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\Dnoparindent


\Dtitle[2 次元非静力学モデルの定式化]
       {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{2007 年 6 月 7 日}




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

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6347}%
$\displaystyle - \DP{}{x_{j}}
\left[
- K_{m} \left(\DP{u_{i}}{x_{j}}
+ \DP{u_{j}}{x_{i}}\right)
+ \frac{2}{3} \delta_{ij} E
\right].$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline728}%
$K_{m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline730}%
$E$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6351}%
$\displaystyle E = \frac{1}{2}
\overline{(u^{\prime})^{2} + (w^{\prime})^{2}}
= \frac{{K_{m}}^{2}}{C_{m}^{2} l^{2}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6354}%
$\displaystyle Turb.{\theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6356}%
$\displaystyle - \DP{}{x_{j}} \overline{u_{i}^{\prime} \theta^{\prime}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6358}%
$\displaystyle - \DP{}{x_{j}} \left(K_{h}\DP{\theta}{x_{j}}\right)
.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline732}%
$K_{h}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6362}%
$\displaystyle \DP{K_{m}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6364}%
$\displaystyle - \left(
u \DP{K_{m}}{x} + w \DP{K_{m}}{z}
\right)
- \frac{3 g C_{m}^{2} l^{2}}{ 2 \overline{\theta_{v}}}
\left(\DP{\theta_{el}}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6365}%
$\displaystyle + \left( C_{m}^{2} l^{2} \right) \left\{
\left( \DP{u}{x} \right)^{2}
+ \left( \DP{w}{z} \right)^{2}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6366}%
$\displaystyle +  \frac{ C_{m}^{2} l^{2} }{2}
\left( \DP{u}{z} + \DP{w}{x}\right)^{2}
- \frac{K_{m}}{3}
\left( \DP{u}{x} + \DP{w}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6367}%
$\displaystyle + \Dinv{2}
\left(\DP[2]{K_{m}^{2}}{x}
+ \DP[2]{K_{m}^{2}}{z}
\right)
+ \left(\DP{K_{m}}{x}\right)^{2}
+ \left(\DP{K_{m}}{z}\right)^{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6368}%
$\displaystyle - \Dinv{2 l^{2}} K_{m}^{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline734}%
$C_{\varepsilon} = C_{m} = 0.2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline736}%
$l = \left(\Delta x \Delta z \right)^{1/2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline738}%
$\Delta x, \Delta z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline740}%
$\theta_{el}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6374}%
$\displaystyle \theta_{el}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6376}%
$\displaystyle \overline{ \theta_{v}} + \theta_{v}^{'} \;\;\; (for \;\; q_{c} = 0)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6379}%
$\displaystyle \overline{\theta_{v}} + \theta_{v}^{'} + \frac{ \sum L
q_{v}}{{c_p}_{d} \bar{\pi}}
\;\;\; (for \;\; q_{c} > 0)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6381}%
$\displaystyle \overline{\theta_{v}} + \theta_{v}^{'}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6383}%
$\displaystyle \bar{\theta_{v}}
\left\{
1 + \frac{\theta}{\bar{\theta}}
+ \frac{\sum q_{v}/M_{v}}{1/M_{d} + \sum  \bar{q_{v}}/M_{v}}
- \frac{\sum q_{v} + \sum q_{c} + \sum q_{r}}
{1 + \sum \bar{q_{v}}}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline742}%
$Q_{dis}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath499}%
\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_inline744}%
$l=(\Delta x\Delta z)^{1/2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
\appendix
\stepcounter{chapter}
\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6406}%
$\displaystyle \DD{u}{t} + \Dinv{\rho}\DP{p}{x} = Turb.u$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6407}%
$\displaystyle \DD{w}{t} + \Dinv{\rho}\DP{p}{z} = -g + Turb.w$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6409}%
$\displaystyle \DD{\rho}{t} + \rho\left( \DP{u}{x} + \DP{w}{z}\right) = 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6411}%
$\displaystyle \rho = \frac{p}{R_{d} T_{v}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6413}%
$\displaystyle {c_{p}}_{d}\DD{T}{t} - \Dinv{\rho_{d}} \DD{p}{t} = Q + Turb.T$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6415}%
$\displaystyle \DD{q_{v}}{t} = Src.q_{v} + Turb.q_{v}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6416}%
$\displaystyle \DD{q_{c}}{t} = Src.q_{c} + Turb.q_{c}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6417}%
$\displaystyle \DD{q_{r}}{t} = Src.q_{r} + Fall.q_{r} + Turb.q_{r}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1987}%
$R_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1991}%
$\rho_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1993}%
$Q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2001}%
$q_{v}, q_{r}, q_{c}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2003}%
$Turb$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6432}%
$\displaystyle \rho_{d} + \sum \rho_{v} + \sum \rho_{c} + \sum \rho_{r}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6434}%
