\batchmode


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




\usepackage{Dennou6}
\usepackage{ascmac}


\Dnoparindent


\Dtitle[2 ¼¡¸µÈóÀÅÎÏ³Ø¥â¥Ç¥ë¤ÎÄê¼°²½]
       {¼¾½áÂçµ¤¤Ë¤ª¤±¤ë 2 ¼¡¸µÈóÀÅÎÏ³Ø¥â¥Ç¥ë¤ÎÄê¼°²½}


\Dauthor{»³²¼ Ã£Ìé, ¿ù»³ ¹Ì°ìÏ¯, ÀÐÅÏ Àµ¼ù}


\Ddate{2010 Ç¯ 4 ·î 28 Æü}




\usepackage[dvips]{color}


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\lthtmlinlinemathA{tex2html_wrap_inline1342}%
$\langle M \rangle$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10774}%
$\displaystyle \rho
= \frac{p}{\langle R \rangle_0 \Pi \theta_v}
= \frac{p_0 \Pi^{\langle c_{v} \rangle_0 / \langle R \rangle_0}}{\langle R
\rangle_0 \theta_v}
 \Deqlab{Ì©ÅÙ¤ÎÄêµÁ}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10776}%
$\displaystyle \theta_v$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10778}%
$\displaystyle \left( \frac{\langle M \rangle_0}{M_d} q_d
     + \sum \frac{\langle M \rangle_0}{ M_v } q_v
         \right) \theta,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10779}%
$\displaystyle \langle M \rangle_0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10781}%
$\displaystyle \frac{q_{d0} + \sum q_{v0}}{q_{d0} / M_d + \sum q_{v0} / M_v}
  \Deqlab{def_M}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1344}%
$M_d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1346}%
$M_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1348}%
$\langle M \rangle_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10786}%
$\displaystyle \overline{\rho}
= 
 \frac{\overline{p}}{\langle R \rangle_0 \overline{\Pi}
 \overline{\theta_v}} 
= 
 \frac{p_0 \overline{\Pi}^{\langle c_{v} \rangle_0 / \langle R
 \rangle_0}}
 {\langle R \rangle_0 \overline{\theta_v}}
 \Deqlab{basic1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10788}%
$\displaystyle \overline{\theta_v}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10790}%
$\displaystyle \left( \frac{\langle M \rangle_0}{M_d} \overline{q_d}
     + \sum \frac{\langle M \rangle_0}{ M_v } \overline{q_v}
         \right) \overline{\theta},  \Deqlab{basic2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10791}%
$\displaystyle \overline{\Pi}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10793}%
$\displaystyle \left( \frac{\overline{p}}{p_0} \right)^{\langle R \rangle_0 / \langle
   c_p \rangle_0},  \Deqlab{basic3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10794}%
$\displaystyle \overline{\theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10796}%
$\displaystyle \overline{T} 
    \left( \frac{p_0}{\overline{p}} \right)^{\langle R \rangle_0 / \langle
    c_p \rangle_0}
    = \frac{\overline{T}}{\overline{\Pi}}  \Deqlab{basic4}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1350}%
$\overline{q_d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1352}%
$\overline{q_v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10800}%
$\displaystyle \overline{q_d} + \sum \overline{q_v} = 1  \Deqlab{basic5}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10802}%
$\displaystyle \DP{\overline{\Pi}}{z} 
= - \frac{g}{\langle c_p \rangle_0 \overline{\theta_v}} 
  \Deqlab{basic6}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10804}%
$\displaystyle \overline{\langle c_s \rangle^2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10806}%
$\displaystyle \frac{\langle c_p \rangle_0 \langle R \rangle_0
    \overline{\Pi} \overline{\theta_v}}{\langle c_v \rangle_0 }
  \Deqlab{basic7}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1354}%
$\overline{T}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1360}%
$u^{\prime}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1362}%
$w^{\prime}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1364}%
$\theta^{\prime}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1366}%
$\Pi^{\prime}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1368}%
$q_a^{\prime}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1370}%
$a = v, c, r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10821}%
$\displaystyle \DP{u^{\prime}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10823}%
$\displaystyle - u^{\prime} \DP{u^{\prime}}{x} 
    - v^{\prime} \DP{u^{\prime}}{y}
    - w^{\prime} \DP{u^{\prime}}{z}
  - \langle c_p \rangle_0 \overline{\theta_v} \DP{\Pi^{\prime}}{x} +
  D_{u}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10824}%
$\displaystyle \DP{v^{\prime}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10826}%
$\displaystyle - u^{\prime} \DP{v^{\prime}}{x} 
    - v^{\prime} \DP{v^{\prime}}{y}
    - w^{\prime} \DP{v^{\prime}}{z}
  - \langle c_p \rangle_0 \overline{\theta_v} \DP{\Pi^{\prime}}{y} +
  D_{v}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10827}%
$\displaystyle \DP{w^{\prime}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10829}%
$\displaystyle - u^{\prime} \DP{w^{\prime}}{x}
    - v^{\prime} \DP{w^{\prime}}{y} 
    - w^{\prime} \DP{w^{\prime}}{z}
  - \langle c_p \rangle_0 \overline{\theta_v} \DP{\Pi^{\prime}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10830}%
$\displaystyle + \frac{\theta^{\prime}}{\overline{\theta}} g
  + \frac{
      \sum (R_v / R_d - 1) q_v^{\prime}
      - \sum ( q_c^{\prime} + q_r^{\prime} )
    }
    { 1 + \sum (R_v / R_d - 1) \overline{q_v} } g
+ D_{w^{\prime}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10832}%
$\displaystyle \DP{ \Pi^{'}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10834}%
$\displaystyle - \frac{\overline{{\langle c_{s} \rangle}^{2}}}
       {\langle c_p \rangle_0  \bar{\rho} \bar{\theta_v}^{2}}
 \Ddiv \left(
        \bar{\rho} \bar{\theta_v} \Dvect{u^{'}}
       \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10835}%
$\displaystyle + \frac{ \overline{\langle c_s \rangle^2} }
      {\langle c_p \rangle_0 \overline{\theta_v} }
\Bigg[
 \Dinv{ \overline{\theta} }
 \left\{ \Dinv{\overline{\Pi}} ( Q_{cond} + Q_{rad} + Q_{dis} )
  + D_{\theta} \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10836}%
$\displaystyle + \Dinv{ 1 + \sum \left( \frac{R_v}{R_d} - 1 \right) \overline{q_v} }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10837}%
$\displaystyle \Bigg\{
   - \sum ( D_{q_v} + D_{q_c} + D_{q_r} )
    + \sum \frac{R_v}{R_d}
      \left[  M_{src} (q_v) + D_{q_v} \right]
  \Bigg\}
\Bigg]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10839}%
$\displaystyle \DP{\theta^{\prime}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10841}%
$\displaystyle - u^{\prime} \DP{\theta^{\prime}}{x}
     - v^{\prime} \DP{\theta^{\prime}}{y}
     - w^{\prime} \DP{\theta^{\prime}}{z}
     - w^{\prime} \DP{\overline{\theta}}{z}
+ \Dinv{\overline{\Pi}} (Q_{cond} + Q_{rad} + Q_{dis})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10842}%
$\displaystyle + D_{\overline{\theta}} + D_{\theta^{\prime}}
\Deqlab{def_theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10844}%
$\displaystyle \DP{q_a^{\prime}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10846}%
$\displaystyle - u^{\prime} \DP{q_a^{\prime}}{x}
     - v^{\prime} \DP{q_a^{\prime}}{y}
     - w^{\prime} \DP{q_a^{\prime}}{z}
     - w^{\prime} \DP{\overline{q_a}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10847}%
$\displaystyle + \Dinv{\overline{\rho}} M_{fall} (\rho_a^{\prime})
     + \Dinv{\overline{\rho}} M_{src} (\rho_a^{\prime})
     - \frac{\overline{q_a}}{\overline{\rho}} \sum M_{fall}
     (\rho_r^{\prime}) 
     + D_{\overline{q_a}}
     + D_{q_a^{\prime}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10848}%
$\displaystyle \Deqlab{def_qa}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1374}%
$Q_{cond}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1376}%
$Q_{rad}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1378}%
$Q_{dis}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1380}%
$M_{src}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1382}%
$M_{fall}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1394}%
$D_{\ast}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1396}%
$CN_{vc}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1398}%
$EV_{cv}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1400}%
$EV_{rv}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1402}%
$CN_{cr}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1404}%
$CL_{cr}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1406}%
$PR_{r}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10889}%
$\displaystyle M_{src} (\rho_v^{\prime})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10891}%
$\displaystyle - \overline{\rho} (CN_{vc} - EV_{cv} - EV_{rv}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10892}%
$\displaystyle M_{src} (\rho_c^{\prime})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10894}%
$\displaystyle \overline{\rho} (CN_{vc} - EV_{cv} - CN_{cr} - CL_{cr}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10895}%
$\displaystyle M_{src} (\rho_r^{\prime})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10897}%
$\displaystyle \overline{\rho} (CN_{cr} + CL_{cr} - EV_{cv}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10898}%
$\displaystyle M_{fall} (\rho_v^{\prime})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10900}%
$\displaystyle 0,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10901}%
$\displaystyle M_{fall} (\rho_c^{\prime})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10904}%
$\displaystyle M_{fall} (\rho_r^{\prime})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10906}%
$\displaystyle PR_r,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10907}%
$\displaystyle Q_{cond}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10909}%
$\displaystyle - \frac{L_v}{\overline{\rho} \langle c_p \rangle_0} 
     M_{src} (\rho_v^{\prime}).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10913}%
$\displaystyle - u^{\prime} \DP{\theta^{\prime}}{x} 
 - v^{\prime} \DP{\theta^{\prime}}{y} 
 - w^{\prime} \DP{\theta^{\prime}}{z} 
 - w^{\prime} \DP{\overline{\theta}}{z} 
 + \frac{L_v}{ \langle c_p \rangle_0 \overline{\Pi}} 
  \left( CN_{vc} - EV_{cv} - EV_{rv} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10914}%
$\displaystyle + \Dinv{\bar{\Pi}} \left(Q_{rad} + Q_{dis}\right)
 + D_{\bar{\theta}}
 + D_{\theta^{\prime}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10915}%
$\displaystyle \DP{q_v^{\prime}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10917}%
$\displaystyle - u^{\prime} \DP{q_v^{\prime}}{x}
     - v^{\prime} \DP{q_v^{\prime}}{y}
     - w^{\prime} \DP{q_v^{\prime}}{z}
     - w^{\prime} \DP{\overline{q_v}}{z}
     - \frac{\overline{q_v}}{\overline{\rho}} \sum PR_r$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10918}%
$\displaystyle - \left( CN_{vc} - EV_{cv} - EV_{rv} \right)
     + D_{\overline{q_v}}
     + D_{q_v^{\prime}},
\Deqlab{def_qv2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10919}%
$\displaystyle \DP{q_c^{\prime}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10921}%
$\displaystyle - u^{\prime} \DP{q_c^{\prime}}{x}
     - v^{\prime} \DP{q_c^{\prime}}{y}
     - w^{\prime} \DP{q_c^{\prime}}{z}
     - \frac{\overline{q_c}}{\overline{\rho}} \sum PR_r$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10922}%
$\displaystyle + CN_{vc} - EV_{cv} - CN_{cr} - CL_{cr} 
     + D_{q_c^{\prime}},
\Deqlab{def_qc2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10923}%
$\displaystyle \DP{q_r^{\prime}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10925}%
$\displaystyle - u^{\prime} \DP{q_r^{\prime}}{x}
     - v^{\prime} \DP{q_r^{\prime}}{y}
     - w^{\prime} \DP{q_r^{\prime}}{z}
     + \Dinv{\overline{\rho}} PR_r
     + CN_{cr} + CL_{cr} - EV_{rv}
     + D_{q_r^{\prime}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1408}%
$L_{v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1410}%
$^{-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1412}%
$\langle c_{p} \rangle$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1416}%
$-CN_{vc} + EV_{cv}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10938}%
$\displaystyle CN_{cr} = 
	      \left( q_{c}^{\prime} - q_{c 0} \right) / \tau_{ac}
	      \Deqlab{def_CNcr}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1420}%
$ q_{c 0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1422}%
$\tau_{ac}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10943}%
$\displaystyle CL_{cr} = 10.344 g^{1/2} 
                \left( \frac{\bar{\rho}}{\rho_w} \right)^{0.375}
                 q_c^{\prime} {q_r^{\prime}}^{0.875} 
	      \Deqlab{def_CLcr}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10946}%
$\displaystyle EV_{rv} = 
	      4.85 \times 10^{-2}
	      \left( q_{vsw} - q_v^{\prime} \right)
	      ( \bar{\rho} q_r^{\prime} )^{0.65}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1428}%
$q_{vsw}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10950}%
$\displaystyle PR_{r} = \DP{}{z} 
	              \left( \bar{\rho} q_r^{\prime} V_{term} \right). 
	      \Deqlab{teishiki:def_PRr}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1432}%
$V_{term}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10954}%
$\displaystyle V_{term} = 0.3224 g^{1/2} 
                 \left( \frac{\rho_w}{\overline{\rho}} \right)^{0.375}
                 {q_r^{\prime}}^{0.125}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1436}%
$\rho_w$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1438}%
$_{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1440}%
$q_c = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1442}%
$CN_{vr}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10970}%
$\displaystyle - \overline{\rho} CN_{vr},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10973}%
$\displaystyle \overline{\rho} CN_{vr},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10982}%
$\displaystyle - \frac{L_s}{\overline{\rho} \langle c_p \rangle_0} 
     M_{src} (\rho_v^{\prime}).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10986}%
$\displaystyle - u^{\prime} \DP{\theta^{\prime}}{x} 
 - v^{\prime} \DP{\theta^{\prime}}{y} 
 - w^{\prime} \DP{\theta^{\prime}}{z}
 - w^{\prime} \DP{\bar{\theta}}{z} 
 + \frac{L_s}{ \langle c_{p} \rangle_0 \overline{\Pi}} 
  CN_{vr}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10990}%
$\displaystyle - u^{\prime} \DP{q_v^{\prime}}{x}
     - v^{\prime} \DP{q_v^{\prime}}{y}
     - w^{\prime} \DP{q_v^{\prime}}{z}
     - w^{\prime} \DP{\overline{q_v}}{z}
     - \frac{\overline{q_v}}{\overline{\rho}} \sum PR_r
     (\rho_r^{\prime})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10991}%
$\displaystyle - CN_{vr} 
     + D_{\overline{q_v}}
     + D_{q_v^{\prime}},
\Deqlab{def_qv3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay10994}%
$\displaystyle - u^{\prime} \DP{q_r^{\prime}}{x}
     - v^{\prime} \DP{q_r^{\prime}}{y}
     - w^{\prime} \DP{q_r^{\prime}}{z}
     + \Dinv{\overline{\rho}} PR_r
     - CN_{vr}
     + D_{q_r^{\prime}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1446}%
$L_s$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1448}%
$_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath665}%
\begin{displaymath}
\frac{4}{3} \rho_I \pi ( r_d^3 - r_{aero}^3) N 
 = q_r^{\prime} \overline{\rho} 
 \Deqlab{CloudA}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1456}%
$\rho_I$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1460}%
$r_d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1462}%
$r_{aero}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1464}%
$N$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1466}%
$\rho_I = 1.565 \times 10^3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1468}%
$^3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath676}%
\begin{displaymath}
CN_{vr} 
 = \frac{4 \pi r_d N}{\overline{\rho} (R_h + R_m)} 
   (S - 1). 
    \Deqlab{CloudB}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1476}%
$R_h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1478}%
$R_m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1480}%
$S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11016}%
$\displaystyle R_h$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11018}%
$\displaystyle \frac{L_s^2}{k R_v T^2} = \frac{L_s^2}{k R_v \theta^2 \Pi^2},
 \Deqlab{CloudC}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11019}%
$\displaystyle R_m$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11021}%
$\displaystyle \frac{R_v T}{D p_{\ast}} = \frac{R_v \theta \Pi}{D p_{\ast}},
 \Deqlab{CloudD}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11022}%
$\displaystyle S$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11024}%
$\displaystyle \frac{p}{p_{\ast}} = \frac{{p_0}^{\frac{c_p}{R}} \Pi}{p_{\ast}}
 \Deqlab{CloudE}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1482}%
$k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1484}%
$D$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1486}%
$p_{\ast}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1490}%
$R_h \gg R_m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath702}%
\begin{displaymath}
CN_{vr} = \frac{4 \pi r_d N}{R_h} (S - 1). \Deqlab{CloudF}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath708}%
\begin{displaymath}
 p_{\ast} = \exp \left( A - \frac{B}{T - C} \right) \Deqlab{CloudG}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1494}%
$A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1496}%
$B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1498}%
$C$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1502}%
$A =
27.4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1504}%
$B = 3103$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1506}%
$C = -0.16$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1508}%
$O(T) \sim 150 $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1510}%
$T
\gg C$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath714}%
\begin{displaymath}
 p_{\ast} \approx \exp \left( A - \frac{B}{T} \right) \Deqlab{CloudH}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1512}%
$PR_r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath721}%
\begin{displaymath}
PR_r = \DP{}{z} \left( \rho_r V_{term} \right) \Deqlab{CloudI}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath728}%
\begin{displaymath}
V_{term} = C_{sc} \frac{2 r_d^2 g \rho_I}{9 \eta} \Deqlab{CloudJ}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1520}%
$C_{sc}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath736}%
\begin{displaymath}
C_{sc} = 1 + 1.255 \frac{\lambda}{r_d} \Deqlab{CloudK}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1522}%
$\lambda$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath742}%
\begin{displaymath}
\lambda = \frac{k_B T}{\sqrt{2} \pi \sigma^2 p_{CO_2}} \Deqlab{CloudL}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1526}%
$k_B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1528}%
$\sigma$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1532}%
$p_{CO_2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1536}%
$k_B = 1.38 \times 10^{-23}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1538}%
$^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1540}%
$^{-2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1544}%
$\sigma = 3.3 \times 10^{-10}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1546}%
$\eta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath753}%
\begin{displaymath}
\eta = \eta_{ref} \left( \frac{T_{ref} + C_{CO_2}}{T + C_{CO_2}} \right)
 \left( \frac{T}{T_{ref}} \right)^{3/2} \Deqlab{CloudM}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1548}%
$\eta_{ref}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1550}%
$T_{ref}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1552}%
$C_{CO_2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1556}%
$\eta_{ref} = 1.47 \times
10^{-5}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1558}%
$\cdot$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1560}%
$T_{ref} = 293$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1562}%
$C_{CO_2} = 240$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1566}%
$F_{net}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1254}%
\begin{displaymath}
  Q_{rad} = - \frac{1}{\overline{\rho} \langle c_{p} \rangle_0 }
            \DD{F_{net}}{z}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11083}%
$\displaystyle D_{u_{i}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11085}%
$\displaystyle - \DP{}{x_{j}} \overline{(u_{i}^{\prime} u_{j}^{\prime})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11087}%
$\displaystyle - \DP{}{x_{j}}
       \left[
          - K_{m} \left(\DP{u_{i}}{x_{j}}
	  	        + \DP{u_{j}}{x_{i}}\right)
	  + \frac{2}{3} \delta_{ij} E_{turb}
       \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1572}%
$K_{m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1574}%
$E_{turb}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11091}%
$\displaystyle E_{turb} = \frac{1}{2}
      \overline{(u^{\prime})^{2} + (v^{\prime})^{2} + (w^{\prime})^{2}}
      = \frac{{K_{m}}^{2}}{C_{m}^{2} l^{2}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1576}%
$C_{m} = 0.2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11095}%
$\displaystyle D_{\theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11097}%
$\displaystyle - \DP{}{x_{j}} \overline{u_{j}^{\prime} \theta^{\prime}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11099}%
$\displaystyle - \DP{}{x_{j}} \left(K_{h}\DP{\theta}{x_{j}}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11105}%
$\displaystyle - \DP{}{x_{j}} 
      \left[
       \left( 
        1 + \sum 
         \frac{L^2 \overline{q_v}}
              { \langle c_p \rangle_0 R_v
	        \overline{\Pi}^2 \overline{\theta}^2 }
       \right)^{-1}
       K_h \DP{\theta_e}{x_j}
      \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1578}%
$K_{h}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1580}%
$\theta_e$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11111}%
$\displaystyle \DP{E_{turb}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11113}%
$\displaystyle - u \DP{E_{turb}}{x} - v \DP{E_{turb}}{y} - w \DP{E_{turb}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11114}%
$\displaystyle - 3 g C_m l E_{turb}^{1/2} \frac{K_h}{\overline{\theta}}
    \DP{\theta}{z}
    - 3 g C_m l E_{turb}^{1/2} \frac{\sum \frac{R_v}{R_d} \DP{q_v}{z}
      - \sum \DP{ q_L }{z} }
    { 1 + \sum \frac{R_v}{R_d} \overline{q_v} - \sum \overline{q_L} }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11115}%
$\displaystyle + 2 C_m l E_{turb}^{1/2} \left\{
       \left( \DP{u}{x} \right)^{2}
     + \left( \DP{v}{y} \right)^{2}
     + \left( \DP{w}{z} \right)^{2}
    \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11116}%
$\displaystyle +  C_m l E_{turb}^{1/2}
    \left\{
     \left(\DP{u}{y} + \DP{v}{x}\right)^{2}
     + \left(\DP{v}{z} + \DP{w}{y}\right)^{2}
     + \left(\DP{w}{x} + \DP{u}{z}\right)^{2}
    \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11117}%
$\displaystyle - \frac{2}{3}
      E_{turb} \left( \DP{u}{x} + \DP{v}{y} + \DP{w}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11118}%
$\displaystyle + \DP{}{x} \left(C_m l E_{turb}^{1/2} \DP{E_{turb}}{x} \right)
     + \DP{}{y} \left(C_m l E_{turb}^{1/2} \DP{E_{turb}}{y} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11119}%
$\displaystyle + \DP{}{z} \left(C_m l E_{turb}^{1/2} \DP{E_{turb}}{z} \right)
      - \left(\frac{C_{\varepsilon}}{l}\right)
          E_{turb}^{\frac{3}{2}}.
