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\Dnoparindent


\Dtitle{湿潤大気における 2 次元非静力学モデルの定式化}


\Dauthor{杉山 耕一朗, 北守 太一, 小高 正嗣}


\Ddate{2006 年 8 月 18 日}




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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4749}%
$\displaystyle - \left(
u \DP{K_{m}}{x} + w \DP{K_{m}}{z}
\right)
- \frac{3 g C_{m}^{2} l^{2}}{ 2 \overline{\theta_{v}}}
\left(\DP{\theta_{el}}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4750}%
$\displaystyle + \left( C_{m}^{2} l^{2} \right) \left\{
\left( \DP{u}{x} \right)^{2}
+ \left( \DP{w}{z} \right)^{2}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4751}%
$\displaystyle +  \frac{ C_{m}^{2} l^{2} }{2}
\left( \DP{u}{z} + \DP{w}{x}\right)^{2}
- \frac{K_{m}}{3}
\left( \DP{u}{x} + \DP{w}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4752}%
$\displaystyle + \Dinv{2}
\left(\DP[2]{K_{m}^{2}}{x}
+ \DP[2]{K_{m}^{2}}{z}
\right)
+ \left(\DP{K_{m}}{x}\right)^{2}
+ \left(\DP{K_{m}}{z}\right)^{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4753}%
$\displaystyle - \Dinv{2 l^{2}} K_{m}^{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline728}%
$C_{\varepsilon} = C_{m} = 0.2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline730}%
$l = \left(\Delta x \Delta z \right)^{1/2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline732}%
$\theta_{el}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4758}%
$\displaystyle \theta_{el}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4760}%
$\displaystyle \overline{ \theta_{v}} + \theta_{v}^{'} \;\;\; (for \;\; q_{c} = 0)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4763}%
$\displaystyle \overline{\theta_{v}} + \theta_{v}^{'} + \frac{ \sum L
q_{v}}{{c_p}_{d} \bar{\pi}}
\;\;\; (for \;\; q_{c} > 0)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4765}%
$\displaystyle \overline{\theta_{v}} + \theta_{v}^{'}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4767}%
$\displaystyle \bar{\theta_{v}}
\left\{
1 + \frac{\theta}{\bar{\theta}}
+ \frac{\sum q_{v}/M_{v}}{1/M_{d} + \sum  \bar{q_{v}}/M_{v}}
- \frac{\sum q_{v} + \sum q_{c} + \sum q_{r}}
{1 + \sum \bar{q_{v}}}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4770}%
$\displaystyle Turb.{u_{i}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4772}%
$\displaystyle - \DP{}{x_{j}} \overline{(u_{i}^{\prime} u_{j}^{\prime})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4774}%
$\displaystyle - \DP{}{x_{j}}
\left[
- K_{m} \left(\DP{u_{i}}{x_{j}}
+ \DP{u_{j}}{x_{i}}\right)
+ \frac{2}{3} \delta_{ij} E
\right].$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline734}%
$K_{m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline736}%
$E$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4778}%
$\displaystyle E = \frac{1}{2}
\overline{(u^{\prime})^{2} + (w^{\prime})^{2}}
= \frac{{K_{m}}^{2}}{C_{m} l^{2}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4781}%
$\displaystyle Turb.{\theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4783}%
$\displaystyle - \DP{}{x_{j}} \overline{u_{i}^{\prime} \theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4785}%
$\displaystyle - \DP{}{x_{j}} \left(K_{h}\DP{\theta}{x_{j}}\right)
.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline738}%
$K_{h}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline740}%
$Q_{dis}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath507}%
\begin{displaymath}
  Q_{dis} = \frac{1}{\overline{c_{p}}}\frac{C_{\varepsilon}}{l}
            \frac{K_{m}^{3}}{(C_{m}l)^{3}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline742}%
$l=(\Delta x\Delta z)^{1/2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
\appendix
\stepcounter{chapter}
\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4810}%
$\displaystyle \DD{u}{t} + \Dinv{\rho}\DP{p}{x} = Turb.u$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4811}%
$\displaystyle \DD{w}{t} + \Dinv{\rho}\DP{p}{z} - g = Turb.w$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4813}%
$\displaystyle \DD{\rho}{t} + \rho\left( \DP{u}{x} + \DP{w}{z}\right) = 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4815}%
$\displaystyle \rho = \frac{p}{R_{d} T_{v}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4817}%
$\displaystyle {c_{p}}_{d}\DD{T}{t} - \Dinv{\rho_{d}} \DD{p}{t} = Q + Turb.T$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4819}%
$\displaystyle \DD{q_{v}}{t} = Src.q_{v} + Turb.q_{v}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4820}%
$\displaystyle \DD{q_{c}}{t} = Src.q_{c} + Turb.q_{c}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4821}%
$\displaystyle \DD{q_{r}}{t} = Src.q_{r} + Fall.q_{r} + Turb.q_{r}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1967}%
$R_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1971}%