$\displaystyle \rho_{d} (1 + \sum q_{v} + \sum q_{c} + \sum q_{r} ).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2009}%
$q_v = \rho_v/\rho_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2015}%
$p_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6440}%
$\displaystyle p_{d}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6442}%
$\displaystyle p \left( 1 - \frac{\sum p_{v}}{p} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6444}%
$\displaystyle p \left( 1 - \frac{\sum p_{v}}{p_{d} + \sum p_{v} }\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6446}%
$\displaystyle p \left( 1 - \frac{\sum \rho_{v} R_{v} T}{\rho_{d} R_{d}T + \sum
\rho_{v} R_{v} T }\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6448}%
$\displaystyle p \left( 1 - \frac{\sum q_{v}/M_{v}}{1/M_{d} + \sum q_{v}/M_{v}
}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6450}%
$\displaystyle \rho_{d}
= \frac{p_{d}}{R_{d} T}
= \frac{p}{R_{d} T} \left(\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}
}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2017}%
$M$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6455}%
$\displaystyle \frac{p}{R_{d}T}
\left( \frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v} }\right)
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r} )$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6457}%
$\displaystyle f \equiv
\left(\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}	}\right)
(1 + \sum q_{v} + \sum q_{x} )$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6461}%
$\displaystyle \frac{p}{R_{d} (T/f)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6465}%
$\displaystyle \frac{p}{R_{d} \pi (\theta /f )}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6467}%
$\displaystyle \frac{p_{0} \pi^{{c_{v}}_{d}/R_{d}}}{R_{d} (\theta/f)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2021}%
$\pi = T/\theta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6471}%
$\displaystyle c_{p}dT - \alpha dp = 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2027}%
$c_{p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2029}%
$\alpha$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6478}%
$\displaystyle \alpha = \frac{RT}{p}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2035}%
$R$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6482}%
$\displaystyle \frac{c_{p}}{T}dT - \frac{R}{p} dp = 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6490}%
$\displaystyle \int^{T_{0}}_{T} \Dinv{T}dT$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6492}%
$\displaystyle \frac{R}{c_{p}} \int^{p_{0}}_{p} \Dinv{p} dp$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6493}%
$\displaystyle \ln{(T_{0}/T)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6495}%
$\displaystyle \frac{R}{c_{p}} \ln{(p_{0}/p)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6496}%
$\displaystyle \theta$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6498}%
$\displaystyle T \left(\frac{p_{0}}{p}\right)^\frac{R}{c_{p}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6516}%
$\displaystyle \DD{p}{t} = \rho {C_{s}}^{2}
\left\{
- \Ddiv{\Dvect{u}}
+ \Dinv{\theta}\DD{\theta}{t}
- \Dinv{f}
\left(
\sum \DP{f}{q_{v}} \DD{q_{v}}{t}
+ \sum  \DP{f}{q_{c}} \DD{q_{c}}{t}
+ \sum  \DP{f}{q_{r}} \DD{q_{r}}{t}
\right)
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6518}%
$\displaystyle \rho = \frac{p_{0}}{R_{d} \theta_{v}}
\left( \frac{p}{p_{0}}\right)^{{c_{v}}_{d}/{c_{p}}_{d}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6520}%
$\displaystyle \DD{\theta}{t} = Q + Turb.\theta$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6527}%
$\displaystyle \theta \equiv T \left(\frac{p_{0}}{p}\right)^{R_{d}/{c_{p}}_{d}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6530}%
$\displaystyle \theta_{v} \equiv \frac{\theta}{f}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2067}%
$C_{s}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6533}%
$\displaystyle {C_{s}}^{2}
\equiv  \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d} T_{v}
=   \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d} \frac{T}{f}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2071}%
${c_{v}}_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2073}%
${c_{v}}_{d} + R_{d} = {c_{p}}_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2075}%
$\rho= \rho(\theta,p,q_{v},q_{x})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6540}%
$\displaystyle d\rho$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6542}%
$\displaystyle d \left[
\frac{p_{0}}{R_{d} \theta_{v}}
\left( \frac{p}{p_{0}} \right)^{{c_{v}}_{d}/{c_{p}}_{d}}
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6544}%
$\displaystyle d \left[
\frac{p_{0}}{R_{d} (\theta / f) }
\left( \frac{p}{p_{0}} \right)^{{c_{v}}_{d}/{c_{p}}_{d}}
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6546}%
$\displaystyle \frac{p_{0} }{R_{d} (\theta/f)}
\frac{{c_{v}}_{d}}{{c_{p}}_{d}}
\left( \frac{p}{p_{0}} \right)^{-R_{d}/{c_{p}}_{d}}
\Dinv{p_{0}}dp
-
\frac{p_{0} f}{R_{d}}