 \Deqlab{kiso:TurbE}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11124}%
$\displaystyle - 3 g C_m l E_{turb}^{1/2}
        \left(
         1
          + \sum
           \frac{L^2 \overline{q_v}}{ \langle c_p \rangle_0 R_v
               \overline{\theta}^2 \overline{\Pi}^2 }
        \right)^{-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11125}%
$\displaystyle \left[
         \Dinv{\overline{\theta}}
         + \Dinv{R_d \overline{\Pi} \overline{\theta}^2}
           \left(
            1 + \sum \frac{R_v}{R_d} \overline{q_v} - \sum
	    \overline{q_L}
           \right)^{-1}
          \left( \sum L \overline{q_v} \right)
        \right]
        \DP{\theta_e}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11126}%
$\displaystyle + 3 g C_m l E_{turb}^{1/2}
         \left(
          1 + \sum \frac{R_v}{R_d} \overline{q_v} - \sum \overline{q_L}
         \right)^{-1}
        \DP{\left( \sum q_L \right)}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11131}%
$\displaystyle + \DP{}{z} \left(C_m l E_{turb}^{1/2} \DP{E_{turb}}{z} \right)
      - \left(\frac{C_{\varepsilon}}{l}\right)
          E_{turb}^{\frac{3}{2}}.
 \Deqlab{kiso:TurbE-moist}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1584}%
$l = \left(\Delta x \Delta y \Delta z
\right)^{1/3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1586}%
$\Delta x, \Delta y, \Delta z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath1045}%
\begin{displaymath}
  Q_{dis} = \frac{1}{\langle c_{p} \rangle_0 }\frac{C_{\varepsilon}}{l}
            \frac{K_{m}^{3}}{(C_{m}l)^{3}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1590}%
$C_{\varepsilon} = 0.2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1592}%
$l=(\Delta x \Delta y \Delta z)^{1/3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1756}%
$^{\prime}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1758}%
$\bf {107}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1760}%
$\bf {83}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1762}%
$\bf {162}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1764}%
$\bf {36}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1766}%
$\bf {164}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\appendix
\stepcounter{chapter}
\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3664}%
$T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3666}%
$p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11164}%
$\displaystyle \DD{u}{t} = - \Dinv{\rho}\DP{p}{x} + D_u 
  \Deqlab{equations:u}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11165}%
$\displaystyle \DD{v}{t} = - \Dinv{\rho}\DP{p}{y} + D_v 
  \Deqlab{equations:v}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11166}%
$\displaystyle \DD{w}{t} = - \Dinv{\rho}\DP{p}{z} -g + D_w
  \Deqlab{equations:w}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11168}%
$\displaystyle \hat{c_p} \DD{T}{t} - \Dinv{\rho} \DD{p}{t}
= \hat{c_p} \left( Q_{cond} + Q_{rad} + Q_{dis} \right) 
  \Deqlab{theta1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11170}%
$\displaystyle p_d$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11172}%
$\displaystyle \rho_d R_d T, 
    \Deqlab{equations:eqsdry}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11173}%
$\displaystyle p_v$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11175}%
$\displaystyle \rho_v R_v T. 
    \Deqlab{equations:eqsvapor}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11177}%
$\displaystyle \DP{\rho_d}{t} + \DP{}{x_j} (\rho_d u_j)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11179}%
$\displaystyle D_{\rho_d}, \Deqlab{renzoku1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11180}%
$\displaystyle \DP{\rho_v}{t} + \DP{}{x_j} (\rho_v u_j)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11182}%
$\displaystyle M_{src}(\rho_v) +
 D_{\rho_v}, \Deqlab{renzoku2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11183}%
$\displaystyle \DP{\rho_c}{t} + \DP{}{x_j} (\rho_c u_j)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11185}%
$\displaystyle M_{src}(\rho_c) +
 D_{\rho_c}, \Deqlab{renzoku3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11186}%
$\displaystyle \DP{\rho_r}{t} + \DP{}{x_j} (\rho_r u_j)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11188}%
$\displaystyle M_{src}(\rho_r) +
 M_{fall}(\rho_r) +  D_{\rho_r} \Deqlab{renzoku4}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3672}%
$\hat{c_p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3674}%
$Q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3680}%
$q_{r}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3682}%
$q_{v}, q_{r}, q_{c}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3696}%
$D_{\rho_d} + \sum D_{\rho_v} + \sum D_{\rho_c} + \sum D_{\rho_r} = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2019}%
\begin{displaymath}
\DP{\rho}{t} + \DP{}{x_j} (\rho u_j) = \sum M_{fall} (\rho_r)
 \Deqlab{renzoku5}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3698}%
$M_{src} (\rho_v) + M_{src} (\rho_c) + M_{src} (\rho_r) = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11206}%
$\displaystyle \DP{}{t} \left( \frac{\rho_d}{\rho} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11208}%
$\displaystyle - \frac{\rho_d}{\rho^2} \DP{\rho}{t} + \Dinv{\rho} \DP{\rho_d}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11210}%
$\displaystyle - \frac{\rho_d}{\rho^2} \left[ - \DP{}{x_j} (\rho u_j) + \sum
  M_{fall} (\rho_r) \right]
  + \Dinv{\rho} 
    \left[ - \DP{}{x_j} (\rho_d u_j) + D_{\rho_d} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11212}%
$\displaystyle - u_j \DP{}{x_j} \left( \frac{\rho_d}{\rho} \right)
    - \frac{\rho_d}{\rho^2} \sum M_{fall} (\rho_r)
    + \Dinv{\rho} D_{\rho_d}, 
  \Deqlab{sphm2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11213}%
$\displaystyle \DP{}{t} \left( \frac{\rho_v}{\rho} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11215}%
$\displaystyle - \frac{\rho_v}{\rho^2} \DP{\rho}{t} + \Dinv{\rho}
  \DP{\rho_v}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11217}%
$\displaystyle - \frac{\rho_v}{\rho^2} \left[ - \DP{}{x_j} (\rho u_j) + \sum
  M_{fall} (\rho_r) \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11218}%
$\displaystyle + \Dinv{\rho} \left[ - \DP{}{x_j} (\rho_v
  u_j) + M_{src} (\rho_v) + D_{\rho_v} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11220}%
$\displaystyle - u_j \DP{}{x_j} \left( \frac{\rho_v}{\rho} \right)
    - \frac{\rho_v}{\rho^2} \sum M_{fall} (\rho_r)
    + \Dinv{\rho} M_{src} (\rho_v)
    + \Dinv{\rho} D_{\rho_v}, 
    \Deqlab{sphm3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11221}%
$\displaystyle \DP{}{t} \left( \frac{\rho_c}{\rho} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11223}%
$\displaystyle - \frac{\rho_c}{\rho^2} \DP{\rho}{t} + \Dinv{\rho}
  \DP{\rho_c}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11225}%
$\displaystyle - \frac{\rho_c}{\rho^2} \left[ - \DP{}{x_j} (\rho u_j) + \sum
  M_{fall} (\rho_r) \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11226}%
$\displaystyle + \Dinv{\rho} \left[ - \DP{}{x_j} (\rho_c
  u_j) + M_{src} (\rho_c) + D_{\rho_c} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11228}%
$\displaystyle - u_j \DP{}{x_j} \left( \frac{\rho_c}{\rho} \right)
    - \frac{\rho_c}{\rho^2} \sum M_{fall} (\rho_r)
    + \Dinv{\rho} M_{src} (\rho_c)
    + \Dinv{\rho} D_{\rho_c}, 
   \Deqlab{sphm4}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11229}%
$\displaystyle \DP{}{t} \left( \frac{\rho_r}{\rho} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11231}%
$\displaystyle - \frac{\rho_r}{\rho^2} \DP{\rho}{t} + \Dinv{\rho}
 \DP{\rho_r}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11233}%
$\displaystyle - \frac{\rho_r}{\rho^2} \left[ - \DP{}{x_j} (\rho u_j) + \sum
  M_{fall} (\rho_r) \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11234}%
$\displaystyle + \Dinv{\rho} \left[ - \DP{}{x_j} (\rho_r u_j) + M_{src} (\rho_r)
  + M_{fall} (\rho_r) + D_{\rho_r} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11236}%
$\displaystyle - u_j \DP{}{x_j} \left( \frac{\rho_r}{\rho} \right)
    - \frac{\rho_r}{\rho^2} \sum M_{fall} + \Dinv{\rho}
    M_{src} (\rho_r) + \Dinv{\rho} M_{fall} (\rho_r)
    + \Dinv{\rho} D_{\rho_r}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11237}%
$\displaystyle \Deqlab{sphm5}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11239}%
$\displaystyle \DD{q_{d}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11241}%
$\displaystyle - \frac{q_{d}}{\rho} \sum M_{fall}(\rho_r)
     + \Dinv{\rho} D_{\rho_d}, 
     \Deqlab{sphm6}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11242}%
$\displaystyle \DD{q_{v}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11244}%
$\displaystyle - \frac{q_{v}}{\rho} \sum M_{fall}(\rho_r)
     + \Dinv{\rho} M_{src}(\rho_v)
     + \Dinv{\rho} D_{\rho_v}, 
     \Deqlab{sphm7}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11245}%
$\displaystyle \DD{q_{c}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11247}%
$\displaystyle - \frac{q_{c}}{\rho} \sum M_{fall}(\rho_r)
     + \Dinv{\rho} M_{src}(\rho_c)
     + \Dinv{\rho} D_{\rho_c}, 
     \Deqlab{sphm8}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11248}%
$\displaystyle \DD{q_r}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11250}%
$\displaystyle - \frac{q_r}{\rho} \sum M_{fall}(\rho_r)
     + \Dinv{\rho} M_{fall}(\rho_r) + \Dinv{\rho} M_{src}(\rho_r)
     + \Dinv{\rho} D_{\rho_r}.
     \Deqlab{sphm9}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3700}%
$q_d + \sum q_v + \sum q_c + \sum q_r = 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3704}%
$H_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3706}%
$U_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3708}%
$S_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3710}%
$v_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3712}%
$\mu_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3714}%
$p^{*}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11262}%
$\displaystyle \mu_c (p^{*}, T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11264}%
$\displaystyle \mu_v (p^{*}, T), 
 \Deqlab{Cl-Cl1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11265}%
$\displaystyle \mu_c (p^{*} + d p^{*}, T + d T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11267}%
$\displaystyle \mu_v (p^{*} + d p^{*}, T + d T), 
 \Deqlab{Cl-Cl2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11269}%
$\displaystyle \mu_c (p^{*} + d p^{*}, T + d T) - \mu_c (p^{*}, T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11271}%
$\displaystyle \mu_v (p^{*} + d p^{*}, T + d T) - \mu_v (p^{*}, T)
 \Deqlab{Cl-Cl3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3716}%
$\mu_v (p^{*} + d p^{*}, T + d T)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3718}%
$\mu_c (p^{*} + d p^{*}, T + d
T)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3720}%
$(p^{*}, T)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11277}%
$\textstyle \simeq$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11278}%
$\displaystyle \mu_c (p^{*}, T)
  + \left( \DP{\mu_c}{p^{*}} \right)_T d p^{*}
  + \left( \DP{\mu_c}{T} \right)_{p^{*}} d T, 
   \Deqlab{Cl-Cl4}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11281}%
$\displaystyle \mu_v (p^{*}, T)
  + \left( \DP{\mu_v}{p^{*}} \right)_T d p^{*}
  + \left( \DP{\mu_v}{T} \right)_{p^{*}} d T 
   \Deqlab{Cl-Cl5}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11283}%
$\displaystyle \left( \DP{\mu_c}{p^{*}} \right)_T d p^{*}
 + \left( \DP{\mu_c}{T} \right)_{p^{*}} d T
 =
  \left( \DP{\mu_v}{p^{*}} \right)_T d p^{*}
  + \left( \DP{\mu_v}{T} \right)_{p^{*}} d T 
   \Deqlab{Cl-Cl6}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11285}%
$\displaystyle \left( \DP{\mu_i}{T} \right)_p$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11287}%
$\displaystyle - S_i, 
   \Deqlab{Cl-Cl7}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11288}%
$\displaystyle \left( \DP{\mu_i}{p} \right)_T$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11290}%
$\displaystyle v_i, 
   \Deqlab{Cl-Cl8}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11292}%
$\displaystyle v_c d p^{*}
 - s_c d T
 =
 v_v d p^{*}
 - s_v d T,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11294}%
$\displaystyle \DD{p^{*}}{T}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11296}%
$\displaystyle \frac{s_v - s_c}{v_v - v_c}
   \Deqlab{Cl-Cl9}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3722}%
$L$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11299}%
$\displaystyle L$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11301}%
$\displaystyle T (s_v - s_c)
   \Deqlab{Cl-Cl10}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11305}%
$\displaystyle \frac{L}{T(v_v - v_c)}
   \Deqlab{Cl-Cl11}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3724}%
$v_v \gg v_c$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11310}%
$\displaystyle \frac{L}{T v_v}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11312}%
$\displaystyle \frac{L p^{*}}{R_v T^2}
   \Deqlab{Cl-Cl12}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11315}%
$\displaystyle c_{pi} = T \left( \DP{S_i}{T} \right)_p
 \Deqlab{thermodyn1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11317}%
$\displaystyle - \left( \DP{S_i}{p} \right)_T
 = \left( \DP{v_i}{T} \right)_p
 \Deqlab{thermodyn2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11319}%
$\displaystyle c_{pi} (p,T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11321}%
$\displaystyle c_{pi} (p_0,T) 
   + \int_{p_0}^{p} \left( \DP{c_{pi}}{p^{\prime}} \right)_T d
   p^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11323}%
$\displaystyle c_{pi} (p_0,T) 
   + \int_{p_0}^{p} 
    \left\{ \DP{}{p^{\prime}}
     \left[
      T \left( \DP{S_i}{T} \right)_{p^{\prime}} 
     \right]_T
    \right\} d p^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11325}%
$\displaystyle c_{pi} (p_0,T) 
   + T \int_{p_0}^{p} 
     \left[ \DP{}{T}
       \left( \DP{S_i}{p^{\prime}} \right)_{T} 
     \right]_{p^{\prime}}
    d p^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11327}%
$\displaystyle c_{pi} (p_0,T) 
   - T \int_{p_0}^{p} 
     \left( \DP[2]{v_i}{T} \right)_{p^{\prime}}
    d p^{\prime}
 \Deqlab{thermodyn3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3726}%
$p_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3728}%
$( \partial^2 v_i / \partial
T^2 )_p = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11333}%
$\displaystyle c_{pi} (p_0,T) 
 \Deqlab{thermodyn4}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11335}%
$\displaystyle d H_i$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11337}%
$\displaystyle T d S_i + v_i d p + \mu_i d q_i$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11339}%
$\displaystyle T \left[ 
     \left( \DP{S_i}{T} \right)_p d T  
     + \left( \DP{S_i}{p} \right)_T d p  
    \right]
   + v_i d p + \mu_i d q_i$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11341}%
$\displaystyle T  \left( \DP{S_i}{T} \right)_p d T  
   + \left[
      T \left( \DP{S_i}{p} \right)_T d p + v_i
     \right] d p
   + \mu_i d q_i
 \Deqlab{thermodyn5}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11343}%
$\displaystyle \left( \DP{H_i}{T} \right)_p$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11345}%
$\displaystyle T  \left( \DP{S_i}{T} \right)_p,  
  \Deqlab{thermodyn6}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11346}%
$\displaystyle \left( \DP{H_i}{p} \right)_T$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11348}%
$\displaystyle T \left( \DP{S_i}{p} \right)_T d p + v_i
  \Deqlab{thermodyn7}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3730}%
$T_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11351}%
$\displaystyle H_i (p,T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11353}%
$\displaystyle H_i (p_0, T_0) 
   + \int_{T_0}^{T} \left( \DP{H_i}{T^{\prime}} \right)_{p_0} 
   d T^{\prime}
   + \int_{p_0}^{p} \left( \DP{H_i}{p^{\prime}} \right)_{T} 
   d p^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11355}%
$\displaystyle H_i (p_0, T_0) 
   + \int_{T_0}^{T} T^{\prime} \left( \DP{S_i}{T^{\prime}} \right)_{p_0} 
   d T^{\prime}
   + \int_{p_0}^{p} 
    \left[
     T \left( \DP{S_i}{p^{\prime}} \right)_{T} + v_i 
    \right]
   d p^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11357}%
$\displaystyle H_i (p_0, T_0) 
   + \int_{T_0}^{T} c_{pi} (p_0, T^{\prime})
   d T^{\prime}
   + \int_{p_0}^{p} 
    \left[
     - T \left( \DP{v_i}{T} \right)_{p^{\prime}} + v_i 
    \right]
   d p^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11359}%
$\displaystyle H_i (p_0, T_0) 
   + \int_{T_0}^{T} c_{pi} (p_0, T^{\prime})
     d T^{\prime}
   - T^2 \int_{p_0}^{p} 
    \left[
     \Dinv{T} \left( \DP{v_i}{T} \right)_{p^{\prime}}
     - \frac{v_i}{T^2} 
    \right]
     d p^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11361}%
$\displaystyle H_i (p_0, T_0) 
   + \int_{T_0}^{T} c_{pi} (p_0, T^{\prime})
     d T^{\prime}
   - T^2 \int_{p_0}^{p} 
    \left\{ \DP{}{T}
      \left[ \frac{v_i (p^{\prime}, T)}{T} \right]_{p^{\prime}}
    \right\}
   d p^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11362}%
$\displaystyle \Deqlab{thermodyn8}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3732}%
$\partial (v_i / T)_{p} / \partial T
= 0 $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11367}%
$\displaystyle H_i (p_0, T_0) 
   + \int_{T_0}^{T} c_{pi} (p_0, T^{\prime})
     d T^{\prime}
 \Deqlab{thermodyn9}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3734}%
$H_c$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3736}%
$H_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11372}%
$\displaystyle H_c (p, T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11374}%
$\displaystyle \mu_c (p, T) + T S_c (p, T), 
 \Deqlab{thermodyn10}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11375}%
$\displaystyle H_v (p, T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11377}%
$\displaystyle \mu_v (p, T) + T S_v (p, T)
 \Deqlab{thermodyn11}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11379}%
$\displaystyle H_c (p, T) - H_v (p, T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11381}%
$\displaystyle \mu_c (p, T) - \mu_v (p, T) 
