\batchmode


\documentclass[a4j,12pt,twoside]{jreport}
\RequirePackage{ifthen}




\usepackage{Dennou6}         
\usepackage{amsmath}
\usepackage{times}
\usepackage{url}
\usepackage{bm}


\pagestyle{Dmyheadings}



\setlength{\parskip}{2ex} 


\setcounter{chapter}{0}


\makeatletter


\makeatother


\allowdisplaybreaks




\usepackage[dvips]{color}


\pagecolor[gray]{.7}

\usepackage[latin1]{inputenc}



\makeatletter

\makeatletter
\count@=\the\catcode`\_ \catcode`\_=8 
\newenvironment{tex2html_wrap}{}{}%
\catcode`\<=12\catcode`\_=\count@
\newcommand{\providedcommand}[1]{\expandafter\providecommand\csname #1\endcsname}%
\newcommand{\renewedcommand}[1]{\expandafter\providecommand\csname #1\endcsname{}%
  \expandafter\renewcommand\csname #1\endcsname}%
\newcommand{\newedenvironment}[1]{\newenvironment{#1}{}{}\renewenvironment{#1}}%
\let\newedcommand\renewedcommand
\let\renewedenvironment\newedenvironment
\makeatother
\let\mathon=$
\let\mathoff=$
\ifx\AtBeginDocument\undefined \newcommand{\AtBeginDocument}[1]{}\fi
\newbox\sizebox
\setlength{\hoffset}{0pt}\setlength{\voffset}{0pt}
\addtolength{\textheight}{\footskip}\setlength{\footskip}{0pt}
\addtolength{\textheight}{\topmargin}\setlength{\topmargin}{0pt}
\addtolength{\textheight}{\headheight}\setlength{\headheight}{0pt}
\addtolength{\textheight}{\headsep}\setlength{\headsep}{0pt}
\setlength{\textwidth}{349pt}
\newwrite\lthtmlwrite
\makeatletter
\let\realnormalsize=\normalsize
\global\topskip=2sp
\def\preveqno{}\let\real@float=\@float \let\realend@float=\end@float
\def\@float{\let\@savefreelist\@freelist\real@float}
\def\liih@math{\ifmmode$\else\bad@math\fi}
\def\end@float{\realend@float\global\let\@freelist\@savefreelist}
\let\real@dbflt=\@dbflt \let\end@dblfloat=\end@float
\let\@largefloatcheck=\relax
\let\if@boxedmulticols=\iftrue
\def\@dbflt{\let\@savefreelist\@freelist\real@dbflt}
\def\adjustnormalsize{\def\normalsize{\mathsurround=0pt \realnormalsize
 \parindent=0pt\abovedisplayskip=0pt\belowdisplayskip=0pt}%
 \def\phantompar{\csname par\endcsname}\normalsize}%
\def\lthtmltypeout#1{{\let\protect\string \immediate\write\lthtmlwrite{#1}}}%
\newcommand\lthtmlhboxmathA{\adjustnormalsize\setbox\sizebox=\hbox\bgroup\kern.05em }%
\newcommand\lthtmlhboxmathB{\adjustnormalsize\setbox\sizebox=\hbox to\hsize\bgroup\hfill }%
\newcommand\lthtmlvboxmathA{\adjustnormalsize\setbox\sizebox=\vbox\bgroup %
 \let\ifinner=\iffalse \let\)\liih@math }%
\newcommand\lthtmlboxmathZ{\@next\next\@currlist{}{\def\next{\voidb@x}}%
 \expandafter\box\next\egroup}%
\newcommand\lthtmlmathtype[1]{\gdef\lthtmlmathenv{#1}}%
\newcommand\lthtmllogmath{\dimen0\ht\sizebox \advance\dimen0\dp\sizebox
  \ifdim\dimen0>.95\vsize
   \lthtmltypeout{%
*** image for \lthtmlmathenv\space is too tall at \the\dimen0, reducing to .95 vsize ***}%
   \ht\sizebox.95\vsize \dp\sizebox\z@ \fi
  \lthtmltypeout{l2hSize %
:\lthtmlmathenv:\the\ht\sizebox::\the\dp\sizebox::\the\wd\sizebox.\preveqno}}%
\newcommand\lthtmlfigureA[1]{\let\@savefreelist\@freelist
       \lthtmlmathtype{#1}\lthtmlvboxmathA}%
\newcommand\lthtmlpictureA{\bgroup\catcode`\_=8 \lthtmlpictureB}%
\newcommand\lthtmlpictureB[1]{\lthtmlmathtype{#1}\egroup
       \let\@savefreelist\@freelist \lthtmlhboxmathB}%
\newcommand\lthtmlpictureZ[1]{\hfill\lthtmlfigureZ}%
\newcommand\lthtmlfigureZ{\lthtmlboxmathZ\lthtmllogmath\copy\sizebox
       \global\let\@freelist\@savefreelist}%
\newcommand\lthtmldisplayA{\bgroup\catcode`\_=8 \lthtmldisplayAi}%
\newcommand\lthtmldisplayAi[1]{\lthtmlmathtype{#1}\egroup\lthtmlvboxmathA}%
\newcommand\lthtmldisplayB[1]{\edef\preveqno{(\theequation)}%
  \lthtmldisplayA{#1}\let\@eqnnum\relax}%
\newcommand\lthtmldisplayZ{\lthtmlboxmathZ\lthtmllogmath\lthtmlsetmath}%
\newcommand\lthtmlinlinemathA{\bgroup\catcode`\_=8 \lthtmlinlinemathB}
\newcommand\lthtmlinlinemathB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA
  \vrule height1.5ex width0pt }%
\newcommand\lthtmlinlineA{\bgroup\catcode`\_=8 \lthtmlinlineB}%
\newcommand\lthtmlinlineB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA}%
\newcommand\lthtmlinlineZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
  \expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetinline}
\newcommand\lthtmlinlinemathZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
  \expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetmath}
\newcommand\lthtmlindisplaymathZ{\egroup %
  \centerinlinemath\lthtmllogmath\lthtmlsetmath}
\def\lthtmlsetinline{\hbox{\vrule width.1em \vtop{\vbox{%
  \kern.1em\copy\sizebox}\ifdim\dp\sizebox>0pt\kern.1em\else\kern.3pt\fi
  \ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}}
\def\lthtmlsetmath{\hbox{\vrule width.1em\kern-.05em\vtop{\vbox{%
  \kern.1em\kern0.8 pt\hbox{\hglue.17em\copy\sizebox\hglue0.8 pt}}\kern.3pt%
  \ifdim\dp\sizebox>0pt\kern.1em\fi \kern0.8 pt%
  \ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}}
\def\centerinlinemath{%
  \dimen1=\ifdim\ht\sizebox<\dp\sizebox \dp\sizebox\else\ht\sizebox\fi
  \advance\dimen1by.5pt \vrule width0pt height\dimen1 depth\dimen1 
 \dp\sizebox=\dimen1\ht\sizebox=\dimen1\relax}

\def\lthtmlcheckvsize{\ifdim\ht\sizebox<\vsize 
  \ifdim\wd\sizebox<\hsize\expandafter\hfill\fi \expandafter\vfill
  \else\expandafter\vss\fi}%
\providecommand{\selectlanguage}[1]{}%
\makeatletter \tracingstats = 1 
\providecommand{\Beta}{\textrm{B}}
\providecommand{\Mu}{\textrm{M}}
\providecommand{\Kappa}{\textrm{K}}
\providecommand{\Rho}{\textrm{R}}
\providecommand{\Epsilon}{\textrm{E}}
\providecommand{\Chi}{\textrm{X}}
\providecommand{\Iota}{\textrm{J}}
\providecommand{\omicron}{\textrm{o}}
\providecommand{\Zeta}{\textrm{Z}}
\providecommand{\Eta}{\textrm{H}}
\providecommand{\Nu}{\textrm{N}}
\providecommand{\Omicron}{\textrm{O}}
\providecommand{\Tau}{\textrm{T}}
\providecommand{\Alpha}{\textrm{A}}


\begin{document}
\pagestyle{empty}\thispagestyle{empty}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength hsize=\the\hsize}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength vsize=\the\vsize}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength hoffset=\the\hoffset}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength voffset=\the\voffset}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength topmargin=\the\topmargin}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength topskip=\the\topskip}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength headheight=\the\headheight}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength headsep=\the\headsep}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength parskip=\the\parskip}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength oddsidemargin=\the\oddsidemargin}\lthtmltypeout{}%
\makeatletter
\if@twoside\lthtmltypeout{latex2htmlLength evensidemargin=\the\evensidemargin}%
\else\lthtmltypeout{latex2htmlLength evensidemargin=\the\oddsidemargin}\fi%
\lthtmltypeout{}%
\makeatother
\setcounter{page}{1}
\onecolumn

% !!! IMAGES START HERE !!!