\left( \frac{p}{p_{0}} \right)^{{c_{v}}_{d}/{c_{p}}_{d}}
\frac{d\theta}{\theta^{2}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6547}%
$\displaystyle +
\frac{p_{0}}{R_{d} \theta}
\left( \frac{p}{p_{0}} \right)^{{c_{v}}_{d}/{c_{p}}_{d}}
\left\{
\sum \DP{f}{q_{v}} dq_{v}
+ \sum \DP{f}{q_{c}} dq_{c}
+ \sum \DP{f}{q_{r}} dq_{r}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6549}%
$\displaystyle \Dinv{{C_{s}}^{2}} dp
- \frac{\rho}{\theta} d\theta
+ \sum \frac{\rho}{f} \DP{f}{q_{v}} dq_{v}
+ \sum \frac{\rho}{f} \DP{f}{q_{c}} dq_{c}
+ \sum \frac{\rho}{f} \DP{f}{q_{r}} dq_{r}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6551}%
$\displaystyle \DD{p}{t}
= {C_{s}}^{2}
\left(
\DD{\rho}{t}
+ \frac{\rho}{\theta} \DD{\theta}{t}
- \sum \frac{\rho}{f} \DP{f}{q_{v}} dq_{v}
- \sum \frac{\rho}{f} \DP{f}{q_{c}} dq_{c}
- \sum \frac{\rho}{f} \DP{f}{q_{r}} dq_{r}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6553}%
$\displaystyle \DD{p}{t}
= \rho {C_{s}}^{2}
\left(
-  \Ddiv \Dvect{u}
+ \Dinv{\theta} \DD{\theta}{t}
- \sum \Dinv{f} \DP{f}{q_{v}} dq_{v}
- \sum \Dinv{f} \DP{f}{q_{c}} dq_{c}
- \sum \Dinv{f} \DP{f}{q_{r}} dq_{r}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6568}%
$\displaystyle \DD{u}{t} + {{c_{p}}_{d}} \theta_{v} \DP{\pi}{x} = Turb.u$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6569}%
$\displaystyle \DD{w}{t} + {{c_{p}}_{d}} \theta_{v} \DP{\pi}{z} = -g + Turb.w$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6571}%
$\displaystyle \DD{\pi}{t}
=  \frac{{C_{s}}^{2}}{ {c_{p}}_{d} \rho \theta_{v} }
\left\{
- \Ddiv \Dvect{u}
+ \Dinv{\theta}\DD{\theta}{t}
- \Dinv{f}
\left(
\sum \DP{f}{q_{v}} \DD{q_{v}}{t}
+ \sum \DP{f}{q_{c}} \DD{q_{c}}{t}
+ \sum \DP{f}{q_{r}} \DD{q_{r}}{t}
\right)
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6573}%
$\displaystyle \rho = \frac{p_{0} \pi^{{c_{v}}_{d}/R_{d}}}{R_{d} \theta_{v}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6578}%
$\displaystyle \DD{q_{x}}{t} = Src.q_{c} + Turb.q_{c}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6579}%
$\displaystyle \DD{q_{x}}{t} = Src.q_{r} + Fall.q_{x} + Turb.q_{r}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6582}%
$\displaystyle \pi \equiv \frac{T}{\theta}
= \left( \frac{p}{p_{0}} \right)^{R_{d}/{c_{p}}_{d}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6585}%
$\displaystyle {C_{s}}^{2}
\equiv  \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d} \pi \theta_{v}
=  \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d} \pi
\left( \frac{\theta}{f} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6587}%
$\displaystyle \Dinv{\rho} dp$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6589}%
$\displaystyle \frac{R_{d}  \pi (\theta/f)}{p}
d \left(
p_{0} \pi^{{c_{p}}_{d}/R_{d}}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6591}%
$\displaystyle \frac{R_{d}  \pi (\theta/f) }{p}
\left(
\frac{p_{0} {c_{p}}_{d}}{R_{d}} \pi^{{c_{p}}_{d}/R - 1}
\right)
d\pi$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6593}%
$\displaystyle \frac{R_{d}  \pi (\theta/f) }{p}
\left(
\frac{{c_{p}}_{d}}{R_{d}} p \pi^{-1}
\right)d\pi$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6595}%
$\displaystyle {c_{p}}_{d} (\theta/f)   d\pi$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6597}%
$\displaystyle {c_{p}}_{d} \theta_{v}   d\pi$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2097}%
$\rho= \rho(\theta, \pi, q_{v}, q_{x})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6603}%
$\displaystyle d \left[
\frac{p_{0} \pi^{c_{v/R_{d}}}}{R_{d} \theta_{v}}
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6605}%
$\displaystyle d \left[
\frac{p_{0} \pi^{c_{v/R_{d}}}}{R_{d} (\theta/f)}
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6607}%
$\displaystyle \frac{p_{0}}{R_{d} (\theta/f) }
\pi^{(c_{v/R_{d}}-1)}
\frac{{c_{v}}_{d}}{R_{d}}
d\pi
-
\frac{p_{0} \pi^{c_{v/R_{d}}} f}{R_{d}}
\frac{d\theta}{\theta^{2}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6608}%
$\displaystyle +
\frac{p_{0} \pi^{c_{v/R_{d}}} }{R_{d} \theta}
\left(
\sum \DP{f}{q_{v}} dq_{v}
+ \sum \DP{f}{q_{c}} dq_{c}
+ \sum \DP{f}{q_{r}} dq_{r}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6610}%
$\displaystyle {c_{p}}_{d} (\theta/f)
\left( \frac{{c_{v}}_{d}}{{c_{p}}_{d} R_{d} \pi (\theta/f) } \right)
\left(\frac{p_{0} \pi^{c_{v/R_{d}}} }{R_{d} (\theta/f)} \right)
d\pi
-
\frac{p_{0} \pi^{c_{v/R_{d}}} }{R_{d} (\theta/f)}
\frac{d\theta}{\theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6611}%
$\displaystyle +
\Dinv{f}
\left(
\frac{p_{0} \pi^{c_{v/R_{d}}} }{R_{d} (\theta / f)}
\right)
\left(
\sum \DP{f}{q_{v}} dq_{v}
+ \sum \DP{f}{q_{c}} dq_{c}
+ \sum \DP{f}{q_{r}} dq_{r}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6613}%
$\displaystyle \frac{ {c_{p}}_{d} \rho (\theta/f)}{{C_{s}}^{2} } d\pi
- \frac{\rho}{\theta} d\theta
+ \rho \Dinv{f}
\left(
\sum \DP{f}{q_{v}} dq_{v}
+ \sum \DP{f}{q_{c}} dq_{c}
+ \sum \DP{f}{q_{r}} dq_{r}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6615}%
$\displaystyle \frac{ {c_{p}}_{d} \rho \theta_{v}}{{C_{s}}^{2} } d\pi