$\rho_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1973}%
$Q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1981}%
$q_{v}, q_{r}, q_{c}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1983}%
$Turb$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4836}%
$\displaystyle \rho_{d} + \sum \rho_{v} + \sum \rho_{c} + \sum \rho_{r}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4838}%
$\displaystyle \rho_{d} (1 + \sum q_{v} + \sum q_{c} + \sum q_{r} ).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1989}%
$q_v = \rho_v/\rho_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1995}%
$p_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4844}%
$\displaystyle p_{d}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4846}%
$\displaystyle p \left( 1 - \frac{\sum p_{v}}{p} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4848}%
$\displaystyle p \left( 1 - \frac{\sum p_{v}}{p_{d} + \sum p_{v} }\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4850}%
$\displaystyle p \left( 1 - \frac{\sum \rho_{v} R_{v} T}{\rho_{d} R_{d}T + \sum
\rho_{v} R_{v} T }\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4852}%
$\displaystyle p \left( 1 - \frac{\sum q_{v}/M_{v}}{1/M_{d} + \sum q_{v}/M_{v}
}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4854}%
$\displaystyle \rho_{d}
= \frac{p_{d}}{R_{d} T}
= \frac{p}{R_{d} T} \left(\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}
}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1997}%
$M$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4859}%
$\displaystyle \frac{p}{R_{d}T}
\left( \frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v} }\right)
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r} )$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4861}%
$\displaystyle f \equiv
\left(\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}	}\right)
(1 + \sum q_{v} + \sum q_{x} )$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4865}%
$\displaystyle \frac{p}{R_{d} (T/f)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4869}%
$\displaystyle \frac{p}{R_{d} \pi (\theta /f )}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4871}%
$\displaystyle \frac{p_{0} \pi^{{c_{v}}_{d}/R_{d}}}{R_{d} (\theta/f)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2001}%
$\pi = T/\theta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4875}%
$\displaystyle c_{p}dT - \alpha dp = 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2007}%
$c_{p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2009}%
$\alpha$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4882}%
$\displaystyle \alpha = \frac{RT}{p}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2015}%
$R$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4886}%
$\displaystyle \frac{c_{p}}{T}dT - \frac{R}{p} dp = 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4894}%
$\displaystyle \int^{T_{0}}_{T} \Dinv{T}dT$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4896}%
$\displaystyle \frac{R}{c_{p}} \int^{p_{0}}_{p} \Dinv{p} dp$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4897}%
$\displaystyle \ln{(T_{0}/T)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4899}%
$\displaystyle \frac{R}{c_{p}} \ln{(p_{0}/p)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

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

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4902}%
$\displaystyle T \left(\frac{p_{0}}{p}\right)^\frac{R}{c_{p}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4921}%
$\displaystyle \DD{p}{t} = \rho {C_{s}}^{2}
\left\{
- \Ddiv{\Dvect{u}}
+ \Dinv{\theta}\DD{\theta}{t}
- \Dinv{f}
\left(
\sum \DP{f}{q_{v}} \DD{q_{v}}{t}
+ \sum  \DP{f}{q_{c}} \DD{q_{c}}{t}
+ \sum  \DP{f}{q_{r}} \DD{q_{r}}{t}
\right)
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4923}%
$\displaystyle \rho = \frac{p_{0}}{R_{d} \theta_{v}}
\left( \frac{p}{p_{0}}\right)^{{c_{v}}_{d}/{c_{p}}_{d}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4925}%
$\displaystyle \DD{\theta}{t} = Q + Turb.\theta$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4932}%
$\displaystyle \theta \equiv T \left(\frac{p_{0}}{p}\right)^{R_{d}/{c_{p}}_{d}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4935}%
$\displaystyle \theta_{v} \equiv \frac{\theta}{f}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2049}%
$C_{s}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4938}%
$\displaystyle {C_{s}}^{2}
\equiv  \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d} T_{v}
=   \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d} \frac{T}{f}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2053}%
${c_{v}}_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2055}%
${c_{v}}_{d} + R_{d} = {c_{p}}_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2057}%