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4260}%
$ T=150$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4262}%
$ p=400$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4264}%
$ T=135$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4266}%
$ p=90$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4268}%
$ 5.0 \times 10^{8}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4270}%
$ ^{-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\setcounter{chapter}{0}
\stepcounter{chapter}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4296}%
$ u$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4298}%
$ w$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4300}%
$ \theta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4302}%
$ \Pi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4304}%
$ \rho_s$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4306}%
$ p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4308}%
$ \rho$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4310}%
$ T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4315}%
$\displaystyle \theta$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4317}%
$\displaystyle \equiv$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4319}%
$\displaystyle T \left( \frac{p_0}{p} \right)^{\frac{R}{c_{pv}}},
\Deqlab{Pottemp}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4323}%
$\displaystyle \Pi$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4327}%
$\displaystyle \left( \frac{p}{p_0} \right)^{\frac{R}{c_{pv}}} =
\frac{T}{\theta}.
\Deqlab{Exner}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4329}%
$ p_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4331}%
$ R$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4333}%
$ c_{pv}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4335}%
$ R \simeq 188.9$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4341}%
$ c_{pv} \simeq
734.1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4347}%
$ p_0 = 700$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4349}%
$ \phi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4351}%
$ \overline{\phi}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4353}%
$ \phi^{\prime}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4358}%
$\displaystyle u(x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4360}%
$\displaystyle =$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4362}%
$\displaystyle u^{\prime}(x,z,t), \Deqlab{ZA}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4366}%
$\displaystyle w(x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4370}%
$\displaystyle w^{\prime}(x,z,t), \Deqlab{ZB}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4374}%
$\displaystyle \theta(x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4378}%
$\displaystyle \theta^{\prime}(x,z,t) + \overline{\theta}(z),
\Deqlab{ZC}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4382}%
$\displaystyle \Pi(x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4386}%
$\displaystyle \Pi^{\prime}(x,z,t) + \overline{\Pi}(z), \Deqlab{ZD}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4390}%
$\displaystyle \rho_s(x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4394}%
$\displaystyle {\rho_s}^{\prime}(x,z,t). \Deqlab{ZE}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4396}%
$ ^{\prime}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4400}%
$\displaystyle \DP{\overline{p}}{z} = - \overline{\rho} g \Deqlab{hydrostat1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4402}%
$ g$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4404}%
$ \overline{\Pi}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4406}%
$ \overline{\theta}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4410}%
$\displaystyle \DP{\overline{\Pi}}{z} = - \frac{g}{c_{pv} \overline{\theta}}  \Deqlab{hydrostat2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4412}%
$ _2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4418}%
$\displaystyle \DP{u}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4422}%
$\displaystyle - u \DP{u}{x} - w \DP{u}{z} - c_{pv} \overline{\theta}
\DP{\Pi^{\prime}}{x} + D_u + D_{u}^{sfc},
\Deqlab{AA}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4426}%
$\displaystyle \DP{w}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4430}%
$\displaystyle - u \DP{w}{x} - w \DP{w}{z} - c_{pv} \overline{\theta}
\DP{\Pi^{\prime}}{z} + D_w
+ g
\left(
\frac{\theta^{\prime}}{\overline{\theta}}
- \frac{R}{p_0}
\frac{\overline{\theta}}{\overline{\Pi}^{c_{vv} / R}}
\rho_s
\right),
\Deqlab{AB}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4432}%
$\displaystyle \DP{\theta^{\prime}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4436}%
$\displaystyle - u \DP{\theta^{\prime}}{x} - w \DP{\theta^{\prime}}{z}
- w \DP{\overline{\theta}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4440}%
$\displaystyle + \Dinv{\overline{\Pi}}
(Q_{cond} + Q_{rad} + Q_{dis}) + D_{\theta}
+ D_{\theta}^{sfc},
\Deqlab{AC}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4442}%
$\displaystyle \DP{\Pi^{\prime}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4446}%
$\displaystyle - \frac{\overline{c}^2}{c_{pv} \overline{\rho} \overline{\theta}^2}
\left[ \DP{ (\overline{\rho} \overline{\theta} u) }{x}
+ \DP{ (\overline{\rho} \overline{\theta} w) }{z} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4450}%
$\displaystyle + \frac{\overline{c}^2}{c_{pv} \overline{\theta}^2}
\Dinv{\overline{\Pi}}
( Q_{cond} + Q_{rad} + Q_{dis} )
- \frac{\overline{c}^2}{c_{pv} \overline{\rho} \overline{\theta}^2}
M_{cond},
\Deqlab{AD}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4454}%
$\displaystyle \DP{\rho_s}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4458}%
$\displaystyle - \DP{(\rho_s u)}{x} - \DP{(\rho_s w)}{z}
+ M_{cond} + M_{fall} + D_{\rho_s}. \Deqlab{AE}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4460}%
$ \overline{c}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4464}%
$\displaystyle {\overline{c}}^2  = \frac{c_{pv}}{c_{vv}} R \overline{T} = \frac{c_{pv}}{c_{vv}} R \overline{\theta} \overline{\Pi}.   \Deqlab{Sound}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4466}%
$ c_{vv}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4472}%
$ c_{vv} \simeq 545.2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4484}%
$ D_u$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4486}%
$ D_w$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4488}%
$ D_{\theta}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4490}%
$ D_{\rho_s}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4492}%
$ D_u^{sfc}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4494}%
$ D_{\theta}^{sfc}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4496}%
$ Q_{cond}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4498}%
$ Q_{rad}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4500}%
$ Q_{dis}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4502}%
$ M_{cond}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4504}%
$ M_{fall}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4526}%
$\displaystyle Q_{cond} = \frac{L M_{cond}}{c_{pv} \overline{\rho}} \Deqlab{AF}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4528}%
$ L$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4532}%
$ L \simeq 5.86 \times 10^5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4550}%
$\displaystyle + \frac{\overline{c}^2}{c_{pv} \overline{\rho} \overline{\theta}}
\left( \frac{L}{c_{pv} \overline{T}} - 1 \right) M_{cond}
+ \frac{\overline{c}^2}{c_{pv} \overline{\theta}^2 \overline{\Pi}}
( Q_{rad} + Q_{dis} ).
\Deqlab{AH}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4552}%
$ O(\overline{T}) \sim 150$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4564}%
$ L / (c_{pv} \overline{T}) > 1 $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4574}%
$\displaystyle \phi(x,z,t) = \phi(x+L,z,t) \Deqlab{BoundaryA}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4576}%
$ D$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4580}%
$ \psi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4585}%
$\displaystyle w$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4589}%
$\displaystyle 0, \quad \quad (z = 0, D) \Deqlab{boundaryB}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4593}%
$\displaystyle \DP{\psi}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4597}%
$\displaystyle 0, \quad \quad (z = 0, D) \Deqlab{boundaryC}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4610}%
$ D_\theta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4617}%
$\displaystyle D_u$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4621}%
$\displaystyle - \DP{}{x}
\left[ - 2 K_m \DP{u}{x} + \frac{2}{3} E_{turb} \right]
- \DP{}{z} \left[ - K_m \left( \DP{u}{x} + \DP{w}{z} \right) \right]
, \Deqlab{TurbA}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4625}%
$\displaystyle D_w$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4629}%
$\displaystyle - \DP{}{x} \left[ - K_m \left( \DP{w}{x} + \DP{u}{z} \right) \right]
- \DP{}{z}
\left[ - 2 K_m \DP{w}{z} + \frac{2}{3} E_{turb} \right]
, \Deqlab{TurbB}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4633}%
$\displaystyle D_{\theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4637}%
$\displaystyle - \DP{}{x} \left[ K_h \DP{\theta^{\prime}}{x} \right]
- \DP{}{z} \left[ K_h \DP{(\theta^{\prime} + \overline{\theta})}{z}
\right], \Deqlab{TurbC}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4641}%
$\displaystyle D_{\rho_s}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4645}%
$\displaystyle - \DP{}{x} \left[ K_h \DP{\rho_s}{x} \right]
- \DP{}{z} \left[ K_h \DP{\rho_s}{z}  \right] \Deqlab{TurbD}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4647}%
$ K_m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4649}%
$ K_h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4651}%
$ E_{turb}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4659}%
$\displaystyle E_{turb} = \left( \frac{K_m}{C_m l} \right)^2 \Deqlab{TurbE}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4661}%
$ l$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4663}%
$ \Delta x$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4665}%
$ \Delta z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4667}%
$ l = (\Delta x \Delta z)^{1/2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4669}%