- \frac{\rho}{\theta} d\theta
+ \rho \Dinv{f}
\left(
\sum \DP{f}{q_{v}} dq_{v}
+ \sum \DP{f}{q_{c}} dq_{c}
+ \sum \DP{f}{q_{r}} dq_{r}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6617}%
$\displaystyle \DD{\pi}{t}
=
\frac{{C_{s}}^{2} }{{c_{p}}_{d} \rho \theta_{v} }
\left\{
\Dinv{\rho} \DD{\rho}{t}
+ \Dinv{\theta}\DD{\theta}{t}
- \Dinv{f}
\left(
\sum \DP{f}{q_{v}} dq_{v}
+ \sum \DP{f}{q_{c}} dq_{c}
+ \sum \DP{f}{q_{r}} dq_{r}
\right)
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6619}%
$\displaystyle \DD{\pi}{t}
= \frac{{C_{s}}^{2} }{{c_{p}}_{d} \rho \theta_{v} }
\left\{
- \Ddiv \Dvect{u}
+ \Dinv{\theta}\DD{\theta}{t}
- \Dinv{f}
\left(
\sum \DP{f}{q_{v}} dq_{v}
+ \sum \DP{f}{q_{c}} dq_{c}
+ \sum \DP{f}{q_{r}} dq_{r}
\right)
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6623}%
$\displaystyle u = u^{'}(x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6624}%
$\displaystyle w = w^{'}(x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6625}%
$\displaystyle \pi = \bar{\pi}(z) + \pi^{'}(x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6626}%
$\displaystyle \theta_{v} = \bar{\theta_{v}}(z) + {\theta_{v}}^{'}(x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6627}%
$\displaystyle \rho = \bar{\rho}(z) + \rho^{'}(x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6628}%
$\displaystyle q_{v} = \bar{q_{v}}(z) + q_{v}^{'}(x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6629}%
$\displaystyle q_{r} = q_{r}^{'}(x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6630}%
$\displaystyle q_{c} = q_{c}^{'}(x,z,t)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3248}%
$\theta_{v} = \theta/f$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6634}%
$\displaystyle \DP{\bar{\pi}}{z}
= - \frac{g}{{c_{p}}_{d} \bar{\theta_{v}}}
= - \frac{g}{{c_{p}}_{d} (\bar{\theta}/\bar{f})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6637}%
$\displaystyle \DP{u^{'}}{t} =
- \left(
u^{'} \DP{u^{'}}{x}
+ w^{'} \DP{u^{'}}{z}
\right)
- {c_{p}}_{d}
\left(
\bar{\theta_{v}} \DP{\bar{\pi}}{x}
+ \bar{\theta_{v}} \DP{\pi^{'}}{x}
+ {\theta_{v}}^{'} \DP{\bar{\pi}}{x}
+ {\theta_{v}}^{'} \DP{\pi^{'}}{x}
\right)
+ Turb.u$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6640}%
$\displaystyle \DP{u^{'}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6642}%
$\displaystyle - \left(
u^{'} \DP{u^{'}}{x}
+ w^{'} \DP{u^{'}}{z}
\right)
- {c_{p}}_{d} \bar{\theta_{v}} \DP{\pi^{'}}{x} + Turb.u$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6644}%
$\displaystyle - \left(
u^{'} \DP{u^{'}}{x}
+ w^{'} \DP{u^{'}}{z}
\right)
-{c_{p}}_{d} \left( \frac{\bar{\theta}}{\bar{f}}\right)
\DP{\pi^{'}}{x}
+ Turb.u$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3254}%
$\bar{f}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6647}%
$\displaystyle \bar{f} =
{\left(
1 - \frac{\sum \bar{q_{v}}/M_{v}}{1/M_{d} + \sum \bar{q_{v}}/M_{v}}
\right)
(1 + \sum \bar{q_{v}} )}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6650}%
$\displaystyle \DP{w^{'}}{t} =
- \left(
u^{'} \DP{w^{'}}{x}
+ w^{'} \DP{w^{'}}{z}
\right)
- {c_{p}}_{d}
\left(
\bar{\theta_{v}} \DP{\bar{\pi}}{z}
+ \bar{\theta_{v}} \DP{\pi^{'}}{z}
+ {\theta_{v}}^{'} \DP{\bar{\pi}}{z}
+ {\theta_{v}}^{'} \DP{\pi^{'}}{z}
\right)
- g
+ Turb.w$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6652}%
$\displaystyle \DP{w^{'}}{t} =
- \left(
u^{'} \DP{w^{'}}{x}
+ w^{'} \DP{w^{'}}{z}
\right)
-{c_{p}}_{d}
\left(
\bar{\theta_{v}} \DP{\bar{\pi}}{z}
+ \bar{\theta_{v}} \DP{\pi^{'}}{z}
+ {\theta_{v}}^{'} \DP{\bar{\pi}}{z}
\right)
- g
+ Turb.w .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6654}%
$\displaystyle \DP{w^{'}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6656}%
$\displaystyle - \left(
u^{'} \DP{w^{'}}{x}
+ w^{'} \DP{w^{'}}{z}
\right)
+ {c_{p}}_{d} \bar{\theta_{v}}
\left( \frac{g}{{c_{p}}_{d} \bar{\theta_{v}}} \right)
-   {c_{p}}_{d} \bar{\theta_{v}} \DP{\pi^{'}}{z}
+   {c_{p}}_{d} {\theta_{v}}^{'}
\left( \frac{g}{{c_{p}}_{d} \bar{\theta_{v}}} \right)
- g + Turb.w$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6658}%
$\displaystyle - \left(
u^{'} \DP{w^{'}}{x}
+ w^{'} \DP{w^{'}}{z}
\right)
-    {c_{p}}_{d} \bar{\theta_{v}} \DP{\pi^{'}}{z}
+   \frac{{\theta_{v}}^{'}}{\bar{\theta_{v}}} g
+ Turb.w$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3256}%
${\theta_{v}}^{'}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6661}%
$\displaystyle {\theta_{v}}^{'}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6663}%
$\displaystyle \Dinv{f}
\left\{
\theta^{'}
- \sum \frac{\theta}{f} \DP{f}{q_{v}} q_{v}^{'}
- \sum \frac{\theta}{f} \DP{f}{q_{c}} q_{c}^{'}
- \sum \frac{\theta}{f} \DP{f}{q_{r}} q_{r}^{'}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6665}%
$\displaystyle \Dinv{f}
\left\{
\frac{\theta^{'}}{\theta}
- \sum \Dinv{f} \DP{f}{q_{v}} q_{v}^{'}
- \sum \Dinv{f} \DP{f}{q_{c}} q_{c}^{'}
- \sum \Dinv{f} \DP{f}{q_{r}} q_{r}^{'}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6667}%
$\displaystyle \sum \Dinv{f}\DP{f}{q_{v}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6669}%