  + T \left[ S_c (p, T) - S_v (p, T) \right]
 \Deqlab{thermodyn12}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11383}%
$\displaystyle S_i (p, T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11385}%
$\displaystyle - \left( \DP{\mu_i}{T} \right)_p
 \Deqlab{thermodyn13}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11389}%
$\displaystyle \mu_c (p, T) - \mu_v (p, T) 
  - T \DP{}{T} \left[ \mu_c (p, T) - \mu_v (p, T) \right]_p$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11390}%
$\displaystyle \Deqlab{thermodyn14}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3740}%
$i=v, c$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11395}%
$\displaystyle \mu_c (p, T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11397}%
$\displaystyle \mu_c (p^{*}, T) 
  + \int_{p^{*}}^{p} v_c (p^{\prime}, T) d p^{\prime}, 
 \Deqlab{thermodyn15}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11398}%
$\displaystyle \mu_v (p, T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11400}%
$\displaystyle \mu_v (p^{*}, T) 
  + \int_{p^{*}}^{p} v_v (p^{\prime}, T) d p^{\prime}
 \Deqlab{thermodyn16}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3746}%
$\mu_c (p^{*}, T)
= \mu_v (p^{*}, T) $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11403}%
$\displaystyle \mu_c (p, T) 
 - \mu_v (p, T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11405}%
$\displaystyle - \int_{p^{*}}^{p} 
    \left[ v_v (p^{\prime}, T) - v_c (p^{\prime}, T) \right]
    d p^{\prime}
 \Deqlab{thermodyn17}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3748}%
$\mu_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3750}%
$\mu_c$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11411}%
$\displaystyle - \int_{p^{*}}^{p} 
    \left[ v_v (p^{\prime}, T) - v_c (p^{\prime}, T) \right]
    d p^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11412}%
$\displaystyle + T \DP{}{T} 
    \left[  
     \int_{p^{*}}^{p} 
      \left[ v_v (p^{\prime}, T) - v_c (p^{\prime}, T) \right]
      d p^{\prime}
    \right]_p$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11414}%
$\displaystyle - \int_{p^{*}}^{p} 
      v_v (p^{\prime}, T) d p^{\prime}
  + T \DP{}{T} 
    \left[  
     \int_{p^{*}}^{p} 
       v_v (p^{\prime}, T) d p^{\prime}
    \right]_p$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11416}%
$\displaystyle - \int_{p^{*}}^{p} 
      v_v (p^{\prime}, T) d p^{\prime}
  + T \int_{p^{*}}^{p} 
      \DP{ v_v (p^{\prime}, T)}{T} d p^{\prime}
  - T \DD{p^{*}}{T} v_v (p^{*}, T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11418}%
$\displaystyle - \int_{p^{*}}^{p} 
      v_v (p^{\prime}, T) d p^{\prime}
   +  \int_{p^{*}}^{p} 
      v_v (p^{\prime}, T) d p^{\prime}
  - L(T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11420}%
$\displaystyle - L(T)
 \Deqlab{thermodyn18}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3752}%
$c_{pc}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11424}%
$\displaystyle c_{pc} (p, T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11426}%
$\displaystyle T \left( \DP{S_c}{T} \right)_p$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11428}%
$\displaystyle T 
   \left\{ 
    \DP{}{T} \left[ \frac{H_c (p, T) - \mu_c (p, T)}{T} \right] 
   \right\}_p$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11430}%
$\displaystyle T 
   \left[
    - \frac{S_c}{T} 
    + \Dinv{T} \left( \DP{H_c}{T} \right)_p
    + \Dinv{T} \left( \DP{\mu_c}{T} \right)_p
   \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11432}%
$\displaystyle \left( \DP{H_c}{T} \right)_p$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11434}%
$\displaystyle \DP{}{T} 
   \left[ H_v (p, T) - L(T) \right]_p$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11436}%
$\displaystyle \DP{}{T}
   \left[ 
    H_v (p_0, T_0) 
    + \int_{T_0}^{T} c_{pv} (p_0, T^{\prime}) d T^{\prime}
    - L(T)  
   \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11438}%
$\displaystyle c_{pv} (p_0, T) - \DD{L}{T}
 \Deqlab{thermodyn19}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11441}%
$\displaystyle L(T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11443}%
$\displaystyle L(T_0) + \left( c_{pv} - c_{pc} \right) (T - T_0)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11445}%
$\displaystyle L_{00} + \left( c_{pv} - c_{pc} \right) T
 \Deqlab{thermodyn20}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11447}%
$\displaystyle L_{00}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11449}%
$\displaystyle L (T_0) - \left( c_{pv} - c_{pc} \right) T_0
 \Deqlab{thermodyn21}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11451}%
$\displaystyle H_d (p, T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11453}%
$\displaystyle H_d (p_0, T_0)
  + \int_{T_0}^{T} c_{pd} (p_0, T_0) d T^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11455}%
$\displaystyle H_d (p_0, T_0) + c_{pd} (T - T_0)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11457}%
$\displaystyle c_{pd} T, 
  \Deqlab{thermodyn22}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11460}%
$\displaystyle H_v (p, T) - L(T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11462}%
$\displaystyle H_v (p_0, T_0)
  + \int_{T_0}^{T} c_{pv} (p_0, T^{\prime}) d T^{\prime}
  - L(T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11464}%
$\displaystyle H_v (p_0, T_0)
  + \int_{T_0}^{T} 
    \left[ 
     c_{pc} (p_0, T^{\prime}) + \DD{L}{T^{\prime}} 
    \right] d T^{\prime}
  - L(T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11466}%
$\displaystyle H_v (p_0, T_0) - L(T_0) + c_{pc} (T - T_0)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11468}%
$\displaystyle H_c (p_0, T_0) - c_{pc} T_0 + c_{pc} T$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11470}%
$\displaystyle c_{pc} T
  \Deqlab{thermodyn23}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11473}%
$\displaystyle H_c (p, T) + L(T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11475}%
$\displaystyle c_{pc} T + L_{00} + (c_{pv} - c_{pc}) T$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11477}%
$\displaystyle c_{pv} T + L_{00}
  \Deqlab{thermodyn24}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11480}%
$\displaystyle U_i (p, T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11482}%
$\displaystyle H_i (p, T) - p v_i (p, T)
  \Deqlab{thermodyn25}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11484}%
$\displaystyle U_d (p, T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11486}%
$\displaystyle H_d (p, T) - p v_d (p, T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11488}%
$\displaystyle c_{pd} T - R_d T$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11490}%
$\displaystyle c_{vd} T, 
  \Deqlab{thermodyn26}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11491}%
$\displaystyle U_v (p, T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11493}%
$\displaystyle H_v (p, T) - p v_v (p, T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11495}%
$\displaystyle c_{pv} T + L_{00}- R_v T$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11497}%
$\displaystyle c_{vv} T + L_{00}, 
  \Deqlab{thermodyn27}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11498}%
$\displaystyle U_c (p, T)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11500}%
$\displaystyle U_v (p, T) + H_c (p, T) - H_v (p, T) - p (v_c - v_v)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11502}%
$\displaystyle U_v (p, T) + H_c (p, T) - H_v (p, T) + p v_v$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11506}%
$\displaystyle c_{pc} T
  \Deqlab{thermodyn28}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3758}%
$U$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2683}%
\begin{displaymath}
 \rho \DD{U}{t}
  + \nabla \cdot \Dvect{F}^{rad}
  + \nabla \cdot \Dvect{F}^{therm}
 =
  - p \nabla \cdot \Dvect{u}
  + \varepsilon
 \Deqlab{netu1}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3760}%
$F_i^{rad}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3762}%
$F_i^{therm}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3764}%
$\varepsilon$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11514}%
$\displaystyle \Dvect{F}^{therm}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11516}%
$\displaystyle H_d \Dvect{i}_d + \sum H_v \Dvect{i}_v - \kappa \nabla T$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11518}%
$\displaystyle c_{pd} T \Dvect{i}_d 
   + \sum \left(c_{pv} T + L_{00} \right) \Dvect{i}_v 
   - \kappa \nabla T, 
 \Deqlab{netu1-A}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11519}%
$\displaystyle \varepsilon$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11521}%
$\displaystyle \Dinv{2} \eta 
    \left( 
     \DP{u_i}{x_j} + \DP{u_j}{x_i} 
      - \frac{2}{3} \delta_{ij} \nabla \cdot \Dvect{u} \right)^2
   + \zeta \left( \nabla \cdot \Dvect{u} \right)^2
 \Deqlab{netu1-B}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3766}%
$H_d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3770}%
$\Dvect{i}_d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3772}%
$\Dvect{i}_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3774}%
$\kappa$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3778}%
$\zeta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3780}%
$L_{00}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3782}%
$L(T)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2721}%
\begin{displaymath}
L_{00} = L(T) - (c_{pv} - c_{pc}) T
  \Deqlab{netu5}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3786}%
$H$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2727}%
\begin{displaymath}
U = H - \frac{p}{\rho}
  \Deqlab{netu2}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3788}%
$dH/dt$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11537}%
$\displaystyle \rho \DD{H}{t}
  + \frac{p}{\rho} \DD{\rho}{t}
  - \DD{p}{t}
  + \nabla \cdot \Dvect{F}^{rad}
  + \nabla \cdot \Dvect{F}^{therm}
  + p \DP{u_i}{x_i}
  - \varepsilon$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11539}%
$\displaystyle \rho \DD{H}{t}
  - p \DP{u_i}{x_i}
  - \DD{p}{t}
  + \nabla \cdot \Dvect{F}^{rad}
  + \nabla \cdot \Dvect{F}^{therm}
  + p \DP{u_i}{x_i}
  - \varepsilon$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11541}%
$\displaystyle \rho \DD{H}{t}
  - \DD{p}{t}
  + \nabla \cdot \Dvect{F}^{rad}
  + \nabla \cdot \Dvect{F}^{therm}
  - \varepsilon$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11545}%
$\displaystyle \DD{H}{t}
 = 
  \Dinv{\rho} 
   \left( 
    \DD{p}{t}
    - \nabla \cdot \Dvect{F}^{rad}
    - \nabla \cdot \Dvect{F}^{therm}
    + \varepsilon
   \right)
  \Deqlab{netu3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11547}%
$\displaystyle H$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11549}%
$\displaystyle q_d H_d + \sum q_v H_v + \sum q_c H_c$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11551}%
$\displaystyle q_d c_{pd} T + \sum q_v \left( c_{pv} T + L_{00} \right)
  + \sum q_c c_{pc} T
  \Deqlab{netu4}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11553}%
$\displaystyle \DD{H}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11555}%
$\displaystyle \left(q_d c_{pd} + \sum q_v c_{pv} + \sum q_c c_{pc} \right) \DD{T}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11556}%
$\displaystyle + c_{pd} T \DD{q_d}{t} 
    + \sum \left( c_{pv} T + L_{00} \right) \DD{q_v}{t} 
    + \sum c_{pc} T \DD{q_c}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11558}%
$\displaystyle \hat{c_p} \DD{T}{t}
    + c_{pd} T \DD{q_d}{t} 
    + \sum \left( c_{pv} T + L_{00} \right) \DD{q_v}{t} 
    + \sum c_{pc} T \DD{q_c}{t}
  \Deqlab{netu6}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2823}%
\begin{displaymath}
\hat{c_p}
 = q_d c_{pd} + \sum q_v c_{pv} + \sum q_c c_{pc}
  \Deqlab{netu7}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3790}%
$\hat{c_p} dT/dt$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11562}%
$\displaystyle \hat{c_p} \DD{T}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11564}%
$\displaystyle \Dinv{\rho}
  \left(
  \DD{p}{t}
  - \nabla \cdot \Dvect{F}^{rad}
  - \nabla \cdot \Dvect{F}^{therm}
  + \varepsilon
  \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11565}%
$\displaystyle - c_{pd} T \DD{q_d}{t} 
    - \sum \left( c_{pv} T + L_{00} \right) \DD{q_v}{t} 
    - \sum c_{pc} T \DD{q_c}{t}
  \Deqlab{netu8}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11569}%
$\displaystyle \Dinv{\rho} D_{\rho_d}, 
     \Deqlab{sphm6-A}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11572}%
$\displaystyle \Dinv{\rho} M_{src}(\rho_v)
     + \Dinv{\rho} D_{\rho_v}, 
     \Deqlab{sphm7-A}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11575}%
$\displaystyle - \Dinv{\rho} M_{src}(\rho_v)
     + \Dinv{\rho} D_{\rho_c}, 
     \Deqlab{sphm8-A}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3792}%
$D_{\rho_d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3794}%
$D_{\rho_v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3796}%
$D_{\rho_c}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11580}%
$\displaystyle D_{\rho_d}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11582}%
$\displaystyle - \nabla \cdot \Dvect{i}_d, 
  \Deqlab{DiffFlux1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11583}%
$\displaystyle D_{\rho_v}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11585}%
$\displaystyle - \nabla \cdot \Dvect{i}_v, 
  \Deqlab{DiffFlux2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11586}%
$\displaystyle D_{\rho_c}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11588}%
$\displaystyle 0
  \Deqlab{DiffFlux3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11592}%
$\displaystyle - \Dinv{\rho} \nabla \cdot \Dvect{i}_d, 
     \Deqlab{sphm6-B}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11595}%
$\displaystyle \Dinv{\rho} M_{src}(\rho_v)
     - \Dinv{\rho} \nabla \cdot \Dvect{i}_v,  
     \Deqlab{sphm7-B}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11598}%
$\displaystyle - \Dinv{\rho} M_{src}(\rho_v)
     \Deqlab{sphm8-B}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11603}%
$\displaystyle + \Dinv{\rho} c_{pd} T \nabla \cdot \Dvect{i}_d 
    - \Dinv{\rho} 
      \sum \left( c_{pv} T + L_{00} \right) 
      \left[ M_{src} (\rho_v) - \nabla \cdot \Dvect{i}_v \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11604}%
$\displaystyle + \Dinv{\rho} \sum c_{pc} T M_{src} (\rho_v)
  \Deqlab{netu9}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11608}%
$\displaystyle \Dvect{i}_d + \sum \Dvect{i}_v$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11610}%
$\displaystyle 0
 \Deqlab{netu10}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11611}%
$\displaystyle \Dvect{i}_v$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11613}%
$\displaystyle - \rho D_v 
     \left( 
      \nabla q_v + \frac{k_T}{T} \nabla T + \frac{k_p}{p} \nabla p
     \right)
 \Deqlab{netu11}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3802}%
$D_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3804}%
$k_T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3806}%
$k_p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3808}%
$q_v \rightarrow 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3810}%
$q_v \rightarrow 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11624}%
$\displaystyle - \rho D_v \nabla q_v 
 \Deqlab{netu11-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3816}%
$\Dvect{F}^{therm}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11631}%
$\displaystyle \Dinv{\rho} \DD{p}{t}
  - \Dinv{\rho} \nabla \cdot \Dvect{F}^{rad}
  - \Dinv{\rho} \nabla \cdot \Dvect{F}^{therm}
  + \frac{\varepsilon}{\rho}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11632}%
$\displaystyle + \Dinv{\rho} c_{pd} T \nabla \cdot \Dvect{i}_d 
    + \Dinv{\rho} 
      \sum \left( c_{pv} T + L_{00} \right) 
      \nabla \cdot \Dvect{i}_v$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11633}%
$\displaystyle - \Dinv{\rho} 
    \sum 
      \left[
       L_{00} + \left( c_{pv} - c_{pc} \right) T 
      \right] M_{src} (\rho_v)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11635}%
$\displaystyle \Dinv{\rho} \DD{p}{t}
  - \Dinv{\rho} \nabla \cdot \Dvect{F}^{rad}
  + \frac{\varepsilon}{\rho}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11636}%
$\displaystyle - \Dinv{\rho} \nabla \cdot 
    \left[
     c_{pd} T \Dvect{i}_d 
     + \sum \left(c_{pv} T + L_{00} \right) \Dvect{i}_v 
     - \kappa \nabla T
    \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11638}%
$\displaystyle - \Dinv{\rho} 
    \sum 
       L M_{src} (\rho_v)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11640}%
$\displaystyle \Dinv{\rho} \DD{p}{t}
  - \Dinv{\rho} \nabla \cdot \Dvect{F}^{rad}
  + \frac{\varepsilon}{\rho} 
  + \Dinv{\rho} \nabla \cdot \left( \kappa \nabla T \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11641}%
$\displaystyle - \Dinv{\rho} \Dvect{i}_d \cdot \nabla \left( c_{pd} T \right) 
    - \Dinv{\rho} \sum \Dvect{i}_v \cdot
      \nabla \left( c_{pv} T + L_{00} \right) 
   - \Dinv{\rho} 
    \sum 
       L M_{src} (\rho_v)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11644}%
$\displaystyle + \Dinv{\rho} \sum \Dvect{i}_v \cdot \nabla \left( c_{pd} T \right) 
    - \Dinv{\rho} \sum \Dvect{i}_v \cdot
      \nabla \left( c_{pv} T \right) 
  - \Dinv{\rho} 
    \sum 
       L M_{src} (\rho_v)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11647}%
$\displaystyle - \sum D_v \nabla q_v \cdot
      \nabla \left[ ( c_{pd} - c_{pv} ) T \right]
  - \Dinv{\rho} 
    \sum 
       L M_{src} (\rho_v)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11648}%
$\displaystyle \Deqlab{netu12}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11650}%
$\displaystyle \hat{c_p} Q_{rad}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11652}%
$\displaystyle - \Dinv{\rho} \nabla \cdot \Dvect{F}^{rad}, 
      \Deqlab{netu13}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11653}%
$\displaystyle \hat{c_p} Q_{dis}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11655}%
$\displaystyle \frac{\varepsilon}{\rho}, 
      \Deqlab{netu14}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11656}%
$\displaystyle \hat{c_p} Q_{cond}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11658}%