$ C_m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4675}%
$\displaystyle K_h = 3 K_m \Deqlab{TurbF}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4681}%
$\displaystyle \DP{K_m}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4685}%
$\displaystyle - \left( u \DP{K_m}{x} + w \DP{K_m}{z} \right)
- \frac{3 g C_{m}^{2} l^{2}}{ 2 }
\left(
\Dinv{\overline{\theta}} \DP{\theta}{z}
- \frac{R \overline{\theta}}{p_0 \overline{\Pi}^{c_v/R}}
\DP{\rho_s}{z}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4687}%
$\displaystyle + {C_m}^2 l^2 \left[ \left( \DP{u}{x} \right)^2 + \left( \DP{w}{z}
\right)^2 \right]
+ \frac{{C_m}^2 l^2}{2} \left( \DP{u}{z} + \DP{w}{x} \right)^2$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4689}%
$\displaystyle - \frac{K_m}{3} \left( \DP{u}{x} + \DP{w}{z} \right)
+ \Dinv{2} \left( \DP[2]{{K_m}^2}{x} + \DP[2]{{K_m}^2}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4693}%
$\displaystyle + \left( \DP{K_m}{x} \right)^2 + \left( \DP{K_m}{z} \right)^2
- \frac{C_{\varepsilon}}{2 C_m l^2} {K_m}^2.
\Deqlab{TurbG}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4695}%
$ C_{\varepsilon}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4697}%
$ C_m = C_{\varepsilon}
= 0.2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4703}%
$\displaystyle Q_{dis}  = \frac{C_{\varepsilon}}{c_{pv} l} E_{turb}^{3/2}  = \frac{C_{\varepsilon}}{c_{pv} l} \left( \frac{K_m}{C_m l} \right)^3  \Deqlab{TurbH}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4709}%
$ F_{u}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4711}%
$ F_{\theta}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4720}%
$\displaystyle D_u^{sfc}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4724}%
$\displaystyle - \Dinv{\rho} \DP{F_{u}}{z},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4728}%
$\displaystyle D_{\theta}^{sfc}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4732}%
$\displaystyle - \Dinv{\Pi \rho c_p} \DP{F_{\theta}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4741}%
$\displaystyle F_{u}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4745}%
$\displaystyle -C_D V_{sfc} \rho u_{z_1},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4749}%
$\displaystyle F_{\theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4753}%
$\displaystyle - c_p C_D V_{sfc} \rho (T_{z_1} - T_{sfc}).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4755}%
$ C_D$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4757}%
$ z_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4759}%
$ T_{sfc}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4761}%
$ V_{sfc}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4766}%
$\displaystyle D_{u}^{sfc}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4768}%
$\displaystyle \approx$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4770}%
$\displaystyle \DP{}{z} (C_D V_{sfc} u_{z_1}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4778}%
$\displaystyle \DP{}{z}
\left[
C_D V_{sfc} \left( \theta_{z_1} - \frac{T_{sfc}}{\Pi_{z_1}} \right)
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4785}%
$\displaystyle V_{sfc} = \sqrt{u_{z_1}^2 + v_0^2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4787}%
$ v_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4789}%
$ v_0 = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4793}%
$ Ri_{B}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4798}%
$\displaystyle C_D$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4802}%
\begin{displaymath}\begin{cases}
C_{DN}
\left( 1 - \frac{A_1 Ri_{B}}{1 + A_3 |Ri_{B}|^{1/2}} \right),
(Ri_{B} < 0) \\
C_{DN} \Dinv{1 + A_2 Ri_{B}}, (Ri_{B} > 0)
\end{cases}\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4806}%
$\displaystyle Ri_{B}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4810}%
$\displaystyle \frac{g z_1 (\theta_1^{\prime} + \overline{\theta}_1 - T_{sfc})}
{ \overline{\theta_1}^x {\rm max} (u_1^2, u_{min}^2)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4812}%
$ u_{min}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4814}%
$ u_{min} = 0.1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4816}%
$ C_{DN}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4818}%
$ A_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4820}%
$ A_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4822}%
$ A_3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4825}%
$\displaystyle C_{DN}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4829}%
$\displaystyle \left[ \frac{\kappa}{\ln (z_1/z_0)} \right]^2,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4831}%
$\displaystyle A_1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4835}%
$\displaystyle 9.4,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4837}%
$\displaystyle A_2$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4841}%
$\displaystyle 4.7,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4845}%
$\displaystyle A_3$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4849}%
$\displaystyle 7.4 C_{DN} A_1 \left( \frac{z_1}{z_0} \right)^{1/2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4851}%
$ \kappa=0.35$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4853}%
$ z_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4855}%
$ 10^{-2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4872}%
$ \mu$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4889}%
$\displaystyle M_{cond} = \frac{4 \pi r_d \overline{\rho} N^{*}}{R_h} (S - 1).   \Deqlab{CloudB}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4891}%
$ R_h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4893}%
$ S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4895}%
$ r_d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4900}%
$\displaystyle R_h$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4904}%
$\displaystyle \frac{L^2}{k R T^2} = \frac{L^2}{k R \theta^2 \Pi^2},
\Deqlab{CloudC}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4908}%
$\displaystyle S$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4912}%
$\displaystyle \frac{p}{p_{\ast}} = \frac{{p_0}^{\frac{c_{pv}}{R}} \Pi}{p_{\ast}}
\Deqlab{CloudE}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4916}%
$\displaystyle r_d$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4920}%
$\displaystyle \left(
r_{aero}^3 + \frac{3 \rho_s}{4 \rho_I \pi \overline{\rho} N^{*}}
\right)^{1/3}
\Deqlab{CloudA}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4922}%
$ k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4924}%
$ p_{\ast}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4928}%
$ \rho_I$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4934}%
$ r_{aero}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4936}%
$ N^{*}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4938}%
$ \rho_I = 1.565 \times 10^3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4940}%
$ ^3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4950}%
$\displaystyle p_{\ast} \simeq \exp \left( A_{ant} - \frac{B_{ant}}{T} \right)  \Deqlab{CloudG}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4952}%
$ A_{ant}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4954}%
$ B_{ant}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4958}%
$ A_{ant} = 27.4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4960}%
$ B_{ant} = 3103$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4970}%
$ V_{term}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4974}%
$\displaystyle M_{fall} = \DP{}{z} \left( \rho_s V_{term} \right) \Deqlab{CloudI}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4978}%
$\displaystyle V_{term} = C_{sc} \frac{2 r_d^2 g \rho_I}{9 \eta} \Deqlab{CloudJ}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4980}%
$ \eta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4984}%
$\displaystyle \eta   =   \eta_{ref}   \left( \frac{T_{ref} + C_{CO_2}}{\overline{T} + C_{CO_2}} \right)  \left( \frac{\overline{T}}{T_{ref}} \right)^{3/2}   =   \eta_{ref}   \left(    \frac{T_{ref} + C_{CO_2}}{\overline{\theta} \overline{\Pi} + C_{CO_2}}   \right)  \left(    \frac{\overline{\theta} \overline{\Pi}}{T_{ref}}   \right)^{3/2}   \Deqlab{CloudM}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4986}%
$ \eta_{ref}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4988}%
$ T_{ref}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4990}%
$ C_{CO_2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4994}%
$ \eta_{ref} = 1.47 \times
10^{-5}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4996}%
$ \cdot$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4998}%
$ T_{ref} = 293$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5000}%
$ C_{CO_2} = 240$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5002}%
$ C_{sc}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5006}%
$\displaystyle C_{sc}   = 1 + \frac{4}{3} K_n  \Deqlab{CloudK}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5008}%
$ K_n \equiv \lambda / r_d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5011}%
$\displaystyle C_{sc} = 1 + 1.255 K_n$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5013}%
$\displaystyle C_{sc}   = 1 + K_n     \left[       1.257 + 0.400 \exp \left( - \frac{1.10}{K_n} \right)     \right].$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5015}%
$ \lambda$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5021}%
$\displaystyle \lambda   =    \frac{k_B \overline{T}}{\sqrt{2} \pi \sigma^2 \overline{p}}   =    \frac{k_B \overline{\theta}}   {\sqrt{2} \pi \sigma^2 p_0 \overline{\Pi}^{c_{vv}/R}}   \Deqlab{CloudL}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5023}%
$ k_B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5025}%
$ \sigma$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5029}%
$ k_B =
1.38 \times 10^{-23}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5031}%
$ ^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5033}%
$ ^{-2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5037}%
$ \sigma =
3.3 \times 10^{-10}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5039}%
$ T \sim 150$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5041}%
$ p \sim 400$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5043}%
$ T \sim 135$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5045}%
$ p \sim 90$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure644}%
\begin{figure} \begin{center}
\Depsf[][][width=6.0cm,angle=270]{ps/radius-dens.ps}