$\rho= \rho(\theta,p,q_{v},q_{x})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4945}%
$\displaystyle d\rho$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4947}%
$\displaystyle d \left[
\frac{p_{0}}{R_{d} \theta_{v}}
\left( \frac{p}{p_{0}} \right)^{{c_{v}}_{d}/{c_{p}}_{d}}
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4949}%
$\displaystyle d \left[
\frac{p_{0}}{R_{d} (\theta / f) }
\left( \frac{p}{p_{0}} \right)^{{c_{v}}_{d}/{c_{p}}_{d}}
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4951}%
$\displaystyle \frac{p_{0} }{R_{d} (\theta/f)}
\frac{{c_{v}}_{d}}{{c_{p}}_{d}}
\left( \frac{p}{p_{0}} \right)^{-R_{d}/{c_{p}}_{d}}
\Dinv{p_{0}}dp
-
\frac{p_{0} f}{R_{d}}
\left( \frac{p}{p_{0}} \right)^{{c_{v}}_{d}/{c_{p}}_{d}}
\frac{d\theta}{\theta^{2}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4952}%
$\displaystyle +
\frac{p_{0}}{R_{d} \theta}
\left( \frac{p}{p_{0}} \right)^{{c_{v}}_{d}/{c_{p}}_{d}}
\left\{
\sum \DP{f}{q_{v}} dq_{v}
+ \sum \DP{f}{q_{c}} dq_{c}
+ \sum \DP{f}{q_{r}} dq_{r}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4954}%
$\displaystyle \Dinv{{C_{s}}^{2}} dp
- \frac{\rho}{\theta} d\theta
+ \sum \frac{\rho}{f} \DP{f}{q_{v}} dq_{v}
+ \sum \frac{\rho}{f} \DP{f}{q_{c}} dq_{c}
+ \sum \frac{\rho}{f} \DP{f}{q_{r}} dq_{r}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4956}%
$\displaystyle \DD{p}{t}
= {C_{s}}^{2}
\left(
\DD{\rho}{t}
+ \frac{\rho}{\theta} \DD{\theta}{t}
- \sum \frac{\rho}{f} \DP{f}{q_{v}} dq_{v}
- \sum \frac{\rho}{f} \DP{f}{q_{c}} dq_{c}
- \sum \frac{\rho}{f} \DP{f}{q_{r}} dq_{r}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4958}%
$\displaystyle \DD{p}{t}
= \rho {C_{s}}^{2}
\left(
-  \Ddiv \Dvect{u}
+ \Dinv{\theta} \DD{\theta}{t}
- \sum \Dinv{f} \DP{f}{q_{v}} dq_{v}
- \sum \Dinv{f} \DP{f}{q_{c}} dq_{c}
- \sum \Dinv{f} \DP{f}{q_{r}} dq_{r}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4974}%
$\displaystyle \DD{u}{t} + {{c_{p}}_{d}} \theta_{v} \DP{\pi}{x} = Turb.u$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4975}%
$\displaystyle \DD{w}{t} + {{c_{p}}_{d}} \theta_{v} \DP{\pi}{z} - g  = Turb.w$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4977}%
$\displaystyle \DD{\pi}{t}
=  \frac{{C_{s}}^{2}}{ {c_{p}}_{d} \rho \theta_{v} }
\left\{
- \Ddiv \Dvect{u}
+ \Dinv{\theta}\DD{\theta}{t}
- \Dinv{f}
\left(
\sum \DP{f}{q_{v}} \DD{q_{v}}{t}
+ \sum \DP{f}{q_{c}} \DD{q_{c}}{t}
+ \sum \DP{f}{q_{r}} \DD{q_{r}}{t}
\right)
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4979}%
$\displaystyle \rho = \frac{p_{0} \pi^{{c_{v}}_{d}/R_{d}}}{R_{d} \theta_{v}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4984}%
$\displaystyle \DD{q_{x}}{t} = Src.q_{c} + Turb.q_{c}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4985}%
$\displaystyle \DD{q_{x}}{t} = Src.q_{r} + Fall.q_{x} + Turb.q_{r}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4988}%
$\displaystyle \pi \equiv \frac{T}{\theta}
= \left( \frac{p}{p_{0}} \right)^{R_{d}/{c_{p}}_{d}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4991}%
$\displaystyle {C_{s}}^{2}
\equiv  \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d} \pi \theta_{v}
=  \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d} \pi
\left( \frac{\theta}{f} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4993}%
$\displaystyle \Dinv{\rho} dp$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4995}%
$\displaystyle \frac{R_{d}  \pi (\theta/f)}{p}
d \left(
p_{0} \pi^{{c_{p}}_{d}/R_{d}}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4997}%
$\displaystyle \frac{R_{d}  \pi (\theta/f) }{p}
\left(
\frac{p_{0} {c_{p}}_{d}}{R_{d}} \pi^{{c_{p}}_{d}/R - 1}
\right)
d\pi$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4999}%
$\displaystyle \frac{R_{d}  \pi (\theta/f) }{p}
\left(
\frac{{c_{p}}_{d}}{R_{d}} p \pi^{-1}
\right)d\pi$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5001}%
$\displaystyle {c_{p}}_{d} (\theta/f)   d\pi$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5003}%
$\displaystyle {c_{p}}_{d} \theta_{v}   d\pi$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2081}%
$\rho= \rho(\theta, \pi, q_{v}, q_{x})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5009}%
$\displaystyle d \left[
\frac{p_{0} \pi^{c_{v/R_{d}}}}{R_{d} \theta_{v}}
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5011}%
$\displaystyle d \left[
\frac{p_{0} \pi^{c_{v/R_{d}}}}{R_{d} (\theta/f)}
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5013}%
$\displaystyle \frac{p_{0}}{R_{d} (\theta/f) }
\pi^{(c_{v/R_{d}}-1)}
\frac{{c_{v}}_{d}}{R_{d}}
d\pi
-
\frac{p_{0} \pi^{c_{v/R_{d}}} f}{R_{d}}
\frac{d\theta}{\theta^{2}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5014}%
$\displaystyle +
\frac{p_{0} \pi^{c_{v/R_{d}}} }{R_{d} \theta}
\left(
\sum \DP{f}{q_{v}} dq_{v}