$\displaystyle - \Dinv{\rho} L M_{src} (\rho_v), 
      \Deqlab{netu15}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11659}%
$\displaystyle \hat{c_p} D_{T}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11661}%
$\displaystyle \Dinv{\rho} \nabla \cdot \left( \kappa \nabla T \right)
    - \sum D_v \nabla q_v \cdot
      \nabla \left[ ( c_{pd} - c_{pv} ) T \right]
  \Deqlab{netu16}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3088}%
\begin{displaymath}
\hat{c_p} \DD{T}{t} - \Dinv{\rho} \DD{p}{t}
 =
  \hat{c_p} \left( Q_{cond} + Q_{rad} + Q_{dis} \right)
  + \hat{c_p} D_{T}
  \Deqlab{netu17}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11665}%
$\displaystyle p$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11667}%
$\displaystyle p_d + \sum p_v$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11669}%
$\displaystyle \left( \rho_d R_d + \sum \rho_v R_v \right) T$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11671}%
$\displaystyle \left( \rho_d + \sum \rho_v \right)
   \frac{q_d R_d + \sum q_v R_v}{q_d + \sum q_v} T.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11673}%
$\displaystyle \langle R \rangle$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11675}%
$\displaystyle \frac{ q_d R_d + \sum q_v R_v}{ q_d + \sum q_v}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11676}%
$\displaystyle \rho_g$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11678}%
$\displaystyle \rho_d + \sum \rho_v$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11680}%
$\displaystyle p = \rho_g \langle R \rangle T
 \Deqlab{theta7}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3828}%
$R_{\ast}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11686}%
$\displaystyle \langle M \rangle$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11688}%
$\displaystyle \frac{R_{\ast}}{\langle R \rangle}
 = 
  \frac{q_d + \sum q_v}{q_d / M_d + \sum q_v / M_v} 
 \Deqlab{Tfaa}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3125}%
\begin{displaymath}
T_v \equiv \left( \frac{\langle M \rangle_0}{M_d} q_d
     + \sum \frac{\langle M \rangle_0}{ M_v } q_v
         \right) T \Deqlab{Tfb}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11700}%
$\displaystyle \rho_g \langle R \rangle T$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11702}%
$\displaystyle \rho_g \langle R \rangle_0 T$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11704}%
$\displaystyle \rho \langle R \rangle_0 
    \frac{\rho_g \langle R \rangle_0}{\rho \langle R \rangle_0} T$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11706}%
$\displaystyle \rho \langle R \rangle_0 
    \frac{ \rho_d R_d + \sum \rho_v R_v }
         {\rho \langle R \rangle_0 } T$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11708}%
$\displaystyle \rho \langle R \rangle_0
    \left( \frac{\langle M \rangle_0}{M_d} q_d
     + \sum \frac{\langle M \rangle_0}{ M_v } q_v
         \right) T$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11710}%
$\displaystyle \rho \langle R \rangle_0 T_v
  \Deqlab{TfA}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11713}%
$\displaystyle \theta 
 \equiv 
  T \left( \frac{p_{0}}{p} \right)^{ \frac{ \langle R \rangle_0}
   {\langle c_{p} \rangle_0} } 
 \Deqlab{theta4}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11715}%
$\displaystyle \Pi 
 \equiv \frac{T}{\theta}
 = \left( \frac{p}{p_{0}} \right)^{ \frac{ \langle R \rangle_0}
   {\langle c_{p} \rangle_0} }
 \Deqlab{theta5}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3160}%
\begin{displaymath}
\theta_v 
 \equiv \frac{T_v}{\Pi} 
 =  \left( \frac{\langle M \rangle_0}{M_d} q_d
     + \sum \frac{\langle M \rangle_0}{ M_v } q_v
         \right) \theta
 \Deqlab{Tfd}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11720}%
$\displaystyle \rho \langle R \rangle_0 \Pi \theta_v \Deqlab{Tff}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11722}%
$\displaystyle \langle c_p \rangle$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11724}%
$\displaystyle \frac{q_d c_{pd} + \sum q_v c_{pv}}{
 q_d + \sum q_v } 
 \Deqlab{cp-def}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3852}%
$\langle
c_{p} \rangle_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11733}%
$\displaystyle \rho 
 = \frac{
    p_{0} \Pi^{ \langle c_v \rangle_0 / \langle R \rangle_0}}
     { \langle R \rangle_0 \theta_v}
 = \frac{p_0 \Pi^{\langle c_v \rangle_0 / \langle R
   \rangle_0 } }{
    \langle R \rangle_0 \left( q_d  \langle M \rangle_0 / M_d
    + \sum q_v \langle M \rangle_0 / M_v \right) \theta }
 \Deqlab{Tfg}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3858}%
$q_d c_{pd} \gg q_c c_{pc}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3860}%
$q_d c_{pv} \gg q_c c_{pc}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3862}%
$\hat{c_p} \approx \langle c_p \rangle$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3200}%
\begin{displaymath}
\langle c_p \rangle \DD{T}{t} - \Dinv{\rho} \DD{p}{t}
\approx \langle c_p \rangle \left( Q_{cond} + Q_{rad} + Q_{dis} \right)
 \Deqlab{theta2}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3211}%
\begin{displaymath}
\langle c_p \rangle_0 \DD{T}{t} - \Dinv{\rho} \DD{p}{t}
\approx \langle c_p \rangle_0 \left( Q_{cond} + Q_{rad} + Q_{dis} \right)
 \Deqlab{theta2-1}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3222}%
\begin{displaymath}
\langle c_p \rangle_0 \DD{T}{t} - \Dinv{\rho_g} \DD{p}{t}
\approx \langle c_p \rangle_0 \left( Q_{cond} + Q_{rad} + Q_{dis} \right) 
 \Deqlab{theta3}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11743}%
$\displaystyle \DD{\theta}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11745}%
$\displaystyle \left( \frac{p_{0}}{p} \right)^{ \frac{ \langle R \rangle_0}
   {\langle c_{p} \rangle} } \DD{T}{t}
   - \frac{ \langle R \rangle_0 }{ \langle c_p \rangle_0} 
     \frac{T}{p} 
    \left( \frac{p_{0}}{p} \right)^{ \frac{ \langle R \rangle_0}
    {\langle c_{p} \rangle} } \DD{p}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11747}%
$\displaystyle \frac{\theta}{ \langle c_p \rangle_0 T }
    \left(
     \langle c_p \rangle_0 \DD{T}{t} - \Dinv{\rho_g} \DD{p}{t}
    \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11749}%
$\displaystyle \frac{ Q_{cond} + Q_{rad} + Q_{dis} }{\Pi}
 \Deqlab{theta6}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3866}%
$p = \rho_g \langle R \rangle_0 T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11752}%
$\displaystyle \DD{\theta}{t}
 = \Dinv{\Pi} \left( Q_{cond} + Q_{rad} + Q_{dis} \right) + D_{\theta}
 \Deqlab{theta8}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11755}%
$\displaystyle d \theta$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11757}%
$\displaystyle \Dinv{\Pi} Q_{cond}
  = - \sum \frac{L}{\Pi \langle c_p \rangle_0} M_{src} (\rho_v), 
 \Deqlab{epot1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11758}%
$\displaystyle d q_v$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11760}%
$\displaystyle \Dinv{\rho} M_{src} (\rho_v)
 \Deqlab{epot2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3868}%
$d q_v / q_v \gg d \Pi / \Pi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11764}%
$\displaystyle d \theta
 \simeq
  \sum \frac{L q_v}{\Pi \langle c_p \rangle}_0
\Deqlab{epot3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11766}%
$\displaystyle \theta_e
 =
 \theta + \sum \frac{L q_v}{\Pi \langle c_p \rangle}_0
\Deqlab{epot4}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11770}%
$\displaystyle \DD{\rho}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11772}%
$\displaystyle \DD{}{t} \left[ \frac{p_0 \Pi^{\langle c_v \rangle_0 / \langle R
   \rangle}}{
    \langle R \rangle_0 \left( q_d  \langle M \rangle_0 / M_d
    + \sum q_v \langle M \rangle_0 / M_v \right) \theta }
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11774}%
$\displaystyle \frac{p_0 \Pi^{(\langle c_v \rangle_0 - 1) / \langle R
   \rangle}}{
    \langle R \rangle_0 \left( q_d  \langle M \rangle_0 / M_d
    + \sum q_v \langle M \rangle_0 / M_v \right) \theta }
    \frac{\langle c_v \rangle_0}{\langle R \rangle_0}
    \DD{\Pi}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11775}%
$\displaystyle - \frac{p_0 \Pi^{\langle c_v \rangle_0 / \langle R
   \rangle}}{
    \langle R \rangle_0 \left( q_d  \langle M \rangle_0 / M_d
    + \sum q_v \langle M \rangle_0 / M_v \right) \theta^2 } 
      \DD{\theta}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11776}%
$\displaystyle - \frac{p_0 \Pi^{\langle c_v \rangle_0 / \langle R
   \rangle}}{
    \langle R \rangle_0 \left( q_d  \langle M \rangle_0 / M_d
    + \sum q_v \langle M \rangle_0 / M_v \right)^2 \theta }
   \left( \frac{\langle M \rangle_0}{M_d} \DD{q_d}{t}
    + \sum \frac{\langle M \rangle_0}{M_v} \DD{q_v}{t}  \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11778}%
$\displaystyle \langle c_p \rangle_0 \theta_v
\left( \frac{\langle c_v \rangle_0}{\langle c_p \rangle_0 \langle R \rangle_0
 \Pi \theta_v} \right)
\rho \DD{\Pi}{t}
- \frac{\rho}{\theta} \DD{\theta}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11779}%
$\displaystyle - \frac{\rho}{q_d  \langle M \rangle_0 / M_d
    + \sum q_v \langle M \rangle_0 / M_v}
\left( \frac{\langle M \rangle_0}{M_d} \DD{q_d}{t}
    + \sum \frac{\langle M \rangle_0}{M_v} \DD{q_v}{t}  \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11781}%
$\displaystyle \frac{\langle c_p \rangle_0 \rho \theta_v}{\langle c_s \rangle^2}
 \DD{\Pi}{t}
- \frac{\rho}{\theta} \DD{\theta}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11782}%
$\displaystyle - \frac{\rho}{q_d  \langle M \rangle_0 / M_d
    + \sum q_v \langle M \rangle_0 / M_v}
\left( \frac{\langle M \rangle_0}{M_d} \DD{q_d}{t}
    + \sum \frac{\langle M \rangle_0}{M_v} \DD{q_v}{t}  \right).
\Deqlab{pressure:theta-pi:drho}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3370}%
\begin{displaymath}
\langle c_s \rangle^2
= \frac{\langle c_p \rangle_0 \langle R \rangle_0
 \Pi \theta_v}{\langle c_v \rangle_0} \Deqlab{SoundVel}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11786}%
$\displaystyle \DD{\Pi}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11788}%
$\displaystyle \frac{\langle c_s \rangle^2}{\langle c_p \rangle_0 \theta_v}
\Bigg[ \Dinv{\rho} \DD{\rho}{t} + \Dinv{\theta} \DD{\theta}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11789}%
$\displaystyle + \Dinv{q_d  \langle M \rangle_0 / M_d
    + \sum q_v \langle M \rangle_0 / M_v}
\left( \frac{\langle M \rangle_0}{M_d} \DD{ q_d}{t}
    + \sum \frac{\langle M \rangle_0}{M_v} \DD{ q_v}{t}  \right)
\Bigg]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11791}%
$\displaystyle \frac{\langle c_s \rangle^2}{\langle c_p \rangle_0 \theta_v}
\Bigg[ - \DP{u_j}{x_j} + \Dinv{\rho} \sum M_{fall} (\rho_r) +
\Dinv{\theta} \DD{\theta}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11792}%
$\displaystyle + \Dinv{q_d  \langle M \rangle_0 / M_d
    + \sum q_v \langle M \rangle_0 / M_v}
\left( \frac{\langle M \rangle_0}{M_d} \DD{ q_d}{t}
    + \sum \frac{\langle M \rangle_0}{M_v} \DD{ q_v}{t}  \right)
\Bigg]
\Deqlab{pressure:theta-p:p}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11795}%
$\displaystyle \Dinv{\rho} \DP{p}{x_i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11797}%
$\displaystyle \frac{ \langle R \rangle_0  \Pi \theta_v }{p} 
   \DP{ \left( 
     p_{0} \Pi^{ \langle c_{p} \rangle / \langle R \rangle_0}
    \right)}{x_i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11799}%
$\displaystyle \frac{ \langle R \rangle_0 \Pi \theta_v }{p} 
   \left(
   \frac{p_{0} {c_{p}}_{d}}{R_{d}} \Pi^{ \langle c_{p} \rangle / \langle
   R \rangle_0 - 1} 
   \right) \DP{\Pi}{x_i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11801}%
$\displaystyle \frac{ \langle R \rangle_0  \Pi \theta_v }{p} 
   \left(
   \frac{ \langle c_{p} \rangle}{ \langle R \rangle_0} p \Pi^{-1} 
   \right) \DP{\Pi}{x_i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11803}%
$\displaystyle \langle c_{p} \rangle \theta_v  \DP{\Pi}{x_i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11805}%
$\displaystyle \DD{u}{t} 
    = - \langle c_{p} \rangle \theta_{v} \DP{\Pi}{x}
      + D_u 
  \Deqlab{equations:u2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11806}%
$\displaystyle \DD{v}{t} 
    = - \langle c_{p} \rangle \theta_{v} \DP{\Pi}{y}
      + D_v 
  \Deqlab{equations:v2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11807}%
$\displaystyle \DD{w}{t} 
    = - \langle c_{p} \rangle \theta_{v} \DP{\Pi}{z}
      - g + D_w
  \Deqlab{equations:w2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11822}%
$\displaystyle \DD{u}{t} = - \langle c_p \rangle_0 \theta_v \DP{\Pi}{x} + D_u
  \Deqlab{equations:u-w-pi-theta:u}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11823}%
$\displaystyle \DD{v}{t} = - \langle c_p \rangle_0 \theta_v \DP{\Pi}{y} + D_v
  \Deqlab{equations:u-w-pi-theta:v}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11824}%
$\displaystyle \DD{w}{t} = - \langle c_p \rangle_0 \theta_v \DP{\Pi}{z} - g + D_w
  \Deqlab{equations:u-w-pi-theta:w}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11826}%
$\displaystyle \DP{\Pi}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11830}%
$\displaystyle \Deqlab{equations:u-w-pi-theta:continue}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11832}%
$\displaystyle \rho
= \frac{p}{\langle R \rangle_0 \Pi \theta_v}
= \frac{p_0 \Pi^{\langle c_{v} \rangle / \langle R \rangle_0}}{\langle R
\rangle \theta_v}
  \Deqlab{equations:u-w-pi-theta:rho}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11834}%
$\displaystyle \DD{\theta}{t} 
   = \Dinv{\Pi} \left( Q_{cond} + Q_{rad} + Q_{dis} \right)
     + D_{\theta}
  \Deqlab{equations:u-w-pi-theta:theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11836}%
$\displaystyle \DD{q_{v}}{t}
   = - \frac{q_{v}}{\rho} \sum M_{fall}(\rho_r)
     + \Dinv{\rho} M_{src}(\rho_v)
     + D_{q_v}
  \Deqlab{equations:u-w-pi-theta:qv}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11837}%
$\displaystyle \DD{q_{c}}{t}
   = - \frac{q_{c}}{\rho} \sum M_{fall}(\rho_r)
     + \Dinv{\rho} M_{src}(\rho_c)
     + D_{q_c}
  \Deqlab{equations:u-w-pi-theta:qc}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11838}%
$\displaystyle \DD{q_r}{t}
   = - \frac{q_r}{\rho} \sum M_{fall}(\rho_r)
     + \Dinv{\rho} M_{fall}(\rho_r) + \Dinv{\rho} M_{src}(\rho_r)
     + D_{q_r}
  \Deqlab{equations:u-w-pi-theta:qr}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11841}%
$\displaystyle \Pi \equiv \left( \frac{p}{p_0} \right)^{\langle R \rangle_0 / \langle
 c_p \rangle_0}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3890}%
$\langle c_{s} \rangle$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11850}%
$\displaystyle u (x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11852}%
$\displaystyle u^{\prime} (x,z,t),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11853}%
$\displaystyle v (x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11855}%
$\displaystyle v^{\prime} (x,z,t),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11856}%
$\displaystyle w (x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11858}%
$\displaystyle w^{\prime} (x,z,t),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11859}%
$\displaystyle \theta (x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11861}%
$\displaystyle \overline{\theta} (z) + \theta^{\prime} (x,z,t),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11862}%
$\displaystyle \Pi (x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11864}%
$\displaystyle \overline{\Pi} (z) + \Pi^{\prime} (x,z,t),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11865}%
$\displaystyle q_d (x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11867}%
$\displaystyle \overline{q_d} (z) +
 {q_d}^{\prime} (x,z,t),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11868}%
$\displaystyle q_v (x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11870}%
$\displaystyle \overline{q_v} (z) +
 {q_v}^{\prime} (x,z,t),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11871}%
$\displaystyle q_c (x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11873}%
$\displaystyle {q_c}^{\prime} (x,z,t),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11874}%
$\displaystyle q_r (x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11876}%
$\displaystyle {q_r}^{\prime} (x,z,t).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5880}%
$w$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11879}%
$\displaystyle \DP{\bar{\Pi}}{z} 
  = - \frac{g}{\langle c_p \rangle_0 \bar{\theta_{v}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11882}%
$\displaystyle \DP{u^{'}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11884}%
$\displaystyle - \left[
      u^{'}  \DP{u^{'}}{x} 
     + v^{'}  \DP{u^{'}}{y} 
     + w^{'} \DP{u^{'}}{z} 
    \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11885}%
$\displaystyle - \langle c_p \rangle_0
  \left(
     \bar{\theta_{v}} \DP{\bar{\Pi}}{x}
   + \bar{\theta_{v}} \DP{\Pi^{'}}{x}
   + {\theta_{v}}^{'} \DP{\bar{\Pi}}{x}
   + {\theta_{v}}^{'} \DP{\Pi^{'}}{x}
  \right)
  + D_{u}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11886}%
$\displaystyle \DP{v^{'}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11888}%
$\displaystyle - \left[
      u^{'}  \DP{v^{'}}{x} 
     + v^{'}  \DP{v^{'}}{y} 
     + w^{'} \DP{v^{'}}{z} 
    \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11889}%
$\displaystyle - \langle c_p \rangle_0
  \left(
     \bar{\theta_{v}} \DP{\bar{\Pi}}{y}
   + \bar{\theta_{v}} \DP{\Pi^{'}}{y}
   + {\theta_{v}}^{'} \DP{\bar{\Pi}}{y}
   + {\theta_{v}}^{'} \DP{\Pi^{'}}{y}
  \right)
  + D_{v}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11894}%
$\displaystyle - u^{\prime} \DP{u^{\prime}}{x}
- v^{\prime} \DP{u^{\prime}}{y} 
- w^{\prime} \DP{u^{\prime}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11895}%
$\displaystyle - \langle c_p \rangle_0 \overline{\theta_v} \DP{\Pi^{\prime}}{x}
  + D_{u}
  \Deqlab{bunri:moist:dudt}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11898}%
$\displaystyle - u^{\prime} \DP{v^{\prime}}{x}
- v^{\prime} \DP{v^{\prime}}{y} 
- w^{\prime} \DP{v^{\prime}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11899}%
$\displaystyle - \langle c_p \rangle_0 \overline{\theta_v} \DP{\Pi^{\prime}}{y}
  + D_{v}.