 \end{center}
  \end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure652}%
\begin{figure} \begin{center}
\Depsf[][][width=6.0cm,angle=270]{ps/Vterm.ps}

 \end{center}
  \end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5097}%
$ \bf {107}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5099}%
$ \bf {108(E7)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5101}%
$ \bf {24}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5103}%
$ \bf {83}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5105}%
$ \bf {57}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5107}%
$ \bf {29}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5109}%
$ \bf {45}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5113}%
$ \bf {160}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5115}%
$ \bf {162}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5117}%
$ \bf {66}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5119}%
$ \bf {10}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5121}%
$ \bf {35}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5123}%
$ \bf {17}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5127}%
$ \bf {110}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5129}%
$ \bf {102}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5131}%
$ \bf {36}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5133}%
$ \bf {30}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5135}%
$ \bf {9}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5141}%
$ \bf {164}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5143}%
$ \bf {20}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\setcounter{equation}{0}
\setcounter{chapter}{1}

\renewcommand{\thechapter}{\Alph{chapter}}

\renewcommand{\theequation}{\thechapter .\arabic{equation}}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5150}%
$ \rho_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5155}%
$\displaystyle \frac{D u}{D t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5159}%
$\displaystyle - \Dinv{\rho} \DP{p}{x} + D_u, \Deqlab{EOM1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5163}%
$\displaystyle \frac{D w}{D t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5167}%
$\displaystyle - \Dinv{\rho} \DP{p}{z} - g + D_w \Deqlab{EOM2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5169}%
$ \rho \equiv \rho_v + \rho_s$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5178}%
$\displaystyle - \Dinv{\rho} \DP{p}{x_i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5182}%
$\displaystyle - \frac{\rho_v}{\rho} \Dinv{\rho_v} \DP{p}{x_i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5186}%
$\displaystyle - \frac{\rho_v}{\rho} \frac{R \theta \Pi}{p}
\DP{}{x_i} \left[ p_0 \Pi^{c_{pv} / R} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5190}%
$\displaystyle - \frac{\rho_v}{\rho} \frac{R \theta \Pi}{p}
\frac{p_0 c_{pv}}{R} \Pi^{(c_{pv} / R) - 1} \DP{\Pi}{x_i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5194}%
$\displaystyle - \frac{\rho_v}{\rho} \frac{R \theta \Pi}{p}
p_0 \Pi^{c_{pv} / R} \frac{c_{pv}}{R \Pi} \DP{\Pi}{x_i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5198}%
$\displaystyle - \frac{\rho_v}{\rho} \frac{R \theta \Pi}{p}
p \frac{c_{pv}}{R \Pi} \DP{\Pi}{x_i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5204}%
$\displaystyle - \frac{\rho_v}{\rho} c_{pv} \theta \DP{\Pi}{x_i}
\Deqlab{EOM3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5206}%
$ p = \rho_v R T = \rho_v R \theta \Pi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5215}%
$\displaystyle - \frac{\rho_v}{\rho} c_{pv} \theta \DP{\Pi}{x}
+ D_u, \Deqlab{EOM4}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5223}%
$\displaystyle - \frac{\rho_v}{\rho} c_{pv} \theta \DP{\Pi}{z}
- g + D_w \Deqlab{EOM5}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5225}%
$ \overline{\rho} = \overline{\rho_v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5227}%
$ \rho^{\prime} = \rho_v^{\prime} + \rho_s^{\prime}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5229}%
$ \rho = \overline{\rho_v} + \rho_v^{\prime} + \rho_s^{\prime}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5232}%
$\displaystyle \DP{u}{t} + u \DP{u}{x} + w \DP{u}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5236}%
$\displaystyle - \frac{\overline{\rho_v} + \rho_v^{\prime}}
{\overline{\rho} + \rho^{\prime}}
c_{pv} (\overline{\theta} + \theta^{\prime})
\DP{\Pi^{\prime}}{x} + D_{u}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5240}%
$\displaystyle - \frac{\overline{\rho_v} + \rho_v^{\prime}}
{\overline{\rho}}
\Dinv{1 + (\rho^{\prime} / \overline{\rho})}
c_{pv} (\overline{\theta} + \theta^{\prime})
\DP{\Pi^{\prime}}{x} + D_{u}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5242}%
$\displaystyle \simeq$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5244}%
$\displaystyle - \frac{\overline{\rho_v} + \rho_v^{\prime}}
{\overline{\rho}}
\left( 1 - \frac{\rho^{\prime}}{\overline{\rho}} \right)
c_{pv} (\overline{\theta} + \theta^{\prime})
\DP{\Pi^{\prime}}{x} + D_{u}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5248}%
$\displaystyle - \frac{\overline{\rho_v} + \rho_v^{\prime}}
{\overline{\rho_v}}
\left( 1 - \frac{\rho^{\prime}}{\overline{\rho}} \right)
c_{pv} (\overline{\theta} + \theta^{\prime})
\DP{\Pi^{\prime}}{x} + D_{u}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5252}%
$\displaystyle - \left( 1 + \frac{\rho_v^{\prime}}{\overline{\rho_v}} \right)
\left( 1 - \frac{\rho^{\prime}}{\overline{\rho}} \right)
c_{pv} (\overline{\theta} + \theta^{\prime})
\DP{\Pi^{\prime}}{x} + D_{u}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5256}%
$\displaystyle -  c_{pv} \overline{\theta} \DP{\Pi^{\prime}}{x} + D_{u},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5264}%
$\displaystyle - u \DP{u}{x} - w \DP{u}{z}
- c_{pv} \overline{\theta} \DP{\Pi^{\prime}}{x} + D_{u}
\Deqlab{EOM6}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5269}%
$\displaystyle 0 = - c_{pv} \overline{\theta} \DP{\overline{\Pi}}{z} - g
\Deqlab{EOM7}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5272}%
$\displaystyle \DP{w}{t} + u \DP{w}{x} + w \DP{w}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5276}%
$\displaystyle - \frac{\overline{\rho_v} + \rho_v^{\prime}}
{\overline{\rho} + \rho^{\prime}}
c_{pv} (\overline{\theta} + \theta^{\prime})
\left( \DP{\overline{\Pi}}{z} + \DP{\Pi^{\prime}}{z} \right)
- g + D_{w}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5280}%
$\displaystyle - \left( 1 + \frac{\rho_v^{\prime}}{\overline{\rho_v}} \right)
\left( 1 - \frac{\rho^{\prime}}{\overline{\rho}} \right)
c_{pv} (\overline{\theta} + \theta^{\prime})
\left( \DP{\overline{\Pi}}{z} + \DP{\Pi^{\prime}}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5282}%
$\displaystyle - g + D_{w}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5286}%
$\displaystyle -  c_{pv} \overline{\theta} \DP{\overline{\Pi}}{z}
-  c_{pv} \overline{\theta} \DP{\Pi^{\prime}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5288}%
$\displaystyle -  \frac{\rho_v^{\prime}}{\overline{\rho_v}}
c_{pv} \overline{\theta} \DP{\overline{\Pi}}{z}
+  \frac{\rho^{\prime}}{\overline{\rho}}
c_{pv} \overline{\theta} \DP{\overline{\Pi}}{z}
-  c_{pv} \theta^{\prime} \DP{\overline{\Pi}}{z}