+ \sum \DP{f}{q_{c}} dq_{c}
+ \sum \DP{f}{q_{r}} dq_{r}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5016}%
$\displaystyle {c_{p}}_{d} (\theta/f)
\left( \frac{{c_{v}}_{d}}{{c_{p}}_{d} R_{d} \pi (\theta/f) } \right)
\left(\frac{p_{0} \pi^{c_{v/R_{d}}} }{R_{d} (\theta/f)} \right)
d\pi
-
\frac{p_{0} \pi^{c_{v/R_{d}}} }{R_{d} (\theta/f)}
\frac{d\theta}{\theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5017}%
$\displaystyle +
\Dinv{f}
\left(
\frac{p_{0} \pi^{c_{v/R_{d}}} }{R_{d} (\theta / f)}
\right)
\left(
\sum \DP{f}{q_{v}} dq_{v}
+ \sum \DP{f}{q_{c}} dq_{c}
+ \sum \DP{f}{q_{r}} dq_{r}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5019}%
$\displaystyle \frac{ {c_{p}}_{d} \rho (\theta/f)}{{C_{s}}^{2} } d\pi
- \frac{\rho}{\theta} d\theta
+ \rho \Dinv{f}
\left(
\sum \DP{f}{q_{v}} dq_{v}
+ \sum \DP{f}{q_{c}} dq_{c}
+ \sum \DP{f}{q_{r}} dq_{r}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5021}%
$\displaystyle \frac{ {c_{p}}_{d} \rho \theta_{v}}{{C_{s}}^{2} } d\pi
- \frac{\rho}{\theta} d\theta
+ \rho \Dinv{f}
\left(
\sum \DP{f}{q_{v}} dq_{v}
+ \sum \DP{f}{q_{c}} dq_{c}
+ \sum \DP{f}{q_{r}} dq_{r}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5023}%
$\displaystyle \DD{\pi}{t}
=
\frac{{C_{s}}^{2} }{{c_{p}}_{d} \rho \theta_{v} }
\left\{
\Dinv{\rho} \DD{\rho}{t}
+ \Dinv{\theta}\DD{\theta}{t}
- \Dinv{f}
\left(
\sum \DP{f}{q_{v}} dq_{v}
+ \sum \DP{f}{q_{c}} dq_{c}
+ \sum \DP{f}{q_{r}} dq_{r}
\right)
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5025}%
$\displaystyle \DD{\pi}{t}
= \frac{{C_{s}}^{2} }{{c_{p}}_{d} \rho \theta_{v} }
\left\{
- \Ddiv \Dvect{u}
+ \Dinv{\theta}\DD{\theta}{t}
- \Dinv{f}
\left(
\sum \DP{f}{q_{v}} dq_{v}
+ \sum \DP{f}{q_{c}} dq_{c}
+ \sum \DP{f}{q_{r}} dq_{r}
\right)
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5029}%
$\displaystyle u = u^{'}(x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5030}%
$\displaystyle w = w^{'}(x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5031}%
$\displaystyle \pi = \bar{\pi}(z) + \pi^{'}(x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5032}%
$\displaystyle \theta_{v} = \bar{\theta_{v}}(z) + {\theta_{v}}^{'}(x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5033}%
$\displaystyle \rho = \bar{\rho}(z) + \rho^{'}(x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5034}%
$\displaystyle q_{v} = \bar{q_{v}}(z) + q_{v}^{'}(x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5035}%
$\displaystyle q_{r} = q_{r}^{'}(x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5036}%
$\displaystyle q_{c} = q_{c}^{'}(x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3232}%
$\theta_{v} = \theta/f$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5040}%
$\displaystyle \DP{\bar{\pi}}{z}
= - \frac{g}{{c_{p}}_{d} \bar{\theta_{v}}}
= - \frac{g}{{c_{p}}_{d} (\bar{\theta}/\bar{f})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5043}%
$\displaystyle \DP{u^{'}}{t} =
- \left(
u^{'} \DP{u^{'}}{x}
+ w^{'} \DP{u^{'}}{z}
\right)
- {c_{p}}_{d}
\left(
\bar{\theta_{v}} \DP{\bar{\pi}}{x}
+ \bar{\theta_{v}} \DP{\pi^{'}}{x}
+ {\theta_{v}}^{'} \DP{\bar{\pi}}{x}
+ {\theta_{v}}^{'} \DP{\pi^{'}}{x}
\right)
+ Turb.u$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5046}%
$\displaystyle \DP{u^{'}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5048}%
$\displaystyle - \left(
u^{'} \DP{u^{'}}{x}
+ w^{'} \DP{u^{'}}{z}
\right)
- {c_{p}}_{d} \bar{\theta_{v}} \DP{\pi^{'}}{x} + Turb.u$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5050}%
$\displaystyle - \left(
u^{'} \DP{u^{'}}{x}
+ w^{'} \DP{u^{'}}{z}
\right)
-{c_{p}}_{d} \left( \frac{\bar{\theta}}{\bar{f}}\right)
\DP{\pi^{'}}{x}
+ Turb.u$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3238}%
$\bar{f}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5053}%
$\displaystyle \bar{f} =
{\left(
1 - \frac{\sum \bar{q_{v}}/M_{v}}{1/M_{d} + \sum \bar{q_{v}}/M_{v}}
\right)
(1 + \sum \bar{q_{v}} )}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5056}%
$\displaystyle \DP{w^{'}}{t} =
- \left(
u^{'} \DP{w^{'}}{x}
+ w^{'} \DP{w^{'}}{z}
\right)
- {c_{p}}_{d}
\left(
\bar{\theta_{v}} \DP{\bar{\pi}}{z}
+ \bar{\theta_{v}} \DP{\pi^{'}}{z}
+ {\theta_{v}}^{'} \DP{\bar{\pi}}{z}
+ {\theta_{v}}^{'} \DP{\pi^{'}}{z}
\right)
- g
+ Turb.w$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5058}%
$\displaystyle \DP{w^{'}}{t} =
- \left(
u^{'} \DP{w^{'}}{x}
+ w^{'} \DP{w^{'}}{z}
\right)
-{c_{p}}_{d}
\left(
\bar{\theta_{v}} \DP{\bar{\pi}}{z}
+ \bar{\theta_{v}} \DP{\pi^{'}}{z}
+ {\theta_{v}}^{'} \DP{\bar{\pi}}{z}
\right)
- g
+ Turb.w .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5060}%
$\displaystyle \DP{w^{'}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5062}%
$\displaystyle - \left(
u^{'} \DP{w^{'}}{x}
+ w^{'} \DP{w^{'}}{z}
\right)
+ {c_{p}}_{d} \bar{\theta_{v}}