$\displaystyle \Dinv{\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}}
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r})}
\DP{\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}}
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r})}{q_{v}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6671}%
$\displaystyle \Dinv{\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}}
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6672}%
$\displaystyle \left[
\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}}
-
\left\{
\frac{\sum 1/M_{d}M_{v}}{(1/M_{d} + \sum q_{v}/M_{v})^{2}}
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r})
\right\}
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6674}%
$\displaystyle \Dinv{1 + \sum q_{v} + \sum q_{c} + \sum q_{r}}
- \frac{\sum 1/M_{v}}{1/M_{d} + \sum  q_{v}/M_{v}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6676}%
$\displaystyle \sum \Dinv{f}\DP{f}{q_{c}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6678}%
$\displaystyle \Dinv{\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}}
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r})}
\DP{\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}}
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r})}{q_{c}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6680}%
$\displaystyle \Dinv{1 + \sum q_{v} + \sum q_{c} + \sum q_{r}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6682}%
$\displaystyle \sum \Dinv{f}\DP{f}{q_{r}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6684}%
$\displaystyle \Dinv{\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}}
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r})}
\DP{\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}}
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r})}{q_{r}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6688}%
$\displaystyle {\theta_{v}}^{'}
= \Dinv{f}
\left\{
\frac{\theta^{'}}{\theta}
+ \frac{\sum q_{v}^{'}/M_{v}}{1/M_{d} + \sum  q_{v}/M_{v}}
- \frac{\sum q_{v}^{'} + \sum q_{c}^{'} + \sum q_{r}^{'}}
{1 + \sum q_{v} + \sum q_{c} + \sum q_{r}}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6690}%
$\displaystyle {\theta_{v}}^{'}
= \frac{\bar{\theta}}{\bar{f}}
\left\{
\frac{\theta^{'}}{\bar{\theta}}
+ \frac{\sum q_{v}^{'}/M_{v}}{1/M_{d} + \sum  \bar{q_{v}}/M_{v}}
- \frac{\sum q_{v}^{'} + \sum q_{c}^{'} + \sum q_{r}^{'}}
{1 + \sum \bar{q_{v}}}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3258}%
$w$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6695}%
$\displaystyle - \left(
u^{'} \DP{w^{'}}{x}
+ w^{'} \DP{w^{'}}{z}
\right)
- {c_{p}}_{d} \bar{\theta_{v}} \DP{\pi^{'}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6696}%
$\displaystyle +
\left(
\frac{\theta^{'}}{\bar{\theta}}
+ \frac{\sum q_{v}^{'}/M_{v}}{1/M_{d} + \sum  \bar{q_{v}}/M_{v}}
- \frac{\sum q_{v}^{'} + \sum q_{c}^{'} + \sum q_{r}^{'}}
{1 + \sum \bar{q_{v}}}
\right) g
+ Turb.w$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6699}%
$\displaystyle \DD{\pi}{t}
=
- \frac{{C_{s}}^{2}}{ {c_{p}}_{d} (\theta/f)}
\Ddiv \Dvect{u}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3260}%
$1/\theta = 1/\bar{\theta}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3262}%
$1/f = 1/\bar{f}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6703}%
$\displaystyle \DP{\bar{\pi} + \pi^{'}}{t}
+ u^{'} \DP{\bar{\pi}+\pi^{'}}{x}
+ w^{'} \DP{\bar{\pi}+\pi^{'}}{z}
=   - \frac{\overline{{C_{s}}^{2} }}{ {c_{p}}_{d} (\bar{\theta}/\bar{f})}
\Ddiv \Dvect{u^{'}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3266}%
$\overline{{C_{s}}^{2}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6707}%
$\displaystyle {C_{s}}^{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6709}%
$\displaystyle \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d} (\bar{\pi} + \pi^{'})
\left( \frac{(\bar{\theta} + \theta^{'})}{\bar{f}} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6710}%
$\textstyle \approx$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6711}%
$\displaystyle \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d}
\left(
\bar{\pi} \frac{\bar{\theta}}{\bar{f}}
+ \bar{\pi} \frac{\theta^{'}}{\bar{f}}
+ \pi^{'} \frac{\bar{\theta}}{\bar{f}}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6713}%
$\displaystyle \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d}
\bar{\pi} \frac{\bar{\theta}}{\bar{f}}
\left(
1 + \frac{\theta^{'}}{\bar{\theta}} + \frac{ \pi^{'} }{\bar{\pi}}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6715}%
$\displaystyle \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d}
\bar{\pi} \frac{\bar{\theta}}{\bar{f}}
\equiv \overline{{C_{s}}^{2}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3268}%
$\theta^{'}/\bar{\theta} \ll 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3270}%
$\pi^{'}/\bar{\pi} \ll 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6720}%
$\displaystyle \DP{\pi^{'}}{t}
=
- w^{'} \DP{\bar{\pi}}{z}
- \frac{\overline{{C_{s}}^{2}} }{ {c_{p}}_{d} (\bar{\theta} /\bar{f})}