- g + D_{w}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5292}%
$\displaystyle -  c_{pv} \overline{\theta} \DP{\Pi^{\prime}}{z}
-  \frac{\rho_v^{\prime}}{\overline{\rho}}
c_{pv} \overline{\theta} \DP{\overline{\Pi}}{z}
+  \frac{\rho^{\prime}}{\overline{\rho}}
c_{pv} \overline{\theta} \DP{\overline{\Pi}}{z}
-  c_{pv} \theta^{\prime} \DP{\overline{\Pi}}{z}
+ D_{w}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5296}%
$\displaystyle -  c_{pv} \overline{\theta} \DP{\Pi^{\prime}}{z}
+  \frac{\rho_s^{\prime}}{\overline{\rho}}
c_{pv} \overline{\theta} \DP{\overline{\Pi}}{z}
-  c_{pv} \theta^{\prime} \DP{\overline{\Pi}}{z}
+ D_{w}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5300}%
$\displaystyle -  c_{pv} \overline{\theta} \DP{\Pi^{\prime}}{z}
-  \frac{\rho_s^{\prime}}{\overline{\rho}}  g
+  \frac{ \theta^{\prime}}{\overline{\theta}} g
+ D_{w}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5304}%
$\displaystyle -  c_{pv} \overline{\theta} \DP{\Pi^{\prime}}{z}
+ g
\left(
\frac{\theta^{\prime}}{\overline{\theta}}
- \frac{R \overline{\theta}}{p_0 \overline{\Pi}^{c_{vv}/R}}
\rho_s^{\prime}
\right)
+ D_{w},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5311}%
$\displaystyle - u \DP{w}{x} - w \DP{w}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5315}%
$\displaystyle -  c_{pv} \overline{\theta} \DP{\Pi^{\prime}}{z}
+ g
\left(
\frac{\theta^{\prime}}{\overline{\theta}}
- \frac{R \overline{\theta}}{p_0 \overline{\Pi}^{c_{vv}/R}}
\rho_s^{\prime}
\right)
+ D_{w}
\Deqlab{EOM8}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\setcounter{chapter}{2}
\setcounter{equation}{0}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5325}%
$\displaystyle \rho_v
= \frac{p}{R T}
= \frac{ p_0 \Pi^{c_{pv}/R}}{R \Pi \theta}
= \frac{p_0}{R} \frac{\Pi^{c_{vv} / R}}{\theta}
\Deqlab{Peq1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5328}%
$\displaystyle \frac{D \rho_v}{D t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5332}%
$\displaystyle \frac{D}{D t}
\left( \frac{p_0}{R} \frac{\Pi^{c_{vv} / R}}{\theta} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5336}%
$\displaystyle \frac{p_0 c_{vv}}{R^2}
\frac{ \Pi^{c_{vv}/R - 1}}{\theta} \frac{D \Pi}{D t}
- \frac{p_0}{R}
\frac{\Pi^{c_{vv}/R}}{\theta^2} \frac{D \theta}{D t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5340}%
$\displaystyle \frac{c_{vv}}{R \Pi}
\left( \frac{p_0}{R} \frac{\Pi^{c_{vv} / R}}{\theta} \right)
\frac{D \Pi}{D t}
-
\Dinv{\theta}
\left( \frac{p_0}{R} \frac{\Pi^{c_{vv} / R}}{\theta} \right)
\frac{D \theta}{D t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5346}%
$\displaystyle \frac{c_{vv} \rho_v}{R \Pi} \frac{D \Pi}{D t}
- \frac{\rho_v}{\theta} \frac{D \theta}{D t}
\Deqlab{Peq2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5350}%
$\displaystyle \frac{D \rho_v}{D t}  = - \rho_v \nabla \cdot \Dvect{u} - M_{cond}  \Deqlab{Peq3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5354}%
$\displaystyle \frac{D \theta}{D t}  =    \Dinv{\Pi}    \left( Q_{cond} + Q_{dis} + Q_{rad} \right) \Deqlab{Peq4}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5357}%
$\displaystyle \frac{D \Pi}{D t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5361}%
$\displaystyle \frac{R \Pi}{c_{vv}}
\left(
\Dinv{\rho_v} \frac{D \rho_v}{D t}
+ \Dinv{\theta} \frac{D \theta}{D t}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5365}%
$\displaystyle \frac{R \Pi}{c_{vv}}
\left[
- \nabla \cdot \Dvect{u}
- \Dinv{\rho_v} M_{cond}
+ \Dinv{\theta \Pi}
\left( Q_{cond} + Q_{dis} + Q_{rad} \right)
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5369}%
$\displaystyle \frac{c^2}{c_{pv} \theta}
\left[
- \nabla \cdot \Dvect{u}
- \Dinv{\rho_v} M_{cond}
+ \Dinv{\theta \Pi}
\left( Q_{cond} + Q_{dis} + Q_{rad} \right)
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5375}%
$\displaystyle - \frac{c^2}{c_{pv} \theta} \nabla \cdot \Dvect{u}
- \frac{c^2}{c_{pv} \rho_v \theta} M_{cond}
+ \frac{c^2 }{c_{pv} \theta^2 \Pi}
\left( Q_{cond} + Q_{dis} + Q_{rad} \right)
\Deqlab{Peq5}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5377}%
$ c$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5381}%
$\displaystyle c^2   = \frac{c_{pv}}{c_{vv}} R \theta \Pi   \Deqlab{Peq6}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5385}%
$ Q_{*}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5392}%
$\displaystyle - w^{\prime} \DP{\overline{\Pi}}{z}
- \frac{\overline{c^2}}{c_{pv} \overline{\theta}}
\nabla \cdot \Dvect{u}^{\prime}
- \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}}
M_{cond}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5396}%
$\displaystyle + \frac{\overline{c^2} }{c_{pv} \overline{\theta}^2 \overline{\Pi}}
\left( Q_{cond + }Q_{dis} + Q_{rad} \right)
\Deqlab{Peq7}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5401}%
$\displaystyle \overline{\rho} \overline{\theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5405}%
$\displaystyle \frac{p_0}{R} \overline{\Pi}^{c_{vv}/R}
\Deqlab{Peq8}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5409}%
$\displaystyle \overline{c^2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5413}%
$\displaystyle \frac{c_{pv}}{c_{vv}} R \overline{\theta} \overline{\Pi}
\Deqlab{Peq9}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5416}%
$\displaystyle \DP{}{z} \left( \overline{\rho} \overline{\theta} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5420}%
$\displaystyle \DP{}{z}
\left( \frac{p_0}{R} \overline{\Pi}^{c_{vv}/R} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5424}%
$\displaystyle \frac{c_{vv}}{R} \frac{p_0}{R} \overline{\Pi}^{c_{vv}/R - 1}
\DP{\overline{\Pi}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5428}%
$\displaystyle \frac{c_{vv}}{R}
\frac{\overline{\rho} \overline{\theta}}{\overline{\Pi}}
\DP{\overline{\Pi}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5434}%
$\displaystyle \frac{c_{pv} \overline{\rho} \overline{\theta}^2}{\overline{c^2}}
\DP{\overline{\Pi}}{z}
\Deqlab{Peq10}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5437}%
$\displaystyle - w^{\prime} \DP{\overline{\Pi}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5441}%
$\displaystyle - \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}^2}
w^{\prime}
\DP{}{z} \left( \overline{\rho} \overline{\theta} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5447}%
$\displaystyle - \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}^2}
\Dvect{u}^{\prime} \cdot \nabla
\left( \overline{\rho} \overline{\theta} \right)
\Deqlab{Peq11}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5454}%
$\displaystyle - \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}^2}
\Dvect{u}^{\prime} \cdot \nabla
\left( \overline{\rho} \overline{\theta} \right)
- \frac{\overline{c^2}}{c_{pv} \overline{\theta}}
\nabla \cdot \Dvect{u}^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5456}%
$\displaystyle + \frac{\overline{c^2} }{c_{pv}^2 \overline{\theta}^2 \overline{\Pi}}
\left( Q_{cond} + Q_{dis} + Q_{rad} \right)
- \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}}
M_{cond}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5460}%
$\displaystyle - \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}^2}
\left[
\Dvect{u}^{\prime} \cdot \nabla
\left( \overline{\rho} \overline{\theta} \right)