  \Deqlab{bunri:moist:dvdt}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11902}%
$\displaystyle \DP{w^{'}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11904}%
$\displaystyle - \left[
       u^{'}  \DP{w^{'}}{x} 
     + v^{'} \DP{w^{'}}{y} 
     + w^{'} \DP{w^{'}}{z} 
    \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11905}%
$\displaystyle - \langle c_p \rangle_0
  \left(
     \bar{\theta_{v}} \DP{\bar{\Pi}}{z}
   + \bar{\theta_{v}} \DP{\Pi^{'}}{z}
   + {\theta_{v}}^{'} \DP{\bar{\Pi}}{z}
   + {\theta_{v}}^{'} \DP{\Pi^{'}}{z}
  \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11906}%
$\displaystyle - g
  + D_{w^{'}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11910}%
$\displaystyle - u^{'} \DP{w^{'}}{x} 
    - v^{'} \DP{w^{'}}{y} 
    - w^{'} \DP{w^{'}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11911}%
$\displaystyle - \langle c_p \rangle_0
  \left(
     \bar{\theta_{v}} \DP{\bar{\Pi}}{z}
   + \bar{\theta_{v}} \DP{\Pi^{'}}{z}
   + {\theta_{v}}^{'} \DP{\bar{\Pi}}{z}
  \right)
    - g
    + D_{w^{'}} .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11913}%
$\displaystyle \DP{\overline{\Pi}}{z} = - \frac{g}{\langle c_p \rangle_0
 \overline{\theta_v}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11918}%
$\displaystyle + \langle c_p \rangle_0 \bar{\theta_{v}} 
  \left( \frac{g}{\langle c_p \rangle_0 \bar{\theta_{v}}} \right)
  -   \langle c_p \rangle_0 \bar{\theta_{v}} \DP{\Pi^{'}}{z}
  +   \langle c_p \rangle_0 {\theta_{v}}^{'} 
  \left( \frac{g}{\langle c_p \rangle_0 \bar{\theta_{v}}} \right)
  - g + D_{w^{\prime}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11920}%
$\displaystyle - u^{'} \DP{w^{'}}{x} 
  - v^{'} \DP{w^{'}}{y} 
  - w^{'} \DP{w^{'}}{z} 
  -   \langle c_p \rangle_0 \bar{\theta_{v}} \DP{\Pi^{'}}{z}
  +   \frac{{\theta_{v}}^{'}}{\bar{\theta_{v}}} g
  + D_{w^{\prime}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11922}%
$\displaystyle \theta_v
  \equiv  \frac{T_v}{\Pi}
  =  \left( \frac{\langle M \rangle_0}{M_d} q_d
     + \sum \frac{\langle M \rangle_0}{ M_v } q_v
         \right) \theta$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11924}%
$\displaystyle \bar{\theta_v}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11926}%
$\displaystyle \left( \frac{\langle M \rangle_0}{M_d} \bar{q_d}
     + \sum \frac{\langle M \rangle_0}{ M_v } \bar{q_v}
         \right) \bar{\theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11928}%
$\displaystyle \left[
  1 + \sum \left( -1 + \frac{R_v}{R_d} \right) \overline{q_v}
 \right] \bar{\theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11929}%
$\displaystyle \theta_v^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11931}%
$\displaystyle \left( \frac{\langle M \rangle_0}{M_d} \overline{q_d}
     + \sum \frac{\langle M \rangle_0}{ M_v } \overline{q_v}
         \right) \theta^{\prime}
+  \left( \frac{\langle M \rangle_0}{M_d} q_d^{\prime}
     + \sum \frac{\langle M \rangle_0}{ M_v } q_v^{\prime}
         \right) \overline{\theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11933}%
$\displaystyle \left[
  1 + \sum \left( -1 + \frac{R_v}{R_d} \right) \overline{q_v}
 \right] \theta^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11934}%
$\displaystyle + \left[
    \sum \left( -1 + \frac{R_v}{R_d} \right) q_v^{\prime}
    - \sum \left( q_c^{\prime} + q_r^{\prime} \right)
 \right] \overline{\theta} 
  \Deqlab{DTheta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11936}%
$\displaystyle \frac{\theta_v^{\prime}}{\overline{\theta_v}} g
 =
\frac{\theta^{\prime}}{\overline{\theta}} g
 + 
  \frac{ 
    \sum \left( -1 + \frac{R_v}{R_d} \right) q_v^{\prime}
    - \sum \left( q_c^{\prime} + q_r^{\prime} \right) }
   {  1 + \sum \left( -1 + \frac{R_v}{R_d} \right) \overline{q_v} } g$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11940}%
$\displaystyle - u^{\prime} \DP{w^{\prime}}{x} 
  - v^{\prime} \DP{w^{\prime}}{y} 
  - w^{\prime} \DP{w^{\prime}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11941}%
$\displaystyle - \langle c_p \rangle_0 \overline{\theta_v} \DP{\Pi^{\prime}}{z}
  + \frac{\theta^{\prime}}{\overline{\theta}} g
  + \frac{ 
    \sum \left( \frac{R_v}{R_d} -1 \right) q_v^{\prime}
    - \sum \left( q_c^{\prime} + q_r^{\prime} \right) }
   {  1 + \sum \left( \frac{R_v}{R_d} -1 \right) \overline{q_v} } g
  + D_{w^{\prime}} 
  \Deqlab{bunri:moist:dwdt}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11946}%
$\displaystyle \frac{\langle c_s \rangle^2}{\langle c_p \rangle_0 \theta_v}
\Bigg[ - \DP{u_j}{x_j} + \Dinv{\rho} \sum M_{fall} (\rho_r) +
\Dinv{\theta }  
 \left\{ \Dinv{\Pi} ( Q_{cond} + Q_{rad} + Q_{dis} ) 
  + D_{\theta} \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11947}%
$\displaystyle + \Dinv{q_d  \langle M \rangle_0 / M_d
    + \sum q_v \langle M \rangle_0 / M_v} 
  \Bigg\{ \frac{\langle M \rangle_0}{M_d} 
 \left( - \frac{q_d}{\rho} \sum M_{fall} (\rho_r) + D_{q_d} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11948}%
$\displaystyle + \sum \frac{\langle M \rangle_0}{M_v} 
 \left( - \frac{q_v}{\rho} \sum M_{fall} (\rho_r) + M_{src} (q_v) +
  D_{q_v} \right) 
\Bigg\}
\Bigg]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11951}%
$\displaystyle + \Dinv{ q_d 
    + M_d \sum q_v  / M_v} 
  \Bigg\{ 
   D_{q_d} + M_d \sum \Dinv{M_v} 
    \left[  M_{src} (q_v) + D_{q_v} \right] 
  \Bigg\}
\Bigg]
\Deqlab{pressEQ1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11955}%
$\displaystyle \DP{\bar{\Pi} + \Pi^{'}}{t} 
 + u^{'} \DP{\bar{\Pi}+\Pi^{'}}{x} 
 + v^{'} \DP{\bar{\Pi}+\Pi^{'}}{y} 
 + w^{'} \DP{\bar{\Pi}+\Pi^{'}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11956}%
$\textstyle \approx$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11957}%
$\displaystyle \DP{\Pi^{'}}{t}
 + w^{'} \DP{\bar{\Pi}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5884}%
$\langle c_{s} \rangle^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5886}%
$\theta_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11962}%
$\displaystyle + \Dinv{ q_d 
    + M_d \sum q_v  / M_v} 
  \Bigg\{ 
   D_{q_d} + M_d \sum \Dinv{M_v} 
    \left[  M_{src} (q_v) + D_{q_v} \right] 
  \Bigg\}
\Bigg]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11964}%
$\displaystyle \frac{ \overline{\langle c_s \rangle^2} }
      {\langle c_p \rangle_0 \overline{\theta_v} }
\Bigg[ - \DP{u_j^{'}}{x_j}  +
\Dinv{ \overline{\theta} }  
 \left\{ \Dinv{\overline{\Pi}} ( Q_{cond} + Q_{rad} + Q_{dis} ) 
  + D_{\theta} \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11965}%
$\displaystyle + \Dinv{ 
    \overline{q_d} + M_d \sum \overline{q_v}  / M_v } 
  \Bigg\{ 
   D_{q_d} + M_d \sum \Dinv{M_v} 
    \left[  M_{src} (q_v) + D_{q_v} \right] 
  \Bigg\}
\Bigg]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11968}%
$\displaystyle + \Dinv{ 1 + \sum \left( \frac{R_v}{R_d} - 1 \right) \overline{q_v} } 
  \Bigg\{ 
   - \sum ( D_{q_v} + D_{q_c} + D_{q_r} ) 
    + \sum \frac{R_v}{R_d} 
      \left[  M_{src} (q_v) + D_{q_v} \right] 
  \Bigg\}
\Bigg]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5888}%
$\overline{q_d} + \overline{q_v} = 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5890}%
$D_{q_d} + D_{q_v} +
D_{q_c} + D_{q_r} = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11972}%
$\displaystyle \overline{\langle c_s \rangle^2} 
 = 
 \frac{\langle c_p \rangle_0 \langle R \rangle_0
 \bar{\Pi} \bar{\theta_v}}{\langle c_v \rangle_0}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11976}%
$\displaystyle - w^{'} \DP{\bar{\Pi}}{z} 
 - \frac{ \overline{\langle c_s \rangle^2} }{\langle c_p \rangle_0
 \bar{\theta_v} } \DP{u_j^{'}}{x_j}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11979}%
$\displaystyle \Deqlab{pressEQ2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11983}%
$\displaystyle - w^{'} \DP{}{z} 
 \left( \frac{\bar{\rho} \langle R \rangle_0 \bar{\theta_v}
  }{p_{0}}\right)^{ \langle R \rangle_0 / \langle c_v \rangle_0 }  
 - \frac{\overline{{ \langle c_{s} \rangle }^{2}} }{ \langle c_p \rangle_0
 \bar{\theta_v} }
   \left( \DP{ u^{'}}{x} + \DP{ w^{'}}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11985}%
$\displaystyle - w^{'} 
 \frac{\langle R \rangle_0}{ \langle c_v \rangle}_0 \bar{\Pi}
 \Dinv{ \left( \frac{\bar{\rho}
	\langle R \rangle_0 \bar{\theta_v} }{p_{0}}\right)}
 \frac{ \langle R \rangle_0}{p_{0}}
 \DP{ ( \bar{\rho} \bar{\theta_v} )}{z} 
 - \frac{\overline{{\langle c_{s} \rangle}^{2}} }{ \langle c_p \rangle_0
 \bar{\theta_v} }
   \left( \DP{u^{'}}{x} + \DP{w^{'}}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11987}%
$\displaystyle - \frac{\overline{ {\langle c_{s} \rangle}^{2} }}{\langle c_p \rangle_0
 \bar{\rho} 
 \bar{\theta_v}^{2}}
 \left\{
 w^{'} 
 \DP{ ( \bar{\rho} \bar{\theta_v} ) }{z} 
 + \bar{\rho} \bar{\theta_v}
   \left( \DP{u^{'}}{x} + \DP{w^{'}}{z} \right)
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11989}%
$\displaystyle - \frac{\overline{{c_{s}}^{2}}}{\langle c_p \rangle_0  \bar{\rho}
 \bar{\theta_v}^{2}}
 \Ddiv \left(
	\bar{\rho} \bar{\theta_v} \Dvect{u^{'}}
       \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11996}%
$\displaystyle \Deqlab{pressEQ3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay11999}%
$\displaystyle \DP{(\bar{\theta} + \theta^{'})}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12001}%
$\displaystyle - u^{'} \DP{(\bar{\theta} + \theta^{'})}{x} 
 - v^{'} \DP{(\bar{\theta} + \theta^{'})}{y} 
 - w^{'}\DP{(\bar{\theta} + \theta^{'})}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12002}%
$\displaystyle + \Dinv{\bar{\Pi} + \Pi^{'}} (Q_{cond} + Q_{rad} + Q_{dis}) 
 + D_{\bar{\theta}} + D_{\theta^{'}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12005}%
$\displaystyle \DP{\theta^{'}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12007}%
$\displaystyle - \left(
    u^{'}\DP{\theta^{'}}{x} 
    + v^{'}\DP{\theta^{'}}{y} 
    + w^{'}\DP{\theta^{'}}{z} 
   \right)
 - w^{'}\DP{\bar{\theta}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12008}%
$\displaystyle + \Dinv{\bar{\Pi}} (Q_{cond} + Q_{rad} + Q_{dis}) 
 + D_{\bar{\theta}}   + D_{\theta^{'}}
 \Deqlab{Thermeq}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12013}%
$\displaystyle - u^{\prime} \DP{q_v^{\prime}}{x}
     - v^{\prime} \DP{q_v^{\prime}}{y}
     - w^{\prime} \DP{q_v^{\prime}}{z}
     - w^{\prime} \DP{\overline{q_v}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12014}%
$\displaystyle - \frac{\overline{q_v}}{\overline{\rho}} \sum M_{fall}
     (\rho_r^{\prime}) + \Dinv{\overline{\rho}} M_{src} (\rho_v^{\prime})
     + D_{\overline{q_v}}
     + D_{q_v^{\prime}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12017}%
$\displaystyle - u^{\prime} \DP{q_c^{\prime}}{x}
     - v^{\prime} \DP{q_c^{\prime}}{y}
     - w^{\prime} \DP{q_c^{\prime}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12018}%
$\displaystyle + \Dinv{\overline{\rho}} M_{src} (\rho_c^{\prime})
     + D_{q_c^{\prime}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12021}%
$\displaystyle - u^{\prime} \DP{q_r^{\prime}}{x}
     - v^{\prime} \DP{q_r^{\prime}}{y}
     - w^{\prime} \DP{q_r^{\prime}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12022}%
$\displaystyle + \Dinv{\overline{\rho}} M_{fall} (\rho_r^{\prime})
     + \Dinv{\overline{\rho}} M_{src} (\rho_r^{\prime})
     + D_{q_r^{\prime}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5894}%
$\overline{\rho} u^{\prime}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5896}%
$\overline{\rho} v^{\prime}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5898}%
$\overline{\rho} w^{\prime}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12028}%
$\displaystyle \DP{ (\overline{\rho} K ) }{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12030}%
$\displaystyle - \overline{\rho} \Dvect{u} \cdot \nabla K 
 - \langle c_p \rangle_0
  \overline{\rho} \overline{\theta_v} \Dvect{u} \cdot \nabla \Pi^{\prime}
 + \overline{\rho} \Dvect{u} \cdot \Dvect{D} 
 + g 
    \frac{\theta_v^{\prime}}
         {\overline{\theta_v}} \overline{\rho} w^{\prime}
\Deqlab{AAA}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5900}%
$\Dvect{u} = (u^{\prime}, v^{\prime},
w^{\prime})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5902}%
$\Dvect{D} = (D_u, D_v, D_w)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5904}%
$K = [{u^{\prime}}^2 + {v^{\prime}}^2 + {w^{\prime}}^2 ]/2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4684}%
\begin{displaymath}
\DP{\rho_d^{\prime}}{t}
 + \DP{}{x} \left( u^{\prime} \overline{\rho_d} \right)
 + \DP{}{z} \left( w^{\prime} \overline{\rho_d} \right)
 = 0, 
 \Deqlab{AAA-2}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4697}%
\begin{displaymath}
\DP{\rho_v^{\prime}}{t}
 + \DP{}{x} \left( u^{\prime} \overline{\rho_v} \right)
 + \DP{}{z} \left( w^{\prime} \overline{\rho_v} \right)
 = M_{src} (\rho_v^{\prime}) 
 \Deqlab{AAA-3}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4712}%
\begin{displaymath}
\DP{}{t} \left( \rho_d^{\prime} + \sum \rho_v^{\prime} \right)
+ \nabla \cdot (\overline{\rho} \Dvect{u})
 = \sum M_{src} (\rho_v^{\prime})
 \Deqlab{AAB}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5906}%
$\overline{\rho} = \overline{\rho_d} + \sum \overline{\rho_v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12039}%
$\displaystyle - \overline{\rho} \Dvect{u} \cdot \nabla K$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12041}%
$\displaystyle - \nabla \cdot ( \overline{\rho} K \Dvect{u} )
 + K \nabla \cdot (\overline{\rho} \Dvect{u})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12043}%
$\displaystyle - \nabla \cdot ( \overline{\rho} K \Dvect{u} )
 - K \DP{}{t} \left( \rho_d^{\prime} + \rho_v^{\prime} \right) 
 + K M_{src} (\rho_v^{\prime})
\Deqlab{AAC}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12045}%
$\displaystyle - \langle c_p \rangle_0 \overline{\rho} \overline{\theta_v} \Dvect{u}
  \cdot \nabla \Pi^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12047}%
$\displaystyle - \nabla \cdot [ \langle c_p \rangle_0 \overline{\rho} \overline{\theta_v}
 \Pi^{\prime} \Dvect{u} ]
 + \langle c_p \rangle_0 \Pi^{\prime} \nabla \cdot (\overline{\rho}
 \overline{\theta_v} \Dvect{u} )$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12049}%
$\displaystyle - \nabla \cdot [ \langle c_p \rangle_0 \overline{\rho} \overline{\theta_v}
 \Pi^{\prime} \Dvect{u} ]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12050}%
$\displaystyle + \Pi^{\prime}
   \frac{\langle c_p \rangle_0^2 \overline{\rho} \overline{\theta_v}^2}
        {\overline{\langle c_s \rangle}^2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12051}%
$\displaystyle \Bigg[
   - \DP{\Pi^{\prime}}{t}
   + \frac{ \overline{\langle c_s \rangle^2} }
     {\langle c_p \rangle_0 \overline{\theta_v} }
   \Bigg[ 
    \Dinv{ \overline{\theta} }  
     \left\{ \Dinv{\overline{\Pi}} ( Q_{cond} + Q_{rad} + Q_{dis} ) 
     + D_{\theta} \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12052}%
$\displaystyle + \Dinv{ 1 + \sum \left( \frac{R_v}{R_d} - 1 \right) \overline{q_v} } 
  \Bigg\{ 
   - \sum ( D_{q_v} + D_{q_c} + D_{q_r} )$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12053}%
$\displaystyle + \sum \frac{R_v}{R_d} 
      \left[  M_{src} (q_v) + D_{q_v} \right] 
  \Bigg\}
  \Bigg] \Bigg]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12055}%
$\displaystyle - \nabla \cdot [ \langle c_p \rangle_0 \overline{\rho} \overline{\theta_v}
 \Pi^{\prime} \Dvect{u} ] 
 - \DP{}{t} 
    \left[ 
     \frac{\overline{\rho}}{2} 
     \frac{\langle c_p \rangle_0^2 \overline{\theta_v}^2 {\Pi^{\prime}}^2}
          {\overline{\langle c_s \rangle}^2}
    \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12056}%
$\displaystyle + \langle c_p \rangle_0 \overline{\rho} \overline{\theta_v} \Pi^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12057}%
$\displaystyle \Bigg[ 
    \Dinv{ \overline{\theta} }  
     \left\{ \Dinv{\overline{\Pi}} ( Q_{cond} + Q_{rad} + Q_{dis} ) 
     + D_{\theta} \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12059}%
$\displaystyle + \sum \frac{R_v}{R_d} 
      \left[  M_{src} (q_v) + D_{q_v} \right] 
  \Bigg\}
  \Bigg]
\Deqlab{AAD}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5908}%
$\phi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4821}%
\begin{displaymath}
\overline{\rho} \DD{\phi}{t}
= \DP{}{t} \left( \overline{\rho} \phi \right)
  + \nabla \cdot \left( \overline{\rho} \phi \Dvect{u} \right)
  + \phi \DP{}{t} \left( \rho_d^{\prime} + \sum \rho_v^{\prime} \right)
  - \phi \sum M_{src} (\rho_v^{\prime})
\Deqlab{AAE}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12063}%
$\displaystyle \frac{\theta^{\prime}}{\overline{\theta}} \overline{\rho} w^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12065}%
$\displaystyle \frac{\theta^{\prime}}{\overline{\theta}} \overline{\rho} \DD{z}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12067}%
$\displaystyle \frac{\overline{\rho}}{\overline{\theta}} \theta^{\prime} \DD{}{t} (g z)
+ \frac{\overline{\rho} g z}{\overline{\theta}}
  \left[ \DD{\theta^{\prime}}{t} + w^{\prime} \DP{\overline{\theta}}{z}
   - \Dinv{\overline{\Pi}}
     \left( Q_{cond} + Q_{rad} + Q_{dis} \right) - D_{\theta} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12069}%
$\displaystyle \frac{\overline{\rho}}{\overline{\theta}} \DD{}{t}
(\theta^{\prime} g z)
+ \frac{\overline{\rho} g z}{\overline{\theta}}
  \left[ w^{\prime} \DP{\overline{\theta}}{z}
   - \Dinv{\overline{\Pi}}
     \left( Q_{cond} + Q_{rad} + Q_{dis} \right) - D_{\theta} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12071}%
$\displaystyle \Dinv{\overline{\theta}} \DP{}{t} \left( \overline{\rho} \theta^{\prime}
 g z \right) + \Dinv{\overline{\theta}}
 \nabla \cdot \left( \overline{\rho} \theta^{\prime} g z \Dvect{u} \right)
 + \frac{\theta^{\prime} g z}{\overline{\theta}}
  \left[ 
   \DP{}{t} \left( \rho_d^{\prime} + \rho_v^{\prime} \right) 
   - \sum M_{src} (\rho_v^{\prime})
  \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12072}%
$\displaystyle + \frac{\overline{\rho} g z}{\overline{\theta}}
  \left[ w^{\prime} \DP{\overline{\theta}}{z}
   - \Dinv{\overline{\Pi}}
     \left( Q_{cond} + Q_{rad} + Q_{dis} \right) - D_{\theta} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12074}%
$\displaystyle \Dinv{\overline{\theta}} \DP{}{t} \left( \overline{\rho} \theta^{\prime}
 g z \right) +
 \nabla \cdot \left( \frac{ \overline{\rho} \theta^{\prime} g z \Dvect{u}
   }{\overline{\theta}} \right)
 + \frac{ \overline{\rho} \theta^{\prime} g z w^{\prime}}
        { {\overline{\theta}}^2}
 \DP{\overline{\theta}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12075}%
$\displaystyle + \frac{\theta^{\prime} g z}{\overline{\theta}}
  \left[ 
    \DP{}{t} \left( \rho_d^{\prime} + \rho_v^{\prime} \right) 
    - \sum M_{src} (\rho_v^{\prime})
  \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12076}%
$\displaystyle + \frac{\overline{\rho} g z}{\overline{\theta}}