\Ddiv \Dvect{u^{'}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6723}%
$\displaystyle \DP{\pi^{'}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6725}%
$\displaystyle - w^{'} \DP{}{z}
\left( \frac{\bar{\rho} R_{d}(\bar{\theta}/\bar{f})}{p_{0}}\right)^{R_{d}/{c_{v}}_{d}}
- \frac{\overline{{C_{s}}^{2}} }{ {c_{p}}_{d} (\bar{\theta}/\bar{f})}
\left( \DP{ u^{'}}{x} + \DP{ w^{'}}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6727}%
$\displaystyle - w^{'}
\frac{R_{d}}{{c_{v}}_{d}} \bar{\pi}
\Dinv{\left( \frac{\bar{\rho}
R_{d}(\bar{\theta}/\bar{f})}{p_{0}}\right)}
\frac{R_{d}}{p_{0}}
\DP{ \bar{\rho} (\bar{\theta}/\bar{f})}{z}
- \frac{\overline{{C_{s}}^{2}} }{ {c_{p}}_{d} (\bar{\theta}/\bar{f})}
\left( \DP{u^{'}}{x} + \DP{w^{'}}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6729}%
$\displaystyle - \frac{\overline{{C_{s}}^{2}}}{{c_{p}}_{d}  \bar{\rho} (\bar{\theta}/\bar{f})^{2}}
\left\{
w^{'}
\DP{ \bar{\rho} (\bar{\theta}/\bar{f})}{z}
+ \bar{\rho} (\bar{\theta}/\bar{f})
\left( \DP{u^{'}}{x} + \DP{w^{'}}{z} \right)
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6731}%
$\displaystyle - \frac{\overline{{C_{s}}^{2}}}{{c_{p}}_{d}  \bar{\rho} (\bar{\theta}/\bar{f})^{2}}
\Ddiv \left\{
\bar{\rho} (\bar{\theta}/\bar{f}) \Dvect{u^{'}}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6733}%
$\displaystyle \DP{\pi^{'}}{t}=
- \frac{\overline{{C_{s}}^{2}}}{{c_{p}}_{d}  \bar{\rho} (\bar{\theta}/\bar{f})^{2}}
\Ddiv \left\{
\bar{\rho} (\bar{\theta}/\bar{f}) \Dvect{u^{'}}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6736}%
$\displaystyle \DP{(\bar{\theta} + \theta^{'})}{t}
=
- u^{'}\DP{(\bar{\theta} + \theta^{'})}{x}
- w^{'}\DP{(\bar{\theta} + \theta^{'})}{x}
+ Q + Turb.(\bar{\theta} + \theta^{'})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6739}%
$\displaystyle \DP{\theta^{'}}{t}
=
- \left(
u^{'}\DP{\theta^{'}}{x}
+ w^{'}\DP{\theta^{'}}{x}
\right)
- w^{'}\DP{\bar{\theta}}{x}
+ Q  + Turb.\bar{\theta}   + Turb.\theta^{'}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6742}%
$\displaystyle \DP{q_{v}^{'}}{t}
=
- \left(
u^{'}\DP{q_{v}^{'}}{x}
+ w^{'}\DP{q_{v}^{'}}{x}
\right)
- w^{'}\DP{\bar{q_{v}}}{x}
+ Src.q_{v}^{'} + Turb.\bar{q_{v}} + Turb.q_{v}^{'},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6743}%
$\displaystyle \DP{q_{c}^{'}}{t}
=
- \left(
u^{'}\DP{q_{c}^{'}}{x}
+ w^{'}\DP{q_{c}^{'}}{x}
\right)
+ Src.q_{c}^{'} + Turb.q_{c}^{'},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6744}%
$\displaystyle \DP{q_{r}^{'}}{t}
= - \left(
u^{'}\DP{q_{r}^{'}}{x}
+ w^{'}\DP{q_{r}^{'}}{x}
\right)
+ Src.q_{r}^{'} + Fall.q_{r}^{'} + Turb.q_{r}^{'}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3278}%
$~^{'}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6757}%
$\displaystyle - \left(
u \DP{w}{x}
+ w \DP{w}{z}
\right)
- {c_{p}}_{d} \bar{\theta_{v}} \DP{\pi}{x}
+ Turb.w$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6760}%
$\displaystyle \DP{\pi}{t}=
- \frac{\overline{{C_{s}}^{2}}}{{c_{p}}_{d}  \bar{\rho} (\bar{\theta}/\bar{f})^{2}}
\Ddiv \left\{
\bar{\rho} (\bar{\theta}/\bar{f}) \Dvect{u}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6762}%
$\displaystyle \DP{\theta}{t}
=
- \left(
u\DP{\theta}{x}
+ w\DP{\theta}{x}
\right)
- w\DP{\bar{\theta}}{x}
+ Q  + Turb.\bar{\theta}   + Turb.\theta$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6764}%
$\displaystyle \DP{q_{v}}{t}
=
- \left(
u\DP{q_{v}}{x}
+ w\DP{q_{v}}{x}
\right)
- w\DP{\bar{q_{v}}}{x}
+ Src.q_{v} + Turb.\bar{q_{v}} + Turb.q_{v},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6765}%
$\displaystyle \DP{q_{c}}{t}
=
- \left(
u\DP{q_{c}}{x}
+ w\DP{q_{c}}{x}
\right)
+ Src.q_{c} + Turb.q_{c},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6766}%
$\displaystyle \DP{q_{r}}{t}
= - \left(
u\DP{q_{r}}{x}
+ w\DP{q_{r}}{x}
\right)
+ Src.q_{r} + Fall.q_{r} + Turb.q_{r}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6770}%
$\displaystyle \DD{E}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6772}%
$\displaystyle B + S + D_{E}
- \left(\frac{C_{\varepsilon}}{l}\right)
E^{\frac{3}{2}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4817}%
$l$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4821}%
$B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4823}%
$S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4825}%
$D_{E}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6779}%
$\displaystyle B$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6781}%
$\displaystyle \frac{g_{j}}{\overline{\theta}}
\overline{u^{\prime}_{j} \theta^{\prime}} ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6782}%
$\displaystyle S$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6784}%
$\displaystyle - \overline{(u_{i}^{\prime} u_{j}^{\prime})}
\DP{u_{i}}{x_{j}} ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6785}%
$\displaystyle D_{E}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6787}%
$\displaystyle \DP{}{x_{j}} \left(K_{m} \DP{E}{x_{j}} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6789}%