+ \overline{\rho} \overline{\theta}
\nabla \cdot \Dvect{u}^{\prime}
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5466}%
$\displaystyle - \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}^2}
\nabla \cdot
\left( \overline{\rho} \overline{\theta} \Dvect{u}^{\prime} \right)
+ \frac{\overline{c^2} }{c_{pv} \overline{\theta}^2 \overline{\Pi}}
\left( Q_{cond} + Q_{dis} + Q_{rad} \right)
- \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}}
M_{cond}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5470}%
$\displaystyle \Deqlab{Peq12}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5474}%
$\displaystyle Q_{cond} = \frac{L M_{cond}}{c_{pv} \overline{\rho}}   \Deqlab{Peq13}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5483}%
$\displaystyle - \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}^2}
\nabla \cdot
\left( \overline{\rho} \overline{\theta} \Dvect{u}^{\prime} \right)
+ \frac{\overline{c^2} }{c_{pv} \overline{\theta}^2 \overline{\Pi}}
\left(
\frac{L M_{cond}}{c_{pv} \overline{\rho}}  + Q_{dis} + Q_{rad}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5485}%
$\displaystyle - \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}}
M_{cond}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5491}%
$\displaystyle + \frac{\overline{c^2} }{c_{pv} \overline{\theta}^2 \overline{\Pi}}
\left( Q_{dis} + Q_{rad} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5495}%
$\displaystyle - \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}^2}
\nabla \cdot
\left( \overline{\rho} \overline{\theta} \Dvect{u}^{\prime} \right)
+ \frac{\overline{c^2} }{c_{pv} \overline{\rho} \overline{\theta}}
\left(
\frac{L}{c_{pv} \overline{\theta} \overline{\Pi}} - 1
\right)  M_{cond}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5501}%
$\displaystyle - \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}^2}
\nabla \cdot
\left( \overline{\rho} \overline{\theta} \Dvect{u}^{\prime} \right)
+ \frac{\overline{c^2} }{c_{pv} \overline{\rho} \overline{\theta}}
\left( \frac{L}{c_{pv} \overline{T}} - 1 \right)  M_{cond}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5505}%
$\displaystyle + \frac{\overline{c^2} }{c_{pv} \overline{\theta}^2 \overline{\Pi} }
\left( Q_{dis} + Q_{rad} \right)
\Deqlab{Peq14}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\setcounter{chapter}{3}
\setcounter{equation}{0}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5512}%
$\displaystyle \frac{D E_{turb}}{D t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5516}%
$\displaystyle B + S + D_{E}
- \left(\frac{C_{\varepsilon}}{l}\right)
E_{turb}^{\frac{3}{2}}
\Deqlab{B:dEdt}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5520}%
$ l = \left(\Delta x \Delta
z\right)^{1/2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5522}%
$ B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5526}%
$ D_{E}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5531}%
$\displaystyle B$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5535}%
$\displaystyle \frac{g_{j}}{\overline{\theta}}
\overline{u^{\prime}_{j} \theta_v^{\prime}} ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5543}%
$\displaystyle - \overline{(u_{i}^{\prime} u_{j}^{\prime})}
\DP{u_{i}}{x_{j}} ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5547}%
$\displaystyle D_{E}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5551}%
$\displaystyle \DP{}{x_{j}} \left(K_{m} \DP{E_{turb}}{x_{j}} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5554}%
$\displaystyle \theta_v^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5558}%
$\displaystyle \theta^{\prime}
- \frac{\overline{\theta}}{\overline{\rho}} \rho_s^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5564}%
$\displaystyle \theta^{\prime}
- \frac{R \overline{\theta}^2}{p_0 \overline{\Pi}^{c_v/R}}
\rho_s^{\prime}
\Deqlab{BuoyTurb101}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5571}%
$\displaystyle \frac{g_{j}}{\overline{\theta}}
\overline{u_{j}^{\prime} \theta_v^{\prime}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5575}%
$\displaystyle \frac{g_{j}}{\overline{\theta}}
\overline{
u_{j}^{\prime}
\left(
\theta^{\prime}
- \frac{R \overline{\theta}^2}{p_0 \overline{\Pi}^{c_v/R}}
\rho_s^{\prime}
\right)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5579}%
$\displaystyle \frac{g_{j}}{\overline{\theta}}
\overline{ u_{j}^{\prime} \theta^{\prime}}
- g_{j} \frac{R \overline{\theta}}{p_0 \overline{\Pi}^{c_v/R}}
\overline{ u_{j}^{\prime} \rho_s }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5583}%
$\displaystyle \Deqlab{BuoyTurb2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5588}%
$\displaystyle \overline{(u_{i}^{\prime} u_{j}^{\prime})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5592}%
$\displaystyle - K_{m} \left(\DP{u_{i}}{x_{j}}
+ \DP{u_{j}}{x_{i}}\right)
+ \frac{2}{3} \delta_{ij} E_{turb},
\Deqlab{¥ì¥¤¥Î¥ë¥º±þÎÏ1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5596}%
$\displaystyle \overline{u_{j}^{\prime} \phi^{\prime} }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5600}%
$\displaystyle - K_{h} \DP{\phi}{x_{j}}.
\Deqlab{¥ì¥¤¥Î¥ë¥º±þÎÏ2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5604}%
$ K_{m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5608}%
$ K_{h}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5619}%
$\displaystyle K_{m}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5623}%
$\displaystyle C_{m} E_{turb}^{\frac{1}{2}} l,
\Deqlab{B:E}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5627}%
$\displaystyle K_{h}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5631}%
$\displaystyle 3 K_{m}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5633}%
$ C_{\varepsilon}, C_{m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5645}%
$\displaystyle \frac{g}{\overline{\theta}}
\overline{w^{\prime}  \theta^{\prime}}
- g \frac{R \overline{\theta}}{p_0 \overline{\Pi}^{c_v/R}}
\overline{ w^{\prime} \rho_s }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5651}%
$\displaystyle - \frac{g}{\overline{\theta}}
\left( K_{h} \DP{\theta}{z} \right)
+ g \frac{R \overline{\theta}}{p_0 \overline{\Pi}^{c_v/R}}
\left( K_{h} \DP{\rho_s}{z} \right)
\Deqlab{B}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5660}%
$\displaystyle - \overline{(u_{i}^{\prime} u_{j}^{\prime})}
\DP{u_{i}}{x_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5664}%
$\displaystyle - \left\{
- K_{m} \left(\DP{u_{i}}{x_{j}} + \DP{u_{j}}{x_{i}}\right)
+ \frac{2}{3} \delta_{ij} E_{turb}
\right\}
\DP{u_{i}}{x_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5668}%
$\displaystyle \left\{
K_{m} \left(\DP{u_{i}}{x_{j}} + \DP{u_{j}}{x_{i}}\right)
- \frac{2}{3} \delta_{ij} E_{turb}
\right\}
\DP{u_{i}}{x_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5672}%
$\displaystyle \left\{
K_{m} \left(\DP{u}{x_{j}} + \DP{u_{j}}{x}\right)
- \frac{2}{3} \delta_{1j} E_{turb}
\right\}
\DP{u}{x_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5674}%
$\displaystyle +
\left\{
K_{m} \left(\DP{w}{x_{j}} + \DP{u_{j}}{z}\right)
- \frac{2}{3} \delta_{3j} E_{turb}
\right\}
\DP{w}{x_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5678}%
$\displaystyle \left\{
2 K_{m} \left(\DP{u}{x} \right)
- \frac{2}{3} E_{turb}
\right\}
\DP{u}{x}
+
K_{m} \left( \DP{w}{x} + \DP{u}{z} \right)