\left( \frac{g}{{c_{p}}_{d} \bar{\theta_{v}}} \right)
-   {c_{p}}_{d} \bar{\theta_{v}} \DP{\pi^{'}}{x}
+   {c_{p}}_{d} {\theta_{v}}^{'}
\left( \frac{g}{{c_{p}}_{d} \bar{\theta_{v}}} \right)
- g + Turb.w$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5064}%
$\displaystyle - \left(
u^{'} \DP{w^{'}}{x}
+ w^{'} \DP{w^{'}}{z}
\right)
-    {c_{p}}_{d} \bar{\theta_{v}} \DP{\pi^{'}}{x}
+   \frac{{\theta_{v}}^{'}}{\bar{\theta_{v}}} g
+ Turb.w$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3240}%
${\theta_{v}}^{'}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5067}%
$\displaystyle {\theta_{v}}^{'}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5069}%
$\displaystyle \Dinv{f}
\left\{
\theta^{'}
- \sum \frac{\theta}{f} \DP{f}{q_{v}} q_{v}^{'}
- \sum \frac{\theta}{f} \DP{f}{q_{c}} q_{c}^{'}
- \sum \frac{\theta}{f} \DP{f}{q_{r}} q_{r}^{'}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5071}%
$\displaystyle \Dinv{f}
\left\{
\frac{\theta^{'}}{\theta}
- \sum \Dinv{f} \DP{f}{q_{v}} q_{v}^{'}
- \sum \Dinv{f} \DP{f}{q_{c}} q_{c}^{'}
- \sum \Dinv{f} \DP{f}{q_{r}} q_{r}^{'}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5073}%
$\displaystyle \sum \Dinv{f}\DP{f}{q_{v}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5075}%
$\displaystyle \Dinv{\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}}
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r})}
\DP{\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}}
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r})}{q_{v}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5077}%
$\displaystyle \Dinv{\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}}
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5078}%
$\displaystyle \left[
\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}}
-
\left\{
\frac{\sum 1/M_{d}M_{v}}{(1/M_{d} + \sum q_{v}/M_{v})^{2}}
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r})
\right\}
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5080}%
$\displaystyle \Dinv{1 + \sum q_{v} + \sum q_{c} + \sum q_{r}}
- \frac{\sum 1/M_{v}}{1/M_{d} + \sum  q_{v}/M_{v}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5082}%
$\displaystyle \sum \Dinv{f}\DP{f}{q_{c}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5084}%
$\displaystyle \Dinv{\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}}
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r})}
\DP{\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}}
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r})}{q_{c}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5086}%
$\displaystyle \Dinv{1 + \sum q_{v} + \sum q_{c} + \sum q_{r}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5088}%
$\displaystyle \sum \Dinv{f}\DP{f}{q_{r}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5090}%
$\displaystyle \Dinv{\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}}
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r})}
\DP{\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}}
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r})}{q_{r}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5094}%
$\displaystyle {\theta_{v}}^{'}
= \Dinv{f}
\left\{
\frac{\theta^{'}}{\theta}
+ \frac{\sum q_{v}^{'}/M_{v}}{1/M_{d} + \sum  q_{v}/M_{v}}
- \frac{\sum q_{v}^{'} + \sum q_{c}^{'} + \sum q_{r}^{'}}
{1 + \sum q_{v} + \sum q_{c} + \sum q_{r}}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5096}%
$\displaystyle {\theta_{v}}^{'}
= \frac{\bar{\theta}}{\bar{f}}
\left\{
\frac{\theta^{'}}{\bar{\theta}}
+ \frac{\sum q_{v}^{'}/M_{v}}{1/M_{d} + \sum  \bar{q_{v}}/M_{v}}
- \frac{\sum q_{v}^{'} + \sum q_{c}^{'} + \sum q_{r}^{'}}
{1 + \sum \bar{q_{v}}}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3242}%
$w$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5101}%
$\displaystyle - \left(
u^{'} \DP{w^{'}}{x}
+ w^{'} \DP{w^{'}}{z}
\right)
- {c_{p}}_{d} \bar{\theta_{v}} \DP{\pi^{'}}{x}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5102}%
$\displaystyle +
\left(
\frac{\theta^{'}}{\bar{\theta}}
+ \frac{\sum q_{v}^{'}/M_{v}}{1/M_{d} + \sum  \bar{q_{v}}/M_{v}}
- \frac{\sum q_{v}^{'} + \sum q_{c}^{'} + \sum q_{r}^{'}}
{1 + \sum \bar{q_{v}}}
\right) g
+ Turb.w$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5105}%
$\displaystyle \DD{\pi}{t}
=
- \frac{{C_{s}}^{2}}{ {c_{p}}_{d} (\theta/f)}
\Ddiv \Dvect{u}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3244}%
$1/\theta = 1/\bar{\theta}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3246}%
$1/f = 1/\bar{f}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5109}%
$\displaystyle \DP{\bar{\pi} + \pi^{'}}{t}
+ u^{'} \DP{\bar{\pi}+\pi^{'}}{x}
+ w^{'} \DP{\bar{\pi}+\pi^{'}}{z}
=   - \frac{\overline{{C_{s}}^{2} }}{ {c_{p}}_{d} (\bar{\theta}/\bar{f})}