$\displaystyle \overline{(u_{i}^{\prime} u_{j}^{\prime})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6791}%
$\displaystyle - K_{m} \left(\DP{u_{i}}{x_{j}}
+ \DP{u_{j}}{x_{i}}\right)
+ \frac{2}{3} \delta_{ij} E,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6792}%
$\displaystyle \overline{u_{j}^{\prime} \theta }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6794}%
$\displaystyle - K_{h}\DP{\theta}{x_{j}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6802}%
$\displaystyle K_{m}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6804}%
$\displaystyle C_{m} E^{\frac{1}{2}} l,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6805}%
$\displaystyle K_{h}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6807}%
$\displaystyle 3 K_{m}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4839}%
$C_{\varepsilon}, C_{m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6811}%
$\displaystyle \DP{\overline{u^{\prime}_{i}u^{\prime}_{j}}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6812}%
$\textstyle +$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6813}%
$\displaystyle \DP{}{x_{k}}\left[
u_{k}\overline{u^{\prime}_{i}u^{\prime}_{j}}
+ \overline{u^{\prime}_{k}u^{\prime}_{i}u^{\prime}_{j}}
-  \nu \DP{}{x_{k}}\overline{u^{\prime}_{i}u^{\prime}_{j}}\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6815}%
$\displaystyle \DP{}{x_{j}}\overline{pu^{\prime}_{i}}
+ \DP{}{x_{i}}\overline{pu^{\prime}_{j}}
+ f_{k}(\varepsilon _{jkl}\overline{u_{l}^{\prime}u^{\prime}_{i}}
+ \varepsilon _{ikl}\overline{u_{l}^{\prime}u^{\prime}_{j}})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6817}%
$\displaystyle -\overline{u^{\prime}_{k}u^{\prime}_{i}}\DP{u_{j}}{x_{k}}
-\overline{u^{\prime}_{k}u^{\prime}_{j}}\DP{u_{i}}{x_{k}}
-\beta(g_{j}\overline{u^{\prime}_{i}\theta }
+ g_{i}\overline{u^{\prime}_{j}\theta })$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6819}%
$\displaystyle \overline{p\left(\DP{u^{\prime}_{i}}{x_{j}}
+ \DP{u^{\prime}_{j}}{x_{i}}\right)}
-  2\nu \overline{\DP{u^{\prime}_{i}}{x_{k}}\DP{u^{\prime}_{j}}{x_{k}}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6821}%
$\displaystyle \DP{\overline{u^{\prime}_{j}\theta^{\prime}}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6823}%
$\displaystyle \DP{}{x_{k}}\left[
u_{k}\overline{\theta^{\prime} u^{\prime}_{j}}
+ \overline{u^{\prime}_{k}u^{\prime}_{j}\theta^{\prime} }
- \alpha \overline{u^{\prime}_{j}\DP{\theta^{\prime} }{x_{k}}}
- \nu \overline{\theta^{\prime} \DP{u^{\prime}_{j}}{x_{k}}}\right]
+ \DP{}{x_{j}}\overline{p\theta^{\prime} }
+ \varepsilon _{jkl}f_{k}\overline{u^{\prime}_{l}\theta^{\prime} }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6825}%
$\displaystyle -\overline{u^{\prime}_{j}u^{\prime}_{k}}\DP{\theta }{x_{k}}
-\overline{\theta^{\prime} u^{\prime}_{k}}\DP{u_{j}}{x_{k}}
-\beta g_{j}\overline{(\theta^{\prime})^{2}}
+ \overline{p\DP{\theta^{\prime} }{x_{k}}}
-(\alpha + \nu )
\overline{\DP{u^{\prime}_{j}}{x_{k}}\DP{\theta^{\prime} }{x_{k}}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4841}%
$i=j$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6828}%
$\displaystyle \DP{q^{2}}{t} + u_{k}\DP{q^{2}}{x_{k}}
+ \DP{}{x_{k}}\left(\overline{u^{\prime}_{k}u^{\prime}_{j}u^{\prime}_{j}}
- \nu \DP{q^{2}}{x_{k}}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6830}%
$\displaystyle - \overline{u^{\prime}_{j}u^{\prime}_{k}}\DP{u_{j}}{x_{k}}
- \DP{}{x_{k}}\overline{pu^{\prime}_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6831}%
$\displaystyle + g_{j}\beta\overline{u^{\prime}_{j}\theta^{\prime}}
- 2\nu \overline{\left(\DP{u^{\prime}_{j}}{x_{k}}\right)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{eqnarraystar3555}%
\begin{eqnarray*}
  q &\equiv&  \sqrt{\overline{(u^{\prime}_{i})^{2}}}  \\
    & = &    \sqrt{2E} 
\end{eqnarray*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4843}%
$\nu, \alpha, \beta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4845}%
$g_{j}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4847}%
$j$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4849}%
$\overline{p\left(\DP{u^{\prime}_{i}}{x_{j}} + \DP{u^{\prime}_{i}}{x_{j}}\right)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4801}%
\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_inline4851}%
$l_{1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

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

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4855}%
$\overline{p\DP{\theta^{\prime} }{x_{k}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4802}%
\begin{displaymath}
          = -\frac{q}{3l_{2}}\overline{u^{\prime}_{i}\theta^{\prime} }
        \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4857}%
$l_{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4859}%
$2\nu \overline{\DP{u^{\prime}_{i}}{x_{k}}\DP{u^{\prime}_{j}}{x_{k}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4861}%
$q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4803}%
\begin{displaymath}
          = \frac{2}{3}\frac{q^{3}}{\Lambda _{1}}\delta _{ij}.
