7039}%
$ \bar{k}_{R,i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7045}%
$ b_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7049}%
$ \delta_R = 1.5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
\stepcounter{chapter}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7062}%
$ q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7067}%
$ \Delta p_s$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7069}%
$ \Delta q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7072}%
$\displaystyle \Delta p_s = g \int \hat{\rho} \Delta q d \hat{z}
= -g \int \hat{\rho} \Delta q \frac{d \hat{p}}{- \hat{\rho} g}
= \int \Delta q d \hat{p}
= \hat{p_s} \int \Delta q d \sigma$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7074}%
$ \hat{p_s}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7076}%
$ \hat{\rho}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7080}%
$ F_{evap} \sim L C (q^{*} - q_s) \rho_s$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7084}%
$ \Delta q_{evap}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7087}%
$\displaystyle \frac{\Delta q_{evap}}{\Delta t}
= \frac{ F_{evap} L^{-1} \rho_s^{-1}}{\Delta z}
= \frac{ F_{evap} L^{-1} \rho_s^{-1}}{\Delta p / (\rho_s g)}
= F_{evap} \frac{g}{L \Delta p}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7090}%
$\displaystyle \Delta q_{evap}
= F_{evap} \frac{g}{L \Delta p} \Delta t$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7093}%
$\displaystyle \Delta q_{cond}
= S^{cond}_{q} \Delta t$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7095}%
$ S^{cond}_{q}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7097}%
$\displaystyle \Delta p_s = F_{evap} \frac{g}{L} \Delta t +    \hat{p_s} \int S^{cond}_{q} \Delta t d \sigma$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7104}%
$\displaystyle \hat{\rho} \hat{q} = \rho q,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7108}%
$ \hat{q}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7110}%
$ \rho$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7114}%
$\displaystyle \frac{\hat{p_{s}} \sigma}{RT} \hat{q} = \frac{p_{s} \sigma}{RT} q$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7116}%
$ p_s = \hat{p_s} + \Delta p_s$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7119}%
$\displaystyle \frac{\hat{p_{s}} \sigma}{RT} \hat{q}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7123}%
$\displaystyle \frac{(\hat{p_s} + \Delta p_s) \sigma}{RT} q,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7125}%
$\displaystyle \hat{p_{s}} \hat{q}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7129}%
$\displaystyle (\hat{p_s} + \Delta p_s) q,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7131}%
$\displaystyle q = \frac{\hat{p_s}}{\hat{p_s} + \Delta p_s} \hat{q}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7138}%
$\displaystyle T_{Bk} = \frac{T_{k+1/2} + T_{k-1/2}}{2}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7140}%
$ 1 \leq k \leq KMAX$%
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\lthtmlinlinemathA{tex2html_wrap_indisplay7146}%
$\displaystyle (T_{k} - T_{k-1}) \cdot (T_{k+1} - T_{k}) < 0$%
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\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7149}%
$ T_{k}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7151}%
$ \hat{T}_{k}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7154}%
$\displaystyle \hat{T}_{k} = T_{k} + S_{grst} (T_{Bk} - T_{k})$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7157}%
$\displaystyle \Delta T_{k} \equiv \hat{T}_{k} - T_{k} = S_{grst} (T_{Bk} - T_{k})$%
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\lthtmlinlinemathA{tex2html_wrap_indisplay7160}%
$\displaystyle \sum^{KMAX}_{k=1} c_v \Delta T_{k} \Delta p_{k}
= \sum^{KMAX}_{k=1} c_v S_{grst} (T_{Bk} - T_{k}) (p_s \Delta \sigma_{k})$%
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\lthtmlinlinemathA{tex2html_wrap_indisplay7163}%
$\displaystyle \sum^{KMAX}_{k=1} \Delta T_{k} \Delta p_{k} = 0$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7166}%
$\displaystyle \hat{T}_{k}
=   T_{k} + S_{grst} (T_{Bk} - T_{k})
- \frac{
\sum^{KMAX}_{k=1} S_{grst} (T_{Bk} - T_{k}) \Delta p_{k}
}{
\sum^{KMAX}_{k=1} \Delta p_{k}
}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7169}%
$\displaystyle \sum^{KMAX}_{k=1} \hat{T}_{k} \Delta p_{k}