\Ddiv \Dvect{u^{'}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3250}%
$\overline{{C_{s}}^{2}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5113}%
$\displaystyle {C_{s}}^{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5115}%
$\displaystyle \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d} (\bar{\pi} + \pi^{'})
\left( \frac{(\bar{\theta} + \theta^{'})}{\bar{f}} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5116}%
$\textstyle \approx$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5117}%
$\displaystyle \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d}
\left(
\bar{\pi} \frac{\bar{\theta}}{\bar{f}}
+ \bar{\pi} \frac{\theta^{'}}{\bar{f}}
+ \pi^{'} \frac{\bar{\theta}}{\bar{f}}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5119}%
$\displaystyle \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d}
\bar{\pi} \frac{\bar{\theta}}{\bar{f}}
\left(
1 + \frac{\theta^{'}}{\bar{\theta}} + \frac{ \pi^{'} }{\bar{\pi}}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5121}%
$\displaystyle \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d}
\bar{\pi} \frac{\bar{\theta}}{\bar{f}}
\equiv \overline{{C_{s}}^{2}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3252}%
$\theta^{'}/\bar{\theta} \ll 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3254}%
$\pi^{'}/\bar{\pi} \ll 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5126}%
$\displaystyle \DP{\pi^{'}}{t}
=
- w^{'} \DP{\bar{\pi}}{z}
- \frac{\overline{{C_{s}}^{2}} }{ {c_{p}}_{d} (\bar{\theta} /\bar{f})}
\Ddiv \Dvect{u^{'}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5129}%
$\displaystyle \DP{\pi^{'}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5131}%
$\displaystyle - w^{'} \DP{}{z}
\left( \frac{\bar{\rho} R_{d}(\bar{\theta}/\bar{f})}{p_{0}}\right)^{R_{d}/{c_{v}}_{d}}
- \frac{\overline{{C_{s}}^{2}} }{ {c_{p}}_{d} (\bar{\theta}/\bar{f})}
\left( \DP{ u^{'}}{x} + \DP{ w^{'}}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5133}%
$\displaystyle - w^{'}
\frac{R_{d}}{{c_{v}}_{d}} \bar{\pi}
\Dinv{\left( \frac{\bar{\rho}
R_{d}(\bar{\theta}/\bar{f})}{p_{0}}\right)}
\frac{R_{d}}{p_{0}}
\DP{ \bar{\rho} (\bar{\theta}/\bar{f})}{z}
- \frac{\overline{{C_{s}}^{2}} }{ {c_{p}}_{d} (\bar{\theta}/\bar{f})}
\left( \DP{u^{'}}{x} + \DP{w^{'}}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5135}%
$\displaystyle - \frac{\overline{{C_{s}}^{2}}}{{c_{p}}_{d}  \bar{\rho} (\bar{\theta}/\bar{f})^{2}}
\left\{
w^{'}
\DP{ \bar{\rho} (\bar{\theta}/\bar{f})}{z}
+ \bar{\rho} (\bar{\theta}/\bar{f})
\left( \DP{u^{'}}{x} + \DP{w^{'}}{z} \right)
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5137}%
$\displaystyle - \frac{\overline{{C_{s}}^{2}}}{{c_{p}}_{d}  \bar{\rho} (\bar{\theta}/\bar{f})^{2}}
\Ddiv \left\{
\bar{\rho} (\bar{\theta}/\bar{f}) \Dvect{u^{'}}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5139}%
$\displaystyle \DP{\pi^{'}}{t}=
- \frac{\overline{{C_{s}}^{2}}}{{c_{p}}_{d}  \bar{\rho} (\bar{\theta}/\bar{f})^{2}}
\Ddiv \left\{
\bar{\rho} (\bar{\theta}/\bar{f}) \Dvect{u^{'}}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5142}%
$\displaystyle \DP{(\bar{\theta} + \theta^{'})}{t}
=
- u^{'}\DP{(\bar{\theta} + \theta^{'})}{x}
- w^{'}\DP{(\bar{\theta} + \theta^{'})}{x}
+ Q + Turb.(\bar{\theta} + \theta^{'})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5145}%
$\displaystyle \DP{\theta^{'}}{t}
=
- \left(
u^{'}\DP{\theta^{'}}{x}
+ w^{'}\DP{\theta^{'}}{x}
\right)
- w^{'}\DP{\bar{\theta}}{x}
+ Q  + Turb.\bar{\theta}   + Turb.\theta^{'}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5148}%
$\displaystyle \DP{q_{v}^{'}}{t}
=
- \left(
u^{'}\DP{q_{v}^{'}}{x}
+ w^{'}\DP{q_{v}^{'}}{x}
\right)
- w^{'}\DP{\bar{q_{v}}}{x}
+ Src.q_{v}^{'} + Turb.\bar{q_{v}} + Turb.q_{v}^{'},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5149}%
$\displaystyle \DP{q_{c}^{'}}{t}
=
- \left(
u^{'}\DP{q_{c}^{'}}{x}
+ w^{'}\DP{q_{c}^{'}}{x}
\right)
+ Src.q_{c}^{'} + Turb.q_{c}^{'},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5150}%
$\displaystyle \DP{q_{r}^{'}}{t}
= - \left(
u^{'}\DP{q_{r}^{'}}{x}
+ w^{'}\DP{q_{r}^{'}}{x}
\right)
+ Src.q_{r}^{'} + Fall.q_{r}^{'} + Turb.q_{r}^{'}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3262}%
$~^{'}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5163}%
$\displaystyle - \left(
u \DP{w}{x}
+ w \DP{w}{z}
\right)
- {c_{p}}_{d} \bar{\theta_{v}} \DP{\pi}{x}
+ Turb.w$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5166}%
$\displaystyle \DP{\pi}{t}=
- \frac{\overline{{C_{s}}^{2}}}{{c_{p}}_{d}  \bar{\rho} (\bar{\theta}/\bar{f})^{2}}
\Ddiv \left\{
\bar{\rho} (\bar{\theta}/\bar{f}) \Dvect{u}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5168}%
$\displaystyle \DP{\theta}{t}
=
- \left(
u\DP{\theta}{x}
+ w\DP{\theta}{x}
\right)
- w\DP{\bar{\theta}}{x}