  \left[ w^{\prime} \DP{\overline{\theta}}{z}
   - \Dinv{\overline{\Pi}}
     \left( Q_{cond} + Q_{rad} + Q_{dis} \right) 
   - D_{\theta} 
  \right], 
\Deqlab{AAF}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12078}%
$\displaystyle \frac{\overline{\rho} g}
     { 1 + \sum \left( \frac{R_v}{R_d} - 1 \right) \overline{q_v} } 
  q_v^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12080}%
$\displaystyle \DP{}{t}
   \left[
    \frac{ q_v^{\prime} \overline{\rho} g z}
     { 1 + \sum \left( \frac{R_v}{R_d} - 1 \right) \overline{q_v} } 
   \right]
  + 
  \nabla \cdot
   \left[
    \frac{ q_v^{\prime} \overline{\rho} g z \Dvect{u} }
     { 1 + \sum \left( \frac{R_v}{R_d} - 1 \right) \overline{q_v} } 
   \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12081}%
$\displaystyle - q_v^{\prime} g z \nabla \cdot
   \left[
    \frac{ \overline{\rho} \Dvect{u} }
     { 1 + \sum \left( \frac{R_v}{R_d} - 1 \right) \overline{q_v} } 
   \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12082}%
$\displaystyle + g z 
  \left[
   w^{\prime} \DP{\overline{q_v}}{z}
   + \frac{\overline{q_v}}{\overline{\rho}} \sum M_{fall} (\rho_r)
   - \Dinv{\overline{\rho}} M_{src} (q_v)
   - D_{q_v}
  \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12083}%
$\displaystyle \Deqlab{AAF-2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12085}%
$\displaystyle \frac{\overline{\rho} g}
     { 1 + \sum \left( \frac{R_v}{R_d} - 1 \right) \overline{q_v} } 
  q_c^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12087}%
$\displaystyle \DP{}{t}
   \left[
    \frac{ q_c^{\prime} \overline{\rho} g z}
     { 1 + \sum \left( \frac{R_v}{R_d} - 1 \right) \overline{q_v} } 
   \right]
  + 
  \nabla \cdot
   \left[
    \frac{ q_c^{\prime} \overline{\rho} g z \Dvect{u} }
     { 1 + \sum \left( \frac{R_v}{R_d} - 1 \right) \overline{q_v} } 
   \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12088}%
$\displaystyle - q_c^{\prime} g z \nabla \cdot
   \left[
    \frac{ \overline{\rho} \Dvect{u} }
     { 1 + \sum \left( \frac{R_v}{R_d} - 1 \right) \overline{q_v} } 
   \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12089}%
$\displaystyle + g z 
  \left[
   - \Dinv{\overline{\rho}} M_{src} (q_c)
   - D_{q_c}
  \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12090}%
$\displaystyle \Deqlab{AAF-3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12092}%
$\displaystyle \frac{\overline{\rho} g}
     { 1 + \sum \left( \frac{R_v}{R_d} - 1 \right) \overline{q_v} } 
  q_r^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12094}%
$\displaystyle \DP{}{t}
   \left[
    \frac{ q_r^{\prime} \overline{\rho} g z}
     { 1 + \sum \left( \frac{R_v}{R_d} - 1 \right) \overline{q_v} } 
   \right]
  + 
  \nabla \cdot
   \left[
    \frac{ q_r^{\prime} \overline{\rho} g z \Dvect{u} }
     { 1 + \sum \left( \frac{R_v}{R_d} - 1 \right) \overline{q_v} } 
   \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12095}%
$\displaystyle - q_r^{\prime} g z \nabla \cdot
   \left[
    \frac{ \overline{\rho} \Dvect{u} }
     { 1 + \sum \left( \frac{R_v}{R_d} - 1 \right) \overline{q_v} } 
   \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12096}%
$\displaystyle + g z 
  \left[
   - \Dinv{\overline{\rho}} M_{fall} (\rho_r)
   - \Dinv{\overline{\rho}} M_{src} (q_r)
   - D_{q_r}
  \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12097}%
$\displaystyle \Deqlab{AAF-3A}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12099}%
$\displaystyle \DP{}{t}
\left\{ 
 \overline{\rho} 
  \left[ 
   K 
   - \frac{\theta_v^{\prime}}{\overline{\theta_v}} g z 
   + \Dinv{2}  
     \left( 
       \frac{\langle c_p \rangle_0 \overline{\theta_v} \Pi^{\prime}}
            {\overline{\langle c_s \rangle}}
     \right)^2
  \right] \right\}
+ \nabla \cdot \left[
  \overline{\rho} \left( K - \frac{\theta_v^{\prime}}{\overline{\theta_v}}
  g z + \langle c_p \rangle_0 \overline{\theta_v} \Pi^{\prime} \right)
  \Dvect{u} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12101}%
$\displaystyle - K \DP{}{t} \left( \rho_d^{\prime} + \rho_v^{\prime} \right) 
+ \overline{\rho} \Dvect{u} \cdot \Dvect{D} 
 + K M_{src} (\rho_v^{\prime})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12105}%
$\displaystyle + \left[ 
    - \sum (q_v^{\prime} + q_c^{\prime} + q_r^{\prime} ) 
    + \sum (R_v / R_d) q_v^{\prime}
    \right]
   \nabla \cdot
   \left[
    \frac{ \overline{\rho} \Dvect{u} }
     { 1 + \sum \left( \frac{R_v}{R_d} - 1 \right) \overline{q_v} } 
   \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12106}%
$\displaystyle - \theta^{\prime} g z 
    \nabla \cdot 
    \left[ \frac{\overline{\rho} \Dvect{u}}{\overline{\theta}} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12107}%
$\displaystyle + \frac{\overline{\rho} g z}
       { 1 + \sum \left( \frac{R_v}{R_d} - 1 \right) \overline{q_v} }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12108}%
$\displaystyle \Bigg[
    \left\{ w^{\prime} \sum \left( -1 + R_v/R_d \right) \DP{q_v}{z} \right\}
    + \left( \sum \frac{\overline{q_v} R_v}{\overline{\rho} R_d} \right)
      \left( \sum M_{fall} (\rho_r) \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12109}%
$\displaystyle + \sum (D_{q_v} + D_{q_c} + D_{q_r})
    - \sum R_v D_{q_v} / R_d
   \Bigg]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12110}%
$\displaystyle + \frac{\overline{\rho} g z}{\overline{\theta}}
    \left[ 
     w^{\prime} \DP{\theta}{z}
     - \Dinv{\overline{\Pi}}
       \left( Q_{cond} + Q_{rad} + Q_{dis} \right) - D_{\theta} \right]
\Deqlab{AAG}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12112}%
$\displaystyle \DP{}{t} \int
\left\{ 
 \overline{\rho} 
  \left[ 
   K 
   - \frac{\theta_v^{\prime}}{\overline{\theta_v}} g z 
   + \Dinv{2}  
     \left( 
       \frac{\langle c_p \rangle_0 \overline{\theta_v} \Pi^{\prime}}
            {\overline{\langle c_s \rangle}}
     \right)^2
  \right] \right\} dV$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12114}%
$\displaystyle - \int K \DP{}{t} \left( \rho_d^{\prime} + \rho_v^{\prime} \right) dV
+ \int \overline{\rho} \Dvect{u} \cdot \Dvect{D} dV
 + \int K M_{src} (\rho_v^{\prime}) dV$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12115}%
$\displaystyle + \int \langle c_p \rangle_0 \overline{\rho} \overline{\theta_v} \Pi^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12117}%
$\displaystyle + \Dinv{ 1 + \sum \left( \frac{R_v}{R_d} - 1 \right) \overline{q_v} } 
  \Bigg\{ 
   - \sum ( D_{q_v} + D_{q_c} + D_{q_r} ) 
    + \sum \frac{R_v}{R_d} 
      \left[  M_{src} (q_v) + D_{q_v} \right] 
  \Bigg\}
  \Bigg] dV$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12118}%
$\displaystyle + \int \left[ 
    - \sum (q_v^{\prime} + q_c^{\prime} + q_r^{\prime} ) 
    + \sum (R_v / R_d) q_v^{\prime}
    \right]
   \nabla \cdot
   \left[
    \frac{ \overline{\rho} \Dvect{u} }
     { 1 + \sum \left( \frac{R_v}{R_d} - 1 \right) \overline{q_v} } 
   \right] dV$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12119}%
$\displaystyle - \int \theta^{\prime} g z 
    \nabla \cdot 
    \left[ \frac{\overline{\rho} \Dvect{u}}{\overline{\theta}} \right]
    dV$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12120}%
$\displaystyle + \int \frac{\overline{\rho} g z}
       { 1 + \sum \left( \frac{R_v}{R_d} - 1 \right) \overline{q_v} }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12122}%
$\displaystyle + \sum (D_{q_v} + D_{q_c} + D_{q_r})
    - \sum R_v D_{q_v} / R_d
   \Bigg] dV$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12123}%
$\displaystyle + \int \frac{\overline{\rho} g z}{\overline{\theta}}
    \left[ 
     w^{\prime} \DP{\theta}{z}
     - \Dinv{\overline{\Pi}}
       \left( Q_{cond} + Q_{rad} + Q_{dis} \right) - D_{\theta} \right]
     dV
\Deqlab{AAH}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12134}%
$\displaystyle - \langle c_p \rangle_0 \overline{\theta_v} \DP{\Pi^{\prime}}{x}
  + D_{u}
  \Deqlab{quasi-equations:u-w-pi-theta:u}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12138}%
$\displaystyle - \langle c_p \rangle_0 \overline{\theta_v} \DP{\Pi^{\prime}}{y}
  + D_{v}.
  \Deqlab{quasi-equations:u-w-pi-theta:v}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12142}%
$\displaystyle - \langle c_p \rangle_0 \overline{\theta_v} \DP{\Pi^{\prime}}{z}
  + \frac{\theta^{\prime}}{\overline{\theta}} g
  + \frac{ 
    \sum \left( -1 + \frac{R_v}{R_d} \right) q_v^{\prime}
    - \sum \left( q_c^{\prime} + q_r^{\prime} \right) }
   {  1 + \sum \left( -1 + \frac{R_v}{R_d} \right) \overline{q_v} } g
  + D_{w^{\prime}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12143}%
$\displaystyle \Deqlab{quasi-equations:u-w-pi-theta:w}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12150}%
$\displaystyle \Deqlab{quasi-equations:u-w-pi-theta:continue}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12154}%
$\displaystyle - u^{'}\DP{\theta^{'}}{x}
 - v^{'}\DP{\theta^{'}}{y}
 - w^{'}\DP{\theta^{'}}{z}
 - w^{'}\DP{\bar{\theta}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12155}%
$\displaystyle + \Dinv{\bar{\Pi}} (Q_{cond} + Q_{rad} + Q_{dis})
 + D_{\bar{\theta}}   + D_{\theta^{'}}
  \Deqlab{quasi-equations:u-w-pi-theta:theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12160}%
$\displaystyle - \frac{\overline{q_v}}{\overline{\rho}} \sum M_{fall}
     (\rho_r^{\prime}) + \Dinv{\overline{\rho}} M_{src}
     (\rho_v^{\prime})
     + D_{\overline{q_v}}
     + D_{q_v^{\prime}},
  \Deqlab{quasi-equations:u-w-pi-theta:qv}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12164}%
$\displaystyle + \Dinv{\overline{\rho}} M_{src} (\rho_c^{\prime})
     + D_{q_c^{\prime}}, 
  \Deqlab{quasi-equations:u-w-pi-theta:qc}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12168}%
$\displaystyle + \Dinv{\overline{\rho}} M_{fall} (\rho_r^{\prime})
     + \Dinv{\overline{\rho}} M_{src} (\rho_r^{\prime})
     + D_{q_r^{\prime}}. 
  \Deqlab{quasi-equations:u-w-pi-theta:qr}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12181}%
$\displaystyle + \int \frac{\overline{\rho} g z}{\overline{\theta}}
    \left[ 
     w^{\prime} \DP{\theta}{z}
     - \Dinv{\overline{\Pi}}
       \left( Q_{cond} + Q_{rad} + Q_{dis} \right) - D_{\theta} \right]
     dV
  \Deqlab{quasi-equations:u-w-pi-theta:energy}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12186}%
$\displaystyle \DD{E_{turb}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12188}%
$\displaystyle B + S + D_{E}  
  - \left(\frac{C_{\varepsilon}}{l}\right)
    E_{turb}^{\frac{3}{2}}
\Deqlab{B:dEdt}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8253}%
$l$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8261}%
$D_{E}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12195}%
$\displaystyle B$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12197}%
$\displaystyle \frac{g_{j}}{\overline{\theta_v}}
  \overline{ u^{\prime}_{j} \theta_v^{\prime} },$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12200}%
$\displaystyle - \overline{(u_{i}^{\prime} u_{j}^{\prime})}
  \DP{u_{i}}{x_{j}} ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12201}%
$\displaystyle D_{E}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12203}%
$\displaystyle \DP{}{x_{j}} \left(K_{m} \DP{E_{turb}}{x_{j}} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12205}%
$\displaystyle \frac{\theta_v^{\prime}}{\overline{\theta_v}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12207}%
$\displaystyle \frac{\theta^{\prime}}{\overline{\theta}}
  + \frac{\sum \frac{R_v}{R_d} q_v^{\prime} - \sum q_L^{\prime}}
         { 1 + \sum \frac{R_v}{R_d} \overline{q_v} - \sum \overline{q_L} }
   \Deqlab{vpot1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12208}%
$\displaystyle q_L$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12210}%
$\displaystyle q_v + q_c + q_r
   \Deqlab{vpot2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath6000}%
\begin{displaymath}
  \overline{(u_{i}^{\prime} u_{j}^{\prime})}
  = - 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}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12214}%
$\displaystyle \overline{(u_{i}^{\prime} \theta)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12216}%
$\displaystyle - K_{h} \DP{\theta}{x_j}
    \Deqlab{¥ì¥¤¥Î¥ë¥º±þÎÏ2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12217}%
$\displaystyle \overline{(u_{i}^{\prime} q_v)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12219}%
$\displaystyle - K_{h} \DP{q_v}{x_j}
    \Deqlab{¥ì¥¤¥Î¥ë¥º±þÎÏ3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12220}%
$\displaystyle \overline{(u_{i}^{\prime} q_L)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12222}%
$\displaystyle 0
    - K_{h} \DP{q_L}{x_j}
    \Deqlab{¥ì¥¤¥Î¥ë¥º±þÎÏ4}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8265}%
$q_c > 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12227}%
$\displaystyle - K_{h} 
     \left( 
      1 + \sum 
       \frac{L^2 \overline{q_v}}
            { \langle c_p \rangle_0 R_v \overline{\theta}^2 
              \overline{\Pi}^2 } 
     \right)^{-1}
   \DP{\theta_e}{x_j}
     \Deqlab{¥ì¥¤¥Î¥ë¥º±þÎÏ5}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12230}%
$\displaystyle - K_{h} 
    \frac{L \overline{q_v}}{R_v \overline{\Pi} \overline{\theta}^2}
     \left( 
      1 + \sum 
       \frac{L^2 \overline{q_v}}
            { \langle c_p \rangle_0 R_v \overline{\theta}^2 
              \overline{\Pi}^2 } 
     \right)^{-1}
   \DP{\theta_e}{x_j}
     \Deqlab{¥ì¥¤¥Î¥ë¥º±þÎÏ6}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12233}%
$\displaystyle - K_{h} \DP{q_L}{x_j}
    \Deqlab{¥ì¥¤¥Î¥ë¥º±þÎÏ7}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12242}%
$\displaystyle K_{m}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12244}%
$\displaystyle C_{m} {E_{turb}}^{1/2} l,
   \Deqlab{B:E}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12245}%
$\displaystyle K_{h}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12247}%
$\displaystyle 3 K_{m}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8281}%
$C_{\varepsilon}, C_{m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12251}%
$\displaystyle \DP{\overline{u^{\prime}_{i}u^{\prime}_{j}}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12252}%
$\textstyle +$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12253}%
$\displaystyle \DP{}{x_{k}}\left[
          u_{k}\overline{u^{\prime}_{i}u^{\prime}_{j}}
       + \overline{u^{\prime}_{k}u^{\prime}_{i}u^{\prime}_{j}}
       -  \nu \DP{}{x_{k}}\overline{u^{\prime}_{i}u^{\prime}_{j}}\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12255}%
$\displaystyle \DP{}{x_{j}}\overline{pu^{\prime}_{i}} 
        + \DP{}{x_{i}}\overline{pu^{\prime}_{j}}
        + f_{k}(\varepsilon _{jkl}\overline{u_{l}^{\prime}u^{\prime}_{i}}
        + \varepsilon _{ikl}\overline{u_{l}^{\prime}u^{\prime}_{j}})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12257}%
$\displaystyle -\overline{u^{\prime}_{k}u^{\prime}_{i}}\DP{u_{j}}{x_{k}}
          -\overline{u^{\prime}_{k}u^{\prime}_{j}}\DP{u_{i}}{x_{k}}
          -\overline{\theta_v}^{-1}
            ( g_{j}\overline{u^{\prime}_{i}\theta_v }
              + g_{i}\overline{u^{\prime}_{j}\theta_v })$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12259}%
$\displaystyle \overline{p\left(\DP{u^{\prime}_{i}}{x_{j}} 
       + \DP{u^{\prime}_{j}}{x_{i}}\right)}
       -  2\nu \overline{\DP{u^{\prime}_{i}}{x_{k}}\DP{u^{\prime}_{j}}{x_{k}}},
           \Deqlab{MY1974:eq(7)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12261}%
$\displaystyle \DP{\overline{u^{\prime}_{j}\theta^{\prime}}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12263}%
$\displaystyle \DP{}{x_{k}}\left[
        u_{k}\overline{\theta^{\prime} u^{\prime}_{j}} 
      + \overline{u^{\prime}_{k}u^{\prime}_{j}\theta^{\prime} }
      - \alpha \overline{u^{\prime}_{j}\DP{\theta^{\prime} }{x_{k}}}
      - \nu \overline{\theta^{\prime} \DP{u^{\prime}_{j}}{x_{k}}}\right] 
      + \DP{}{x_{j}}\overline{p\theta^{\prime} } 
      + \varepsilon _{jkl}f_{k}\overline{u^{\prime}_{l}\theta^{\prime} }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12265}%
$\displaystyle -\overline{u^{\prime}_{j}u^{\prime}_{k}}\DP{\theta }{x_{k}} 
          -\overline{\theta^{\prime} u^{\prime}_{k}}\DP{u_{j}}{x_{k}} 
          -\overline{\theta_v}^{-1} g_{j}\overline{(\theta^{\prime})^{2}} 
          + \overline{p \DP{\theta^{\prime} }{x_{j}}}
          -(\alpha + \nu )
            \overline{\DP{u^{\prime}_{j}}{x_{k}}\DP{\theta^{\prime} }{x_{k}}}.
         \Deqlab{MY1974:eq(8)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8283}%
$i=j$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12268}%
$\displaystyle \DP{q^{2}}{t} + u_{k}\DP{q^{2}}{x_{k}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12270}%
$\displaystyle \DP{}{x_{k}}\left(\overline{u^{\prime}_{k}u^{\prime}_{j}u^{\prime}_{j}}
    - \nu \DP{q^{2}}{x_{k}}\right)
    + 2 f_k \varepsilon _{jkl} \overline{u_{l}^{\prime} u^{\prime}_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12272}%
$\displaystyle - 2 \overline{u^{\prime}_{j}u^{\prime}_{k}}\DP{u_{j}}{x_{k}} 
    - 2 \DP{}{x_{j}}\overline{pu^{\prime}_{j}} 
    + 2 g_{j}\overline{\theta_v}^{-1}\overline{u^{\prime}_{j} \theta_v}
    - 2 \nu \overline{\left(\DP{u^{\prime}_{j}}{x_{k}}\right)^2}
    \Deqlab{q¤ÎÍ½Êó¼°}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{eqnarraystar6267}%
\begin{eqnarray*}
  q &\equiv&  \sqrt{\overline{(u^{\prime}_{i})^{2}}}  \\
    & = &    \sqrt{2E_{turb}} 
\end{eqnarray*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8285}%
$\nu$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8287}%
$\alpha$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8289}%
$g_{j}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8291}%
$j$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8293}%
$\overline{p\left(\DP{u^{\prime}_{i}}{x_{j}} + \DP{u^{\prime}_{i}}{x_{j}}\right)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8237}%
\begin{displaymath}
          = - \frac{q}{3l_{1}}(\overline{u^{\prime}_{i}u^{\prime}_{j}} - 
                              \frac{\delta _{ij}}{3}q^{2})
            + Cq^{2}\left(\DP{u_{i}}{x_{j}} 
            + \DP{u_{j}}{x_{i}}\right),
        \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8295}%
$l_{1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8299}%
$\overline{p\DP{\theta^{\prime} }{x_{j}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8238}%
\begin{displaymath}
          = -\frac{q}{3l_{2}}\overline{u^{\prime}_{j}\theta^{\prime} }
        \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8301}%
$l_{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8303}%
$2\nu \overline{\DP{u^{\prime}_{i}}{x_{k}}\DP{u^{\prime}_{j}}{x_{k}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8305}%
$q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8239}%
\begin{displaymath}
          = \frac{2}{3}\frac{q^{3}}{\Lambda _{1}}\delta _{ij}.