\DP{u}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5680}%
$\displaystyle +
K_{m} \left(\DP{w}{x} + \DP{u}{z}\right)
\DP{w}{x}
+
\left\{
2 K_{m} \left(\DP{w}{z}  \right)
- \frac{2}{3} E_{turb}
\right\}
\DP{w}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5684}%
$\displaystyle 2 K_{m} \left\{
\left( \DP{u}{x} \right)^{2}
+ \left( \DP{w}{z} \right)^{2}
\right\}
+  K_{m}
\left(\DP{u}{z} + \DP{w}{x}\right)^{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5688}%
$\displaystyle - \frac{2}{3} E_{turb} \left( \DP{u}{x} + \DP{w}{z} \right)
\Deqlab{S}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5697}%
$\displaystyle \DP{}{x_{j}} \left(K_{m} \DP{E_{turb}}{x_{j}} \right),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5703}%
$\displaystyle \DP{}{x} \left(K_{m} \DP{E_{turb}}{x} \right)
+ \DP{}{z} \left(K_{m} \DP{E_{turb}}{z} \right)
\Deqlab{De}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5710}%
$\displaystyle - \frac{g}{\overline{\theta}}
\left( K_{h} \DP{\theta}{z} \right)
+ g \frac{R \overline{\theta}}{p_0 \overline{\Pi}^{c_v/R}}
\left( K_{h} \DP{\rho_s}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5712}%
$\displaystyle + 2 K_{m} \left\{
\left( \DP{u}{x} \right)^{2}
+ \left( \DP{w}{z} \right)^{2}
\right\}
+  K_{m}
\left(\DP{u}{z} + \DP{w}{x}\right)^{2}
- \frac{2}{3} E_{turb} \left( \DP{u}{x} + \DP{w}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5716}%
$\displaystyle + \DP{}{x} \left(K_{m} \DP{E_{turb}}{x} \right)
+ \DP{}{z} \left(K_{m} \DP{E_{turb}}{z} \right)
- \left(\frac{C_{\varepsilon}}{l}\right)
E_{turb}^{\frac{3}{2}}.
\Deqlab{B:TurbE}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5722}%
$\displaystyle \DP{}{x} \left(K_{m} \DP{E_{turb}}{x}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5724}%
$\displaystyle +$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5726}%
$\displaystyle \DP{}{z} \left(K_{m} \DP{E_{turb}}{z}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5730}%
$\displaystyle \frac{1}{C_{m}^{2} l^{2}}
\Biggl\{\DP{}{x}
\left(K_{m} \DP{K_{m}^{2}}{x}\right)
+ \DP{}{z}
\left(K_{m} \DP{K_{m}^{2}}{z}\right)
\Biggr\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5734}%
$\displaystyle \frac{1}{C_{m}^{2} l^{2}}
\Biggl\{K_{m} \DP[2]{K_{m}^{2}}{x}
+ \DP{K_{m}}{x}
\DP{K_{m}^{2}}{x}
+ K_{m} \DP[2]{K_{m}^{2}}{z}
+ \DP{K_{m}}{z}
\DP{K_{m}^{2}}{z}
\Biggr\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5738}%
$\displaystyle \frac{K_{m}}{C_{m}^{2} l^{2}}
\left(\DP[2]{K_{m}^{2}}{x}
+ \DP[2]{K_{m}^{2}}{z}
\right)
+ \frac{2 K_{m}}{C_{m}^{2} l^{2}}
\Biggl\{\left(\DP{K_{m}}{x}\right)^{2}
+ \left(\DP{K_{m}}{z}\right)^{2}
\Biggr\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5741}%
$\displaystyle \frac{2 K_{m}}{C_{m}^{2} l^{2}}  \frac{D K_{m}}{D t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5745}%
$\displaystyle - \frac{g}{\overline{\theta}}
\left( K_{h} \DP{\theta}{z} \right)
+ g \frac{R \overline{\theta}}{p_0 \overline{\Pi}^{c_v/R}}
\left( K_{h} \DP{\rho_s}{z} \right)
+ 2 K_{m} \left\{
\left( \DP{u}{x} \right)^{2}
+ \left( \DP{w}{z} \right)^{2}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5747}%
$\displaystyle +  K_{m}
\left(\DP{u}{z} + \DP{w}{z}\right)^{2}
- \frac{2}{3} \frac{K_{m}^{2}}{C_{m}^{2} l^{2}} \left( \DP{u}{x} +
\DP{w}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5749}%
$\displaystyle + \frac{K_{m}}{C_{m}^{2} l^{2}}
\left(\DP[2]{K_{m}^{2}}{x}
+ \DP[2]{K_{m}^{2}}{z}
\right)
+ \frac{2 K_{m}}{C_{m}^{2} l^{2}}
\Biggl\{\left(\DP{K_{m}}{x}\right)^{2}
+ \left(\DP{K_{m}}{z}\right)^{2}
\Biggr\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5753}%
$\displaystyle - \frac{C_{\varepsilon}}{C_{m}^{3} {l}^{4}}
K_{m}^{3}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5756}%
$\displaystyle \DP{K_{m}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5760}%
$\displaystyle - \left(
u \DP{K_{m}}{x} + w \DP{K_{m}}{z}
\right)
- \frac{g C_{m}^{2} l^{2}}{ 2 } \frac{K_{h}}{K_{m}}
\left(
\Dinv{\overline{\theta}} \DP{\theta}{z}
- \frac{R \overline{\theta}}{p_0 \overline{\Pi}^{c_v/R}}
\DP{\rho_s}{z}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5762}%
$\displaystyle + \left( C_{m}^{2} l^{2} \right) \left\{
\left( \DP{u}{x} \right)^{2}
+ \left( \DP{w}{z} \right)^{2}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5764}%
$\displaystyle +  \frac{ C_{m}^{2} l^{2} }{2}
\left( \DP{u}{z} + \DP{w}{z}\right)^{2}
- \frac{K_{m}}{3}
\left( \DP{u}{x} + \DP{w}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5766}%
$\displaystyle + \Dinv{2}
\left(\DP[2]{K_{m}^{2}}{x}
+ \DP[2]{K_{m}^{2}}{z}
\right)
+ \left(\DP{K_{m}}{x}\right)^{2}
+ \left(\DP{K_{m}}{z}\right)^{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5768}%
$\displaystyle - \frac{C_{\varepsilon}}{2 C_{m} l^{2}} K_{m}^{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5770}%
$ C_{m} = C_{\varepsilon} = 0.2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5772}%
$ K_{h} = 3 K_{m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5779}%
$\displaystyle - \left(
u \DP{K_{m}}{x} + w \DP{K_{m}}{z}
\right)
- \frac{3 g C_{m}^{2} l^{2}}{ 2 }
\left(
\Dinv{\overline{\theta}} \DP{\theta}{z}
- \frac{R \overline{\theta}}{p_0 \overline{\Pi}^{c_v/R}}
\DP{\rho_s}{z}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5783}%
$\displaystyle +  \frac{ C_{m}^{2} l^{2} }{2}
\left( \DP{u}{z} + \DP{w}{x}\right)^{2}
- \frac{K_{m}}{3}
\left( \DP{u}{x} + \DP{w}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5789}%
$\displaystyle - \Dinv{2 l^{2}} K_{m}^{2}
\Deqlab{close_1.5}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\setcounter{chapter}{4}
\setcounter{equation}{0}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5792}%
$ m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5797}%
$\displaystyle \DD{m}{t} = 4 \pi r_d^2 D \DP{\rho}{r}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5799}%
$ r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5808}%
$\displaystyle \DD{m}{t} = - 4 \pi r_d D (\rho_{r_d} - \rho_{\infty})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5810}%
$ r=r_d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5812}%
$ \rho = \rho_{r_d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5814}%
$ r\rightarrow \infty$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5816}%
$ \rho \rightarrow \rho_{\infty}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5818}%
$ p = \rho R T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5823}%
$\displaystyle \DD{m}{t} = - 4 \pi r_d D
\left(\frac{p_*(T_{r_d})}{RT_{r_d}}
- \frac{p_{\infty}}{RT_{\infty}}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5825}%
$ p*(T_{\infty})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5828}%
$\displaystyle \frac{1}{p_*(T_{\infty})} \DD{m}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5832}%
$\displaystyle - \frac{4 \pi r_d D}{R} \left(\frac{p_*(T_{r_d})}{p_*(T_{r_d})T_{r_d}}
- \frac{p_{\infty}}{p_*(T_{r_d})T_{\infty}}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5838}%
$\displaystyle - \frac{4 \pi r_d D}{RT_{\infty}} \left(\frac{p_*(T_{r_d})}{p_*(T_{\infty})}
- \frac{p_{\infty}}{p_*(T_{\infty})}\right)
\Deqlab{±ÀÎ³¼ÁÎÌ¤Î»þ´ÖÊÑ²½}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5840}%
$ (T_{r_d}-T_{\infty})/T_{\infty} \ll 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5845}%