+ Q  + Turb.\bar{\theta}   + Turb.\theta$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5170}%
$\displaystyle \DP{q_{v}}{t}
=
- \left(
u\DP{q_{v}}{x}
+ w\DP{q_{v}}{x}
\right)
- w\DP{\bar{q_{v}}}{x}
+ Src.q_{v} + Turb.\bar{q_{v}} + Turb.q_{v},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5171}%
$\displaystyle \DP{q_{c}}{t}
=
- \left(
u\DP{q_{c}}{x}
+ w\DP{q_{c}}{x}
\right)
+ Src.q_{c} + Turb.q_{c},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5172}%
$\displaystyle \DP{q_{r}}{t}
= - \left(
u\DP{q_{r}}{x}
+ w\DP{q_{r}}{x}
\right)
+ Src.q_{r} + Fall.q_{r} + Turb.q_{r}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5176}%
$\displaystyle \DD{E}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5178}%
$\displaystyle B + S + D_{E}
- \left(\frac{C_{\varepsilon}}{l}\right)
E^{\frac{3}{2}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3908}%
$l$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3912}%
$B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3914}%
$S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3916}%
$D_{E}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5185}%
$\displaystyle B$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5187}%
$\displaystyle \frac{g_{j}}{\overline{\theta}}
\overline{u^{\prime}_{j} \theta^{\prime}} ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5188}%
$\displaystyle S$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5190}%
$\displaystyle - \overline{(u_{i}^{\prime} u_{j}^{\prime})}
\DP{u_{i}}{x_{j}} ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5191}%
$\displaystyle D_{E}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5193}%
$\displaystyle \DP{}{x_{j}} \left(K_{m} \DP{E}{x_{j}} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5195}%
$\displaystyle \overline{(u_{i}^{\prime} u_{j}^{\prime})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5197}%
$\displaystyle - K_{m} \left(\DP{u_{i}}{x_{j}}
+ \DP{u_{j}}{x_{i}}\right)
+ \frac{2}{3} \delta_{ij} E$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5198}%
$\displaystyle \overline{u_{j}^{\prime} \theta }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5200}%
$\displaystyle K_{h}\DP{\theta}{x_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5208}%
$\displaystyle K_{m}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5210}%
$\displaystyle C_{m} E^{\frac{1}{2}} l,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5211}%
$\displaystyle K_{h}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5213}%
$\displaystyle 3 K_{m}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5219}%
$\displaystyle - \frac{g}{\overline{\theta}}
\overline{w^{\prime}  \theta^{\prime}} ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5221}%
$\displaystyle - \frac{g}{\overline{\theta}}
\left( K_{h} \DP{\theta}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5228}%
$\displaystyle - \left\{
- K_{m} \left(\DP{u_{i}}{x_{j}} + \DP{u_{j}}{x_{i}}\right)
+ \frac{2}{3} \delta_{ij} E
\right\}
\DP{u_{i}}{x_{j}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5230}%
$\displaystyle \left\{
K_{m} \left(\DP{u_{i}}{x_{j}} + \DP{u_{j}}{x_{i}}\right)
- \frac{2}{3} \delta_{ij} E
\right\}
\DP{u_{i}}{x_{j}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5232}%
$\displaystyle \left\{
K_{m} \left(\DP{u}{x_{j}} + \DP{u_{j}}{x}\right)
- \frac{2}{3} \delta_{1j} E
\right\}
\DP{u}{x_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5233}%
$\displaystyle +
\left\{
K_{m} \left(\DP{w}{x_{j}} + \DP{u_{j}}{z}\right)
- \frac{2}{3} \delta_{3j} E
\right\}
\DP{w}{x_{j}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5235}%
$\displaystyle \left\{
2 K_{m} \left(\DP{u}{x} \right)
- \frac{2}{3} E
\right\}
\DP{u}{x}
+
K_{m} \left( \DP{w}{x} + \DP{u}{z} \right)
\DP{u}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5236}%
$\displaystyle +
K_{m} \left(\DP{w}{x} + \DP{u}{z}\right)
\DP{w}{x}
+
\left\{
2 K_{m} \left(\DP{w}{z}  \right)
- \frac{2}{3} E
\right\}
\DP{w}{z},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5238}%
$\displaystyle 2 K_{m} \left\{
\left( \DP{u}{x} \right)^{2}
+ \left( \DP{w}{z} \right)^{2}
\right\}
+  K_{m}
\left(\DP{u}{z} + \DP{w}{x}\right)^{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5239}%
$\displaystyle - \frac{2}{3} E \left( \DP{u}{x} + \DP{w}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5244}%
$\displaystyle \DP{}{x_{j}} \left(K_{m} \DP{E}{x_{j}} \right),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5246}%
$\displaystyle \DP{}{x} \left(K_{m} \DP{E}{x} \right)
+ \DP{}{x} \left(K_{m} \DP{E}{x} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5251}%
$\displaystyle + 2 K_{m} \left\{
\left( \DP{u}{x} \right)^{2}
+ \left( \DP{w}{z} \right)^{2}
\right\}
+  K_{m}
\left(\DP{u}{z} + \DP{w}{x}\right)^{2}