        \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8307}%
$\Lambda _{1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8309}%
$(\alpha + \nu )
          \overline{\DP{u^{\prime}_{j}}{x_{k}}\DP{\theta^{\prime} }{x_{k}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8240}%
\begin{displaymath}
          = 0
        \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8311}%
$\overline{u^{\prime}_{k}u^{\prime}_{i}u^{\prime}_{j}}, 
        \overline{u^{\prime}_{k}u^{\prime}_{j}\theta^{\prime} }, 
        \overline{u^{\prime}_{k}(\theta^{\prime})^{2}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{eqnarraystar6353}%
\begin{eqnarray*}
          \overline{u^{\prime}_{k}u^{\prime}_{i}u^{\prime}_{j}} 
          &=& -q\lambda _{1}\left(
            \DP{\overline{u^{\prime}_{i}u^{\prime}_{j}}}{x_{k}} + 
            \DP{\overline{u^{\prime}_{i}u^{\prime}_{k}}}{x_{j}} + 
            \DP{\overline{u^{\prime}_{j}u^{\prime}_{k}}}{x_{i}}\right), \\
          \overline{u^{\prime}_{k}u^{\prime}_{j}\theta^{\prime} } 
          &=& -q\lambda _{2}\left( 
            \DP{\overline{u^{\prime}_{k}\theta^{\prime} }}{x_{j}} + 
            \DP{\overline{u^{\prime}_{j}\theta^{\prime} }}{x_{k}}\right), \\
          \overline{u^{\prime}_{k}(\theta^{\prime})^{2}} &=& -q\lambda _{3}
                   \DP{\overline{(\theta^{\prime})^{2}}}{x_{k}}. 
        \end{eqnarray*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8315}%
$\lambda _{i}(i=1,2,3)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8317}%
$\overline{pu^{\prime}_{i}}, \overline{p\theta^{\prime} }$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8241}%
\begin{displaymath}
            \overline{pu^{\prime}_{i}} =  \overline{p\theta^{\prime} } = 0
        \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8319}%
$f_{k}(\varepsilon _{jkl}\overline{u_{l}^{\prime}u^{\prime}_{i}}
         + \varepsilon _{ikl}\overline{u_{l}^{\prime}u^{\prime}_{j}}), \;
         f_{k}\varepsilon _{jkl}\overline{u_{l}^{\prime}\theta^{\prime} }$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8242}%
\begin{displaymath}
           f_{k}\varepsilon _{jkl}\overline{u_{l}^{\prime}u^{\prime}_{i}} =
           f_{k}\varepsilon _{ikl}\overline{u_{l}^{\prime}u^{\prime}_{j}} = 0,
        \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8243}%
\begin{displaymath}
           f_{k}\varepsilon _{jkl}\overline{u_{l}^{\prime}\theta^{\prime}} = 0
        \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8321}%
$\alpha \overline{u^{\prime}_{j}\DP{\theta^{\prime} }{x_{k}}}, \;
          \nu \overline{\theta^{\prime} \DP{u^{\prime}_{j}}{x_{k}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12303}%
$\displaystyle \DD{\overline{u^{\prime}_{i}u^{\prime}_{j}}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12304}%
$\textstyle -$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12305}%
$\displaystyle \DP{}{x_{k}}\left[
              q\lambda _{1}\left(
                \DP{\overline{u^{\prime}_{i}u^{\prime}_{j}}}{x_{k}} + 
                \DP{\overline{u^{\prime}_{i}u^{\prime}_{k}}}{x_{j}} + 
                \DP{\overline{u^{\prime}_{j}u^{\prime}_{k}}}{x_{i}}\right)
		-\nu\DP{}{x_{k}}\overline{u^{\prime}_{i}u^{\prime}_{j}}\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12307}%
$\displaystyle - \overline{u^{\prime}_{k}u^{\prime}_{i}}\DP{u_{j}}{x_{k}}
              - \overline{u^{\prime}_{k}u^{\prime}_{j}}\DP{u_{i}}{x_{k}}
	      - \overline{\theta_v}^{-1}
               ( g_{j}\overline{u^{\prime}_{i}\theta_{v}^{\prime} }
                + g_{i}\overline{u^{\prime}_{j}\theta_{v}^{\prime} })$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12308}%
$\displaystyle - \frac{q}{3l_{1}}(\overline{u^{\prime}_{i}u^{\prime}_{j}}
              - \frac{\delta _{ij}}{3}q^{2})
              + Cq^{2}\left(\DP{u_{i}}{x_{j}} 
              + \DP{u_{j}}{x_{i}}\right)
              - \frac{2}{3}\frac{q^{3}}{\Lambda _{1}}\delta _{ij},
	      \Deqlab{MY1974:Level4(1)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12309}%
$\displaystyle \DD{\overline{u^{\prime}_{j}\theta^{\prime} }}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12311}%
$\displaystyle \DP{}{x_{k}}\left[q\lambda _{2}\left(
              \DP{\overline{u^{\prime}_{k}\theta^{\prime} }}{x_{j}}
              + \DP{\overline{u^{\prime}_{j}\theta^{\prime} }}{x_{k}}\right)\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12313}%
$\displaystyle - \overline{u^{\prime}_{j}u^{\prime}_{k}}\DP{\theta }{x_{k}} 
              - \overline{\theta^{\prime} u^{\prime}_{k}}\DP{u^{\prime}_{j}}{x_{k}} 
              - \overline{\theta_v}^{-1} g_{j}\overline{(\theta^{\prime})^{2}} 
              - \frac{q}{3l_{2}}\overline{u^{\prime}_{j}\theta^{\prime} }, 
	      \Deqlab{MY1974:Level4(2)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12314}%
$\displaystyle \DD{q^{2}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12316}%
$\displaystyle \DP{}{x_{k}}\left[
         q\lambda _{1}\left(
               \DP{q^{2}}{x_{k}} + 
               2 \DP{\overline{u^{\prime}_{j}u^{\prime}_{k}}}{x_{j}}\right)
        - \nu \DP{q^{2}}{x_{k}}\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12318}%
$\displaystyle - 2\overline{u^{\prime}_{j}u^{\prime}_{k}}\DP{u_{j}}{x_{k}} 
    + 2 g_{j} \overline{\theta_v}^{-1} 
        \overline{u^{\prime}_{j}\theta_v^{\prime}}
    - 2\frac{q^{3}}{\Lambda _{1}}
	      \Deqlab{MY1974:Level4(3)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8244}%
\begin{displaymath}
  \DD{}{t} \equiv \DP{}{t} + u_{k}\DP{}{x_{k}}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8323}%
$C=-1/3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8325}%
$\overline{u^{\prime}_{j}u^{\prime}_{k}}\sim q^{2}\delta_{jk}/3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8327}%
$\lambda_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12324}%
$\displaystyle \overline{u^{\prime}_{i}u^{\prime}_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12326}%
$\displaystyle \frac{\delta _{ij}}{3}q^{2}
       - ql_{1}\left(\DP{u_{i}}{x_{j}} + \DP{u_{j}}{x_{i}}\right)
    \Deqlab{MY1974:Level1(1)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12327}%
$\displaystyle \overline{u^{\prime}_{j}\theta^{\prime}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12329}%
$\displaystyle - ql_{2}\DP{\theta }{x_{j}} 
    \Deqlab{MY1974:Level1(2)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12332}%
$\displaystyle - 2\overline{u^{\prime}_{j}u^{\prime}_{k}}\DP{u_{j}}{x_{k}} 
    + 2 g_{j} \overline{\theta_v}^{-1} 
        \overline{u^{\prime}_{j} \theta_v^{\prime}}
    + \DP{}{x_{k}}\left[\nu \DP{q^{2}}{x_{k}}\right]
    - 2\frac{q^{3}}{\Lambda _{1}}
    \Deqlab{MY1974:Level3(1)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8329}%
$\overline{u^{\prime}_{i}u^{\prime}_{j}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8331}%
$\overline{u^{\prime}_{j}\theta^{\prime}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8333}%
$\overline{(\theta^{\prime})^{2}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8335}%
$q^{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8337}%
$q_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8339}%
$q_L$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12344}%
$\displaystyle \overline{u^{\prime}_{j} q_v^{\prime}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12346}%
$\displaystyle - ql_{3} \DP{ q_v }{x_{j}}, 
   \Deqlab{MY1974:Level1(3)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12347}%
$\displaystyle \overline{u^{\prime}_{j} q_L^{\prime}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12349}%
$\displaystyle - ql_{4} \DP{ q_L }{x_{j}} 
   \Deqlab{MY1974:Level1(4)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8349}%
$l_3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8351}%
$l_4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8353}%
$ql_{1}=K_{m}, ql_{2} = ql_{3} = ql_{4} = K_{h}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12358}%
$\displaystyle \frac{2}{3}\delta _{ij}E_{turb}
       - K_{m}\left(\DP{u_{i}}{x_{j}} + \DP{u_{j}}{x_{i}}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12359}%
$\displaystyle \overline{\theta_v}^{-1}
   \overline{u^{\prime}_{j}\theta_v^{\prime}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12361}%
$\displaystyle \frac{ \overline{ u_j^{\prime} \theta^{\prime}} }{\overline{\theta}}
      + \frac{\sum \frac{R_v}{R_d} \overline{u_j^{\prime} q_v^{\prime}} 
        - \sum \overline{ u_j^{\prime} q_L^{\prime}} }
      { 1 + \sum \frac{R_v}{R_d} \overline{q_v} - \sum \overline{q_L} }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12363}%
$\displaystyle - \frac{K_h}{\overline{\theta}}  \DP{\theta}{x_j}
      - K_h \frac{\sum \frac{R_v}{R_d} \DP{q_v}{x_j} 
        - \sum \DP{ q_L }{x_j} }
      { 1 + \sum \frac{R_v}{R_d} \overline{q_v} - \sum \overline{q_L} }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12366}%
$\displaystyle - \overline{u^{\prime}_{j}u^{\prime}_{k}}\DP{u_{j}}{x_{k}} 
    + g_{j} \overline{\theta_v}^{-1} 
       \overline{u^{\prime}_{j}\theta_v^{\prime}}
    + \DP{}{x_{k}}\left[K_{m} \DP{q^{2}}{x_{k}}\right]
    - \frac{2^{3/2}}{\Lambda _{1}}E_{turb}^{3/2}
  \Deqlab{ÍðÎ®¥¨¥Í¥ë¥®¡¼¤Î¼°}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8365}%
$q_v^{\prime}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8367}%
$\theta_e^{\prime}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8369}%
$q_L^{\prime}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8371}%
$q_v^{*} (T,p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12376}%
$\displaystyle q_v^{*} (T,p)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12378}%
$\displaystyle q_v^{*} (\overline{T},\overline{p})
   + \left( \DP{q_v^{*}}{T} \right)_{(\overline{T},\overline{p})} 
     T^{\prime}
   + \left( \DP{q_v^{*}}{p} \right)_{(\overline{T},\overline{p})} 
     p^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12380}%
$\displaystyle \overline{q_v^{*}} 
   + \left( \DP{q_v^{*}}{T} \right)_{(\overline{T},\overline{p})} 
     T^{\prime}
   + \left( \DP{q_v^{*}}{p} \right)_{(\overline{T},\overline{p})} 
     p^{\prime}
 \Deqlab{moistturb1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12382}%
$\displaystyle \left( \DP{q_v^{*}}{T} \right)_{(\overline{T},\overline{p})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12384}%
$\displaystyle \DP{}{T} 
   \left( 
     \frac{p_v^{*} / R_v}{p / \langle R \rangle_0 } 
   \right)_{(\overline{T},\overline{p})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12386}%
$\displaystyle \frac{\langle R \rangle_0}{R_v \overline{p}}
    \left( \DP{p_v^{*}}{T} \right)_{(\overline{T},\overline{p})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12388}%
$\displaystyle \frac{L \langle R \rangle_0}{R_v^2 \overline{T}^2}
   \frac{\overline{p_v}^{*}}{ \overline{p}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12390}%
$\displaystyle \frac{L \overline{q_v}^{*}}{R_v \overline{T}^2}, 
 \Deqlab{moistturb2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12391}%
$\displaystyle \left( \DP{q_v^{*}}{p} \right)_{(\overline{T},\overline{p})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12393}%
$\displaystyle \DP{}{p} 
   \left( 
     \frac{p_v^{*} / R_v}{p / \langle R \rangle_0 } 
   \right)_{(\overline{T},\overline{p})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12395}%
$\displaystyle - \frac{\overline{q_v^{*}}}{\overline{p}}
 \Deqlab{moistturb3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12397}%
$\displaystyle \DP{p_v^{*}}{T}
 = 
   \frac{L p_v^{*}}{R_v T^2}
 \Deqlab{moistturb3-2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12399}%
$\displaystyle {q_v^{*}}^{\prime} (T,p)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12401}%
$\displaystyle \frac{L \overline{q_v}^{*}}{R_v \overline{T}^2} 
     T^{\prime}
   - \frac{\overline{q_v^{*}}}{\overline{p}}
     p^{\prime}
 \Deqlab{moistturb4}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath6871}%
\begin{displaymath}
 \frac{T^{\prime}}{\overline{T}}
  \simeq
    \frac{\theta^{\prime}}{\overline{\theta}}
    + \frac{\langle R \rangle_0}{\langle c_p \rangle_0}
      \frac{p^{\prime}}{\overline{p}}
 \Deqlab{moistturb5}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12406}%
$\displaystyle \frac{L \overline{q_v}^{*}}{R_v \overline{T}} 
    \left(
     \frac{\theta^{\prime}}{\overline{\theta}}
      + \frac{\langle R \rangle_0}{\langle c_p \rangle_0}
        \frac{p^{\prime}}{\overline{p}}
    \right)
   - \frac{\overline{q_v^{*}}}{\overline{p}}
    p^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12408}%
$\displaystyle \frac{L \overline{q_v}^{*}}{R_v \overline{\Pi} \overline{\theta}^2}
   \theta^{\prime}
  + 
    \left( 
     \frac{L \langle R \rangle_0}{R_v \langle c_p \rangle_0
     \overline{T}} 
      - 1 
    \right)
    \frac{\overline{q_v^{*}}}{\overline{p}}
    p^{\prime}
 \Deqlab{moistturb6}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12410}%
$\displaystyle \overline{ u_j^{\prime} {q_v^{*}}^{\prime} }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12412}%
$\displaystyle \frac{L \overline{q_v}^{*}}{R_v \overline{\Pi} \overline{\theta}^2}
   \overline{ u_j^{\prime} \theta^{\prime} }
  + 
    \left( 
     \frac{L \langle R \rangle_0}{R_v \langle c_p \rangle_0
     \overline{T}} 
      - 1 
    \right)
    \frac{\overline{q_v^{*}}}{\overline{p}}
    \overline{ u_j^{\prime} p^{\prime}}
 \Deqlab{moistturb7}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8373}%
$\overline{u_j^{\prime} p^{\prime}} = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12417}%
$\displaystyle \frac{L \overline{q_v}^{*}}{R_v \overline{\Pi} \overline{\theta}^2}
   \overline{ u_j^{\prime} \theta^{\prime} }
 \Deqlab{moistturb8}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12419}%
$\displaystyle \theta_e^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12421}%
$\displaystyle \theta^{\prime} 
  + \sum \frac{L}{\langle c_p \rangle_0 \overline{\Pi}}
  {q_v^{*}}^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12423}%
$\displaystyle \theta^{\prime}
  + \sum \frac{L}{\langle c_p \rangle_0 \overline{\Pi}}
   \left[
     \frac{L \overline{q_v}^{*}}{R_v \overline{\Pi} \overline{\theta}^2}
     \theta^{\prime}
    + 
     \left( 
     \frac{L \langle R \rangle_0}{R_v \langle c_p \rangle_0
     \overline{T}} 
      - 1 
     \right)
      \frac{\overline{q_v^{*}}}{\overline{p}}
       p^{\prime}
   \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12425}%
$\displaystyle \theta^{\prime}
   \left(
    1 +
     \sum 
      \frac{ L^2 \overline{q_v}^{*}}
       { \langle c_p \rangle_0 R_v \overline{\Pi}^2 
         \overline{\theta}^2 }
   \right)
  + \sum \frac{L}{\langle c_p \rangle_0 \overline{\Pi}}
     \left( 
     \frac{L \langle R \rangle_0}{R_v \langle c_p \rangle_0
     \overline{T}} 
      - 1 
     \right)
      \frac{\overline{q_v^{*}}}{\overline{p}}
       p^{\prime}
 \Deqlab{moistturb9}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12427}%
$\displaystyle \overline{ u_j^{\prime} \theta^{\prime}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12429}%
$\displaystyle \left(
    1 +
     \sum 
      \frac{ L^2 \overline{q_v}^{*}}
       { \langle c_p \rangle_0 R_v \overline{\Pi}^2 
         \overline{\theta}^2 }
   \right)^{-1}
    \overline{u_j^{\prime} \theta_e^{\prime}}
 \Deqlab{moistturb10}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12431}%
$\displaystyle \overline{ u_j^{\prime} {q_v^{*}}^{\prime} }
 =
  \frac{L \overline{q_v}^{*}}
       {R_v \overline{\Pi} \overline{\theta}^2}
   \left(
    1 +
     \sum 
      \frac{ L^2 \overline{q_v}^{*}}
       { \langle c_p \rangle_0 R_v \overline{\Pi}^2 
         \overline{\theta}^2 }
   \right)^{-1}
    \overline{u_j^{\prime} \theta_e^{\prime}}
 \Deqlab{moistturb11}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12436}%
$\displaystyle \overline{u^{\prime}_{j} \theta_e^{\prime}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12438}%
$\displaystyle - ql_{5} \DP{ \theta_e }{x_{j}}, 
    \Deqlab{moistturb12}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12441}%
$\displaystyle - ql_{6} \DP{ q_L }{x_{j}} 
    \Deqlab{moistturb13}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8381}%
$l_5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8383}%
$l_6$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8385}%
$q l_5 = q l_6 = K_h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12455}%
$\displaystyle - K_h 
        \left( 
         1 
          + \sum 
           \frac{L^2 \overline{q_v}}{ \langle c_p \rangle_0 R_v 
               \overline{\theta}^2 \overline{\Pi}^2 } 
        \right)^{-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12456}%
$\displaystyle \left[
         \Dinv{\overline{\theta}}
         + \Dinv{R_d \overline{\Pi} \overline{\theta}^2}
           \left( 
            1 + \sum \frac{R_v}{R_d} \overline{q_v} - \sum \overline{q_L}
           \right)^{-1}
          \left( \sum L \overline{q_v} \right)
        \right]
        \DP{\theta_e}{x_j}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12457}%
$\displaystyle + K_h 
         \left( 
          1 + \sum \frac{R_v}{R_d} \overline{q_v} - \sum \overline{q_L}
         \right)^{-1}
        \DP{\left( \sum q_L \right)}{x_j},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12460}%
$\displaystyle - \overline{u^{\prime}_{j}u^{\prime}_{k}}\DP{u_{j}}{x_{k}} 
    + g_{j} \overline{\theta_v}^{-1} 
       \overline{u^{\prime}_{j}\theta_v^{\prime}}
    + \DP{}{x_{k}}\left[K_{m} \DP{q^{2}}{x_{k}}\right]
    - \frac{2^{3/2}}{\Lambda _{1}}E_{turb}^{3/2}
  \Deqlab{ÍðÎ®¥¨¥Í¥ë¥®¡¼¤Î¼°2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12465}%
$\displaystyle \frac{g_{j}}{\overline{\theta_v}} 
  \overline{u^{\prime}_{j} \theta^{\prime}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12467}%
$\displaystyle \frac{g}{\overline{\theta}} 
  \overline{w^{\prime}  \theta^{\prime}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12469}%
$\displaystyle - g \frac{K_h}{\overline{\theta}}  \DP{\theta}{z}
    - g K_h \frac{\sum \frac{R_v}{R_d} \DP{q_v}{z} 
      - \sum \DP{ q_L }{z} }
    { 1 + \sum \frac{R_v}{R_d} \overline{q_v} - \sum \overline{q_L} } 
\Deqlab{B}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12477}%
$\displaystyle - g K_h 
        \left( 
         1 
          + \sum 
           \frac{L^2 \overline{q_v}}{ \langle c_p \rangle_0 R_v 
               \overline{\theta}^2 \overline{\Pi}^2 } 
        \right)^{-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12479}%
$\displaystyle + g K_h 
         \left( 
          1 + \sum \frac{R_v}{R_d} \overline{q_v} - \sum \overline{q_L}
         \right)^{-1}
        \DP{\left( \sum q_L \right)}{z}
\Deqlab{B-moist}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12484}%
$\displaystyle - \overline{(u_{i}^{\prime} u_{j}^{\prime})}
  \DP{u_{i}}{x_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12486}%
$\displaystyle - \left\{
     - K_{m} \left(\DP{u_{i}}{x_{j}} + \DP{u_{j}}{x_{i}}\right)
	  + \frac{2}{3} \delta_{ij} E_{turb}
    \right\}
  \DP{u_{i}}{x_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12488}%
$\displaystyle \left\{ 
      K_{m} \left(\DP{u_{i}}{x_{j}} + \DP{u_{j}}{x_{i}}\right)
	  - \frac{2}{3} \delta_{ij} E_{turb}
   \right\} 
  \DP{u_{i}}{x_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12490}%
$\displaystyle \left\{ 
    K_{m} \left(\DP{u}{x_{j}} + \DP{u_{j}}{x}\right)
    - \frac{2}{3} \delta_{1j} E_{turb}
   \right\} 
  \DP{u}{x_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12491}%
$\displaystyle +  
   \left\{ 
      K_{m} \left(\DP{v}{x_{j}} + \DP{u_{j}}{y}\right)
	  - \frac{2}{3} \delta_{2j} E_{turb}
   \right\} 
  \DP{v}{x_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12492}%
$\displaystyle +  
   \left\{ 
      K_{m} \left(\DP{w}{x_{j}} + \DP{u_{j}}{z}\right)
	  - \frac{2}{3} \delta_{3j} E_{turb}
   \right\} 
  \DP{w}{x_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12494}%
$\displaystyle \left\{ 
      2 K_{m} \DP{u}{x}
	  - \frac{2}{3} E_{turb}
   \right\} 
  \DP{u}{x}
  +  
   K_{m} \left( \DP{u}{y} + \DP{v}{x} \right)
  \DP{u}{y}
  +  
   K_{m} \left( \DP{w}{x} + \DP{u}{z} \right)
  \DP{u}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12495}%
$\displaystyle +  
   K_{m} \left( \DP{v}{x} + \DP{u}{y} \right)
  \DP{v}{x}
  +  \left\{ 
      2 K_{m} \DP{v}{y}
	  - \frac{2}{3} E_{turb}
   \right\} 
  \DP{v}{y}
  +  
   K_{m} \left( \DP{v}{z} + \DP{w}{y} \right)
  \DP{v}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12496}%
$\displaystyle +  
   K_{m} \left(\DP{w}{x} + \DP{u}{z}\right)
  \DP{w}{x}
   + K_{m} \left(\DP{w}{y} + \DP{v}{z}\right)
  \DP{w}{y}
  +  
   \left\{ 
     2 K_{m} \DP{w}{z}  
	  - \frac{2}{3} E_{turb}
   \right\} 
  \DP{w}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12498}%
$\displaystyle 2 K_{m} \left\{ 
       \left( \DP{u}{x} \right)^{2}
     + \left( \DP{v}{y} \right)^{2}
     + \left( \DP{w}{z} \right)^{2}
    \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12499}%
$\displaystyle +  K_{m}
     \left\{
      \left(\DP{u}{y} + \DP{v}{x}\right)^{2}
      + \left(\DP{v}{z} + \DP{w}{y}\right)^{2}
      + \left(\DP{w}{x} + \DP{u}{z}\right)^{2}
     \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12500}%
$\displaystyle - \frac{2}{3} E_{turb} 
     \left( \DP{u}{x} + \DP{v}{y} + \DP{w}{z} \right) 
\Deqlab{S}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12505}%
$\displaystyle \DP{}{x_{j}} \left(K_{m} \DP{E_{turb}}{x_{j}} \right),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12507}%
$\displaystyle \DP{}{x} \left(K_{m} \DP{E_{turb}}{x} \right)  
       + \DP{}{y} \left(K_{m} \DP{E_{turb}}{y} \right)  
       + \DP{}{z} \left(K_{m} \DP{E_{turb}}{z} \right)  
\Deqlab{De}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12511}%
$\displaystyle - g \frac{K_h}{\overline{\theta}}  \DP{\theta}{z}
    - g K_h \frac{\sum \frac{R_v}{R_d} \DP{q_v}{z} 
      - \sum \DP{ q_L }{z} }
    { 1 + \sum \frac{R_v}{R_d} \overline{q_v} - \sum \overline{q_L} }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12512}%
$\displaystyle + 2 K_{m} \left\{ 
       \left( \DP{u}{x} \right)^{2}
     + \left( \DP{v}{y} \right)^{2}
     + \left( \DP{w}{z} \right)^{2}
    \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12515}%
$\displaystyle + \DP{}{x} \left(K_{m} \DP{E_{turb}}{x} \right)  
      + \DP{}{y} \left(K_{m} \DP{E_{turb}}{y} \right)  
      + \DP{}{z} \left(K_{m} \DP{E_{turb}}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12516}%
$\displaystyle - \left(\frac{C_{\varepsilon}}{l}\right)
	  E_{turb}^{\frac{3}{2}}.