$\displaystyle L \DD{m}{t} = - 4 \pi r^2 k \DD{T}{r}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5852}%
$\displaystyle L \DD{m}{t} = 4 \pi r k (T_{r_d} - T_{\infty})
\Deqlab{ÀøÇ®¤Î»þ´ÖÊÑ²½}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5856}%
$ T = T_{r_d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5860}%
$ T \rightarrow T_{\infty}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5863}%
$\displaystyle \DD{p_*}{T} = \frac{L p_*}{R T^2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5866}%
$\displaystyle \ln \frac{p_*(T_{r_d})}{p_*(T_{\infty})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5870}%
$\displaystyle \frac{L}{R}\frac{T_{r_d} - T_{\infty}}{T_{r_d}T_{\infty}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5874}%
$\displaystyle \sim$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5876}%
$\displaystyle \frac{L}{R}\frac{T_{r_d} - T_{\infty}}{T_{\infty}^2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5879}%
$\displaystyle \frac{p_*(T_{r_d})}{p_*(T_{\infty})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5883}%
$\displaystyle \exp\left(\frac{L}{R}\frac{T_{r_d} - T_{\infty}}{T_{r_d}T_{\infty}}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5887}%
$\displaystyle 1 + \frac{L}{R}\frac{T_{r_d} - T_{\infty}}{T_{\infty}^2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5893}%
$\displaystyle 1 + \frac{L^2}{4 \pi r_d k R T_{\infty}^2} \DD{m}{t}
\Deqlab{Ë°ÏÂ¾øµ¤°µÈæ¤Î¼°}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5898}%
$\displaystyle \DD{m}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5902}%
$\displaystyle - \frac{4 \pi r D p_*(T_{\infty})}{RT_{\infty}}
\left(1 + \frac{L^2}{4 \pi r_d k R T_{\infty}^2} \DD{m}{t}
- \frac{p_{\infty}}{p_*(T_{\infty})}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5907}%
$\displaystyle \left( \frac{RT_{\infty}}{D p_*(T_{\infty})}
+ \frac{L^2}{k R T_{\infty}^2} \right) \DD{m}{t}
= 4 \pi r_d \left(\frac{p_{\infty}}{p_*(T_{\infty})} - 1 \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5910}%
$\displaystyle R_m$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5914}%
$\displaystyle \frac{RT_{\infty}}{D p_*(T_{\infty})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5920}%
$\displaystyle \frac{L^2}{k R T_{\infty}^2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5926}%
$\displaystyle \frac{p_{\infty}}{p_*(T_{\infty})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5931}%
$\displaystyle \DD{m}{t} = \frac{4 \pi r_d}{R_m + R_h} (S - 1)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5933}%
$ R_m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5939}%
$ N$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5946}%
$\displaystyle M_{cond} = N \DD{m}{t} = \frac{4 \pi r_d N}{R_m + R_h} (S - 1)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5948}%
$ R_m \ll R_h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5953}%
$\displaystyle M_{cond} \sim \frac{4 \pi r_d N}{R_h} (S - 1)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\setcounter{chapter}{5}
\setcounter{equation}{0}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5956}%
$ \overline{T}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5958}%
$ T_{iso}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5960}%
$ S_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5962}%
$ p_s$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5964}%
$ T_{S_0}(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5969}%
$\displaystyle \DD{p}{z} = - \rho g
\Deqlab{Tprof1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5971}%
$ p_{*}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5976}%
$\displaystyle p = S_0 p_{*}
\Deqlab{Tprof2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5981}%
$\displaystyle \DD{p}{z}
= S_0 \DD{p_{*}}{z}
= S_0 \DD{p_{*}}{T} \DD{T}{z}
= - \rho g
\Deqlab{Tprof3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5986}%
$\displaystyle \DD{p_{*}}{T} = \frac{L p_{*}}{R T^2}
\Deqlab{Tprof4}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5991}%
$\displaystyle S_0 \frac{L p_{*}}{R T^2} \DD{T}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5995}%
$\displaystyle - \frac{S_0 p_{*}}{R T} g,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5999}%
$\displaystyle \DD{T}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6003}%
$\displaystyle - \frac{g}{L} T
\Deqlab{Tprof5}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6005}%
$ z=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6007}%
$ T_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6011}%
$ z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6016}%
$\displaystyle T_{S_0}(z) = T_0 \exp \left( - \frac{g}{L} z \right)
\Deqlab{Tprof6}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6021}%
$\displaystyle p_{*} = \exp \left(A_{ant} - \frac{B_{ant}}{T} \right)
\Deqlab{Tprof7}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6026}%
$\displaystyle \frac{p_s}{S_0}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6030}%
$\displaystyle \exp \left(A_{ant} - \frac{B_{ant}}{T_0} \right),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6034}%
$\displaystyle T_0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6038}%
$\displaystyle \frac{B_{ant}}{A_{ant} - \ln (p_s / S_0)}
\Deqlab{Tprof8}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6043}%
$\displaystyle T_{S_0} (z)
=
\frac{B_{ant}}{A_{ant} - \ln (p_s / S_0)}
\exp \left( - \frac{g}{L} z \right)
\Deqlab{Tprof9}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6045}%
$ T=T_{iso}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6047}%
$ T=T_{S_0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6049}%
$ z_{T}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6052}%
$\displaystyle T_{iso}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6056}%
$\displaystyle \frac{B_{ant}}{A_{ant} - \ln (p_s / S_0)}
\exp \left( - \frac{g}{L} z_{T} \right),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6060}%
$\displaystyle z_T$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6064}%
$\displaystyle - \frac{L}{g}
\ln \left[ \frac{A - \ln (p_s/S_0)}{B} T_{iso} \right]
\Deqlab{Tprof10}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6068}%
$\displaystyle \overline{T}(z)   =   \begin{cases}   \frac{B_{ant}}{A_{ant} - \ln (p_s / S_0)}   \exp \left( - \frac{g}{L} z \right),    \hspace{5mm} (z \leq z_T) \\T_{iso}   \hspace{43mm} (z > z_T)  \end{cases}  \Deqlab{Tprof11}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6070}%
$ z=z_{T}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6072}%
$ W(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6077}%
$\displaystyle \overline{T}(z)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6081}%
$\displaystyle [1 - W(z)]
\frac{B_{ant}}{A_{ant} - \ln (p_s / S_0)}
\exp \left( - \frac{g}{L} z \right)
+ W(z) T_{iso},
\Deqlab{Tprof12}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6085}%
$\displaystyle W(z)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6089}%
$\displaystyle \Dinv{2}
\left[ \tanh \left( \frac{z - z_T}{\Delta h} \right) + 1 \right].
\Deqlab{Tprof13}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6091}%
$ \Delta h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}


\end{document}