- \frac{2}{3} E \left( \DP{u}{x} + \DP{w}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5252}%
$\displaystyle + \DP{}{x} \left(K_{m} \DP{E}{x} \right)
+ \DP{}{x} \left(K_{m} \DP{E}{x} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5253}%
$\displaystyle - \left(\frac{C_{\varepsilon}}{l}\right)
E^{\frac{3}{2}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5256}%
$\displaystyle \DP{}{x} \left(K_{m} \DP{E}{x}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5257}%
$\textstyle +$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5258}%
$\displaystyle \DP{}{z} \left(K_{m} \DP{E}{z}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5260}%
$\displaystyle \frac{1}{C_{m}^{2} l^{2}}
\Biggl\{\DP{}{x}
\left(K_{m} \DP{K_{m}^{2}}{x}\right)
+ \DP{}{z}
\left(K_{m} \DP{K_{m}^{2}}{z}\right)
\Biggr\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5262}%
$\displaystyle \frac{1}{C_{m}^{2} l^{2}}
\Biggl\{K_{m} \DP[2]{K_{m}^{2}}{x}
+ \DP{K_{m}}{x}
\DP{K_{m}^{2}}{x}
+ K_{m} \DP[2]{K_{m}^{2}}{z}
+ \DP{K_{m}}{z}
\DP{K_{m}^{2}}{z}
\Biggr\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5264}%
$\displaystyle \frac{K_{m}}{C_{m}^{2} l^{2}}
\left(\DP[2]{K_{m}^{2}}{x}
+ \DP[2]{K_{m}^{2}}{z}
\right)
+ \frac{2 K_{m}}{C_{m}^{2} l^{2}}
\Biggl\{\left(\DP{K_{m}}{x}\right)^{2}
+ \left(\DP{K_{m}}{z}\right)^{2}
\Biggr\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5266}%
$\displaystyle \frac{2 K_{m}}{C_{m}^{2} l^{2}}  \DD{K_{m}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5268}%
$\displaystyle - \frac{g}{\overline{\theta}}
\left( K_{h} \DP{\theta}{z} \right)
+ 2 K_{m} \left\{
\left( \DP{u}{x} \right)^{2}
+ \left( \DP{w}{z} \right)^{2}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5269}%
$\displaystyle +  K_{m}
\left(\DP{u}{z} + \DP{w}{z}\right)^{2}
- \frac{2}{3} \frac{K_{m}^{2}}{C_{m}^{2} l^{2}} \left( \DP{u}{x} + \DP{w}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5270}%
$\displaystyle + \frac{K_{m}}{C_{m}^{2} l^{2}}
\left(\DP[2]{K_{m}^{2}}{x}
+ \DP[2]{K_{m}^{2}}{z}
\right)
+ \frac{2 K_{m}}{C_{m}^{2} l^{2}}
\Biggl\{\left(\DP{K_{m}}{x}\right)^{2}
+ \left(\DP{K_{m}}{z}\right)^{2}
\Biggr\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5271}%
$\displaystyle - \frac{C_{\varepsilon}}{C_{m}^{3} {l}^{4}}
K_{m}^{3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5274}%
$\displaystyle - \left(
u \DP{K_{m}}{x} + w \DP{K_{m}}{z}
\right)
- \frac{g C_{m}^{2} l^{2}}{ 2 \overline{\theta}} \frac{K_{h}}{K_{m}}
\left(\DP{\theta}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5276}%
$\displaystyle +  \frac{ C_{m}^{2} l^{2} }{2}
\left( \DP{u}{z} + \DP{w}{z}\right)^{2}
- \frac{K_{m}}{3}
\left( \DP{u}{x} + \DP{w}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5278}%
$\displaystyle - \frac{C_{\varepsilon}}{2 C_{m} l^{2}} K_{m}^{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3936}%
$C_{m} = C_{\varepsilon} = 0.2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3938}%
$K_{h} = 3 K_{m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5284}%
$\displaystyle - \left(
u \DP{K_{m}}{x} + w \DP{K_{m}}{z}
\right)
- \frac{3 g C_{m}^{2} l^{2}}{ 2 \overline{\theta}}
\left(\DP{\theta}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3998}%
$C_{\varepsilon}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4000}%
$C_{m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4004}%
$\bar{c}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4008}%
$c_{v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4010}%
$D_{u_{i}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4012}%
$x_{i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4014}%
$D_{\theta}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4018}%
$f$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4020}%
$g$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4030}%
$\overline{p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4032}%
$p_{0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4034}%
$\Pi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4036}%
$\overline{\Pi}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4042}%
$\overline{\rho}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4044}%
$\rho_{0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4048}%
$\overline{T}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4050}%
$\overline{\theta}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4054}%
$u_{i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4056}%
$i = 1, 3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4058}%
$(u_{1}, u_{3}) = (u, w)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4064}%
$(x_{1}, x_{3}) = (x, z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3996}%
\begin{displaymath}
  \mbox{dcstaff@gfd-dennou.org}
 \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}


\end{document}