=   \sum^{KMAX}_{k=1}
\left\{
S_{grst} (T_{Bk} - T_{k}) \Delta p_{k}
- \frac{
\sum^{KMAX}_{k=1} S_{grst} (T_{Bk} - T_{k}) \Delta p_{k}
}{
\sum^{KMAX}_{k=1} \Delta p_{k}
}
\Delta p_{k}
\right\}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7172}%
$\displaystyle \hat{T}_{k-1}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7176}%
$\displaystyle T_{k-1} + S_{grst} (T_{Bk-1} - T_{k-1})
- \frac{
\sum^{k+1}_{k=k-1} S_{grst} (T_{Bk} - T_{k}) \Delta p_{k}
}{
\sum^{k+1}_{k=k-1} \Delta p_{k}
},$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7178}%
$\displaystyle \hat{T}_{k}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7182}%
$\displaystyle T_{k} + S_{grst} (T_{Bk} - T_{k})
- \frac{
\sum^{k+1}_{k=k-1} S_{grst} (T_{Bk} - T_{k}) \Delta p_{k}
}{
\sum^{k+1}_{k=k-1} \Delta p_{k}
},$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7184}%
$\displaystyle \hat{T}_{k+1}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7188}%
$\displaystyle T_{k+1} + S_{grst} (T_{Bk+1} - T_{k+1})
- \frac{
\sum^{k+1}_{k=k-1} S_{grst} (T_{Bk} - T_{k}) \Delta p_{k}
}{
\sum^{k+1}_{k=k-1} \Delta p_{k}
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7190}%
$ \hat{T}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7193}%
$\displaystyle \hat{\hat{T}}_{k}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7197}%
$\displaystyle \hat{T}_{k} + S_{grst} (T_{Bk} - \hat{T}_{k})
- \frac{
\sum^{k+2}_{k=k} S_{grst} (T_{Bk} - \hat{T}_{k}) \Delta p_{k}
}{
\sum^{k+2}_{k=k} \Delta p_{k}
},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7199}%
$\displaystyle \hat{\hat{T}}_{k+1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7203}%
$\displaystyle \hat{T}_{k+1} + S_{grst} (T_{Bk+1} - \hat{T}_{k+1})
- \frac{
\sum^{k+2}_{k=k} S_{grst} (T_{Bk} - \hat{T}_{k}) \Delta p_{k}
}{
\sum^{k+2}_{k=k} \Delta p_{k}
},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7205}%
$\displaystyle \hat{T}_{k+2}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7209}%
$\displaystyle T_{k+1} + S_{grst} (T_{Bk+2} - T_{k+2})
- \frac{
\sum^{k+2}_{k=k} S_{grst} (T_{Bk} - \hat{T}_{k}) \Delta p_{k}
}{
\sum^{k+2}_{k=k} \Delta p_{k}
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7213}%
$ k+2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7215}%
$ \hat{T}_{k+2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7217}%
$ T_{k+2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7225}%
$ (k-1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7228}%
$\displaystyle (T_{k} - T_{k-1}) \cdot (T_{k+1} - T_{k}) \geq 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
\stepcounter{section}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7236}%
$\displaystyle e^{*}(T) = p^{*}_{0} \exp \left( - \frac{L}{RT} \right)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7238}%
$ p^{*}_{0} = 1.4 \times 10^{11}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7241}%
$\displaystyle q^{*}(T, p) = p^{*}_{0} \exp \left( - \frac{L}{RT} \right) \frac{1}{p}$%
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\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{chapter}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7246}%
$ a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7248}%
$ \times 10^6$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7250}%
$ g$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7252}%
$ ^{-2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7256}%
$ ^{-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7272}%
$ C_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7278}%
$ R_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7284}%
$ d_{\mathrm{H}_2\mathrm{O}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7290}%
$ \epsilon_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7292}%
$ \delta_v = \epsilon_v^{-1} - 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7296}%
$ \sigma_{SB}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7300}%
$ ^{-4}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7302}%
$ \times 10^{-8}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7359}%
$ _2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7363}%
$ \times 10^{10}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7409}%
$ -$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
\stepcounter{subsection}

\end{document}