\Deqlab{B:TurbE}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8395}%
$K_m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12528}%
$\displaystyle + \DP{}{z} \left(C_m l E_{turb}^{1/2} \DP{E_{turb}}{z} \right)  
      - \left(\frac{C_{\varepsilon}}{l}\right)
	  E_{turb}^{\frac{3}{2}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12534}%
$\displaystyle + g K_h 
         \left( 
          1 + \sum \frac{R_v}{R_d} \overline{q_v} - \sum \overline{q_L}
         \right)^{-1}
        \DP{\left( \sum q_L \right)}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12539}%
$\displaystyle - \left(\frac{C_{\varepsilon}}{l}\right)
	  E_{turb}^{\frac{3}{2}}.
\Deqlab{B:TurbE-moist}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8940}%
$V_D$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8948}%
$F_D$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12563}%
$\displaystyle F_D = \Dinv{8} \rho V_D^2 C_D D^2 \Deqlab{shuutan1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8950}%
$C_D$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12567}%
$\displaystyle \Dinv{6} \pi \rho_w D^3 g = \Dinv{8} \rho V_D^2 C_D D^2 \Deqlab{shuutan2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12570}%
$\displaystyle V_D 
 = \left( \frac{ 4 \rho_w g D}{3 C_D \rho} \right)^{1/2}
 \Deqlab{shuutan3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8956}%
$\rho_w = 10^3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8960}%
$g = 9.8$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8964}%
$\rho_0 = 1.2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8968}%
$C_D = 0.644$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12579}%
$\displaystyle V_D 
 = 130 \left( \frac{\rho_0}{\rho} \right)^{0.5} D^{0.5}
 \Deqlab{shuutan4}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8976}%
$\rho_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8509}%
\begin{displaymath}
V_D 
 = 1.4389 \left( \frac{\rho_w g D}{\rho} \right)^{1/2}
 \Deqlab{shuutan5}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8984}%
$(dm(D)/dt)_{cr}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8988}%
$D+dD$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8990}%
$N_{D}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8519}%
\begin{displaymath}
  CL_{cr} = \Dinv{\rho}\int_{0}^{\infty}\left(\DD{m}{t}\right)_{cr}
   N_{D}\Dd D
  \Deqlab{¾×ÆÍÊ»¹ç¤Ë¤è¤ë±«¿åº®¹çÈæ¤ÎÊÑ²½Î¨}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8531}%
\begin{displaymath}
  \left(\DD{m}{t}\right)_{cr} = \frac{\pi}{4}D^{2} V_D E \rho q_{c}
  \Deqlab{¾×ÆÍÊ»¹ç¤Ë¤è¤ë±«Î³¤ÎÀ®Ä¹ÊýÄø¼°}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8996}%
$E$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12601}%
$\displaystyle N_{D}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12603}%
$\displaystyle N_{0}\exp (-\lambda D), \Deqlab{¥Þ¡¼¥·¥ã¥ë¡¦¥Ñ¥ë¥Þ¡¼·¿Ê¬ÉÛ´Ø
   ¿ô1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12604}%
$\displaystyle V_D$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12606}%
$\displaystyle 1.4389 \left( \frac{\rho_w g D}{\rho} \right)^{1/2}
   \Deqlab{¥Þ¡¼¥·¥ã¥ë¡¦¥Ñ¥ë¥Þ¡¼·¿Ê¬ÉÛ´Ø¿ô2}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9000}%
$N_{0}, \lambda $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9002}%
$N_{0}=10^{7}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12610}%
$\displaystyle CL_{cr}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12612}%
$\displaystyle \frac{1.4389 \pi}{4} \left( \frac{\rho_w g D}{\rho}
				   \right)^{1/2} E N_{0} q_{c} 
            \int_{0}^{\infty}D^{2.5}\exp(-\lambda D)\Dd D$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12614}%
$\displaystyle \frac{1.4389 \pi}{4} 
              \left( \frac{\rho_w g D}{\rho} \right)^{1/2} E N_{0} q_{c}
	      \frac{3.75}{\lambda ^{3}}\frac{1}{2} 
             \sqrt{\frac{\pi}{\lambda}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12616}%
$\displaystyle \frac{1.4389 \times 3.75 \pi^{3/2}}{8} 
              \left( \frac{\rho_w g D}{\rho} \right)^{1/2}
              E N_{0} q_{c} \lambda ^{-3.5}
  \Deqlab{CL_cr ¹à}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9008}%
$E=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12623}%
$\displaystyle q_{r}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12625}%
$\displaystyle \frac{1}{\rho}\int _{0}^{\infty} \rho_{w}
            \frac{\pi}{6} D^{3} 
            N_{D}\Dd D$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12627}%
$\displaystyle \frac{\pi N_{0}\rho_{w}}{6 \rho}\int _{0}^{\infty}
            D^{3}\exp(-\lambda D)\Dd D$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12629}%
$\displaystyle \frac{\pi N_{0}\rho_{w}}{6 \rho}\frac{6}{\lambda ^{4}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12631}%
$\displaystyle \frac{\pi N_{0}\rho_{w}}{\rho}\lambda ^{-4}.
   \Deqlab{¦Ë¤Î¼°}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9014}%
$\rho_{w}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12637}%
$\displaystyle \frac{1.4389 \times 3.75 \pi^{3/2}}{8} 
              \left( \frac{\rho_w g D}{\rho} \right)^{1/2}
              E N_{0} q_{c} 
              \left( \frac{\rho q_r}{\pi N_0 \rho_w} \right)^{0.875}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12639}%
$\displaystyle \frac{1.4389 \times 3.75 \pi^{5/8}}{8} 
        E N_{0}^{1/8} 
        g^{1/2} \left( \frac{\rho}{\rho_w} \right)^{0.375}
        q_{c} q_r^{0.875}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12641}%
$\displaystyle 10.344
        g^{1/2} \left( \frac{\rho}{\rho_w} \right)^{0.375}
        q_{c} q_r^{0.875}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9018}%
$N_{0}=10^{7}, E=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9022}%
$F_r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12648}%
$\displaystyle V_{term} = \frac{F_r}{\rho_r} \Deqlab{TermVel1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12652}%
$\displaystyle \rho_r$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12654}%
$\displaystyle \int_0^{\infty} N_D m dD, \Deqlab{TermVel2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12655}%
$\displaystyle F_r$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12657}%
$\displaystyle \int_0^{\infty} N_D m V_D dD. \Deqlab{TermVel3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9030}%
$m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12661}%
$\displaystyle m = \frac{\pi}{6} D^3 \rho_w \Deqlab{TermVel4}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12665}%
$\displaystyle \int_0^{\infty} N_0 \exp(- \lambda D) \frac{\pi}{6} \rho_w
  D^3 dD$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12667}%
$\displaystyle \frac{\pi \rho_w N_0}{\lambda^4} \Deqlab{TermVel5}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12670}%
$\displaystyle \int_0^{\infty} N_0 \exp(- \lambda D) \frac{\pi}{6} \rho_w
  D^3 1.4389 \left( \frac{\rho_w g D}{\rho} \right)^{1/2} dD$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12672}%
$\displaystyle \frac{1.4389 \times 105 \pi^{3/2}}{96}
   \rho_w^{3/2} g^{1/2} \rho^{-1/2} N_0 \lambda^{- 9/2}
  \Deqlab{TermVel6}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12677}%
$\displaystyle \frac{1.4389 \times 105 \pi^{3/2}}{96}
   \rho_w^{3/2} g^{1/2} \rho^{-1/2} N_0 
   \left( \frac{\rho_r}{\pi N_0 \rho_w} \right)^{9/8}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12679}%
$\displaystyle \frac{1.4389 \times 105 \pi^{3/8}}{96}
   \rho_w^{3/8} g^{1/2} \rho^{-1/2} N_0^{-1/8} \rho_r^{9/8}
      \Deqlab{TermVel7}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12681}%
$\displaystyle V_{term}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12683}%
$\displaystyle \frac{1.4389 \times 105 \pi^{3/8}}{96}
   \rho_w^{3/8} g^{1/2} \rho^{-1/2} N_0^{-1/8} \rho_r^{1/8}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12685}%
$\displaystyle 0.3224 g^{1/2} \left( \frac{\rho_w}{\rho} \right)^{0.375}
   q_r^{0.125}
 \Deqlab{TermVel8}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmldisplayA{displaymath8738}%
\begin{displaymath}
  EV_{rv} = \frac{1}{\rho_{d}}\int _{0}^{\infty}\left(\DD{m}{t}\right)_{ev}
  N_{D}\Dd D
  \Deqlab{¾øÈ¯¤Ë¤è¤ë±«¿åº®¹çÈæ¤ÎÁý²ÃÎ¨}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9038}%
$(dm(D)/dt)_{ev}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9042}%
$F$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8751}%
\begin{displaymath}
  \left(\DD{m}{t}\right)_{ev} = - 4\pi r_{d}^{2}F(r_{d})
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9044}%
$r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9046}%
$r_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8930}%
\begin{displaymath}
   F = - K_{d}\DD{\rho_{v}}{r}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9050}%
$\rho_{v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9052}%
$K_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8931}%
\begin{displaymath}
  \frac{1}{r^{2}}\DP{}{r}\left(r^{2}F\right) = 0
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8932}%
\begin{displaymath}
   \rho _{v} = -\frac{C_{1}}{r} + C_{2}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9054}%
$r=r_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9056}%
$\rho_{v} = \rho_{v,s}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9058}%
$r=\infty$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9060}%
$\rho_{v}=\rho_{v,\infty}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8933}%
\begin{displaymath}
  C_{1} = (\rho _{v,\infty}-\rho_{v,s})r_{d}, 
  \quad C_{2} = \rho _{v,\infty}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12707}%
$\displaystyle F(r_{d})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12709}%
$\displaystyle - K_{d}\left.\DD{\rho_{v}}{r}\right|_{r=r_{d}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12711}%
$\displaystyle K_{d}\frac{\rho_{v,s} - \rho _{v,\infty}}{r_{d}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8796}%
\begin{displaymath}
  \left(\DD{m}{t}\right)_{ev} = - 4\pi r_{d}K_{d}(\rho_{v,s}-\rho_{v,\infty})
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8806}%
\begin{displaymath}
  \left(\DD{m}{t}\right)_{ev} = - 4\pi r_{d}\left(1+\frac{Fr}{s}\right)
                K_{d}(\rho_{v,s}-\rho_{v,\infty})
  \Deqlab{¾øÈ¯¤Ë¤è¤ë±«Î³¤ÎÀ®Ä¹ÊýÄø¼°}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9066}%
$s$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{eqnarraystar8820}%
\begin{eqnarray*}
  4\pi r_{d}\left(1+\frac{Fr}{s}\right) &\sim& 2.24\times 10^{3}D^{1.6}, \\
  K_{d}(\rho _{v,s} - \rho_{v,\infty}) &\sim& 10^{-5}(\rho_{v,s}-\rho_{v,\infty}).
\end{eqnarray*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8834}%
\begin{displaymath}
  \left(\DD{m}{t}\right)_{ev} \sim 
     - 2.24\times 10^{-2}(\rho_{v,s}-\rho_{v,\infty})D^{1.6}
  \Deqlab{¶á»÷¤µ¤ì¤¿¾øÈ¯¤Ë¤è¤ë±«Î³¤ÎÀ®Ä¹ÊýÄø¼°}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12721}%
$\displaystyle EV_{rv}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12723}%
$\displaystyle - \frac{1}{\rho_{d}}2.24\times 10^{-2}(q_{v,s} -q_{v,\infty})\int _{0}^{\infty}
              D^{1.6}N_{D}\Dd D,$%
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\lthtmlinlinemathA{tex2html_wrap_indisplay12725}%
$\displaystyle - 2.24\times 10^{-2}(q_{v,s} -q_{v,\infty})\int _{0}^{\infty}
              D^{1.6}N_{0}\exp(-\lambda D)\Dd D$%
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\lthtmlinlinemathA{tex2html_wrap_indisplay12727}%
$\displaystyle - 2.24\times 10^{-2}(q_{v,s} -q_{v,\infty})
              N_{0}\frac{\Gamma(2.6)}{\lambda ^{13/5}}$%
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\lthtmlinlinemathA{tex2html_wrap_indisplay12729}%
$\displaystyle - 2.24\times 10^{-2}
              \Gamma(2.6) (\pi \rho_{w})^{-0.65}
	      N_{0}^{0.35}
	      (q_{v,s} -q_{v,\infty})
	      (\rho_{d}q_{r})^{0.65}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12731}%
$\displaystyle - 1.7\times 10^{-4}N_{0}^{0.35}(q_{v,s} -q_{v,\infty})
                (\rho_{d}q_{r})^{0.65}$%
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\lthtmlinlinemathA{tex2html_wrap_indisplay12733}%
$\displaystyle - 4.81\times 10^{-2}(q_{v,s} -q_{v,\infty})
                (\rho_{d}q_{r})^{0.65}$%
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$\Gamma(2.6)=1.4296245$%
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\begin{displaymath}
  EV_{rv} = 4.85\times 10^{-2}(q_{v,s} -q_{v,\infty})(\rho_{d}q_{r})^{0.65}
\end{displaymath}%
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\stepcounter{chapter}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9160}%
$C_{\varepsilon}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9162}%
$C_{m}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9164}%
$c_s$%
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{\newpage\clearpage
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$\bar{c_s}$%
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{\newpage\clearpage
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$\langle c_{v} \rangle$%
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$D_{*}$%
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{\newpage\clearpage
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$f$%
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{\newpage\clearpage
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$g$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9188}%
$\overline{p}$%
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{\newpage\clearpage
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$p_{0}$%
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{\newpage\clearpage
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$\overline{\Pi}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9202}%
$R_{d}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9204}%
$R_{v}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9208}%
$\overline{\rho}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9210}%
$\rho_{0}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9218}%
$\overline{\theta}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9222}%
$u_{i}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9224}%
$i = 1, 3$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9226}%
$(u_{1}, u_{3}) = (u, w)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9228}%
$x_{i}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9232}%
$(x_{1}, x_{3}) = (x, z)$%
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{\newpage\clearpage
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\begin{displaymath}
  \mbox{dcstaff@gfd-dennou.org}
 \end{displaymath}%
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\end{document}