        \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4863}%
$\Lambda _{1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4865}%
$(\alpha + \nu )
          \overline{\DP{u^{\prime}_{j}}{x_{k}}\DP{\theta^{\prime} }{x_{k}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4804}%
\begin{displaymath}
          = 0
        \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4867}%
$\overline{u^{\prime}_{k}u^{\prime}_{i}u^{\prime}_{j}}, 
        \overline{u^{\prime}_{k}u^{\prime}_{j}\theta^{\prime} }, 
        \overline{u^{\prime}_{k}(\theta^{\prime})^{2}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{eqnarraystar3641}%
\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}_{j}}}{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_inline4871}%
$\lambda _{i}(i=1,2,3)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4873}%
$\overline{pu^{\prime}_{i}}, \overline{p\theta^{\prime} }$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4805}%
\begin{displaymath}
            \overline{pu^{\prime}_{i}} =  \overline{p\theta^{\prime} } = 0
        \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4875}%
$f_{k}(\varepsilon _{jkl}\overline{u_{l}^{\prime}u^{\prime}_{i}}
         + \varepsilon _{ikl}\overline{u_{l}^{\prime}u^{\prime}_{j}}), \;
         f_{k}\varepsilon _{jkl}\overline{u_{l}^{\prime}\theta^{\prime} }$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4806}%
\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{displaymath4807}%
\begin{displaymath}
           f_{k}\varepsilon _{jkl}\overline{u_{l}^{\prime}\theta^{\prime}} = 0
        \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4877}%
$\alpha \overline{u^{\prime}_{j}\DP{\theta^{\prime} }{x_{k}}}, \;
          \nu \overline{\theta^{\prime} \DP{u^{\prime}_{j}}{x_{k}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6861}%
$\displaystyle \DD{\overline{u^{\prime}_{i}u^{\prime}_{j}}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6862}%
$\textstyle -$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6863}%
$\displaystyle \DP{}{x_{k}}\left[
q\lambda _{1}\left(
\DP{\overline{u^{\prime}_{i}u^{\prime}_{j}}}{x_{k}} +
\DP{\overline{u^{\prime}_{i}u^{\prime}_{k}}}{x_{j}} +
\DP{\overline{u^{\prime}_{j}u^{\prime}_{i}}}{x_{i}}\right)
-\nu\DP{}{x_{k}}\overline{u^{\prime}_{i}u^{\prime}_{j}}\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6865}%
$\displaystyle - \overline{u^{\prime}_{k}u^{\prime}_{i}}\DP{u_{j}}{x_{k}}
- \overline{u^{\prime}_{k}u^{\prime}_{j}}\DP{u_{i}}{x_{k}}
- \beta(g_{j}\overline{u^{\prime}_{i}\theta^{\prime} }
+ g_{i}\overline{u^{\prime}_{j}\theta^{\prime} })$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6866}%
$\displaystyle - \frac{q}{3l_{1}}(\overline{u^{\prime}_{i}u^{\prime}_{j}}
- \frac{\delta _{ij}}{3}q^{2})
+ Cq^{2}\left(\DP{u_{i}}{x_{j}}
+ \DP{u_{j}}{x_{i}}\right)
- \frac{2}{3}\frac{q^{3}}{\Lambda _{1}}\delta _{ij},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6867}%
$\displaystyle \DD{\overline{u^{\prime}_{j}\theta^{\prime} }}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6869}%
$\displaystyle \DP{}{x_{k}}\left[q\lambda _{2}\left(
\DP{\overline{u^{\prime}_{k}\theta^{\prime} }}{x_{j}}
+ \DP{\overline{u^{\prime}_{j}\theta^{\prime} }}{x_{k}}\right)\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6871}%
$\displaystyle - \overline{u^{\prime}_{j}u^{\prime}_{k}}\DP{\theta }{x_{k}}
- \overline{\theta^{\prime} u^{\prime}_{k}}\DP{u^{\prime}_{j}}{x_{k}}
- \beta g_{j}\overline{(\theta^{\prime})^{2}}
- \frac{q}{3l_{2}}\overline{u^{\prime}_{j}\theta^{\prime} },$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6872}%
$\displaystyle \DD{q^{2}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6874}%
$\displaystyle \DP{}{x_{k}}\left[
q\lambda _{1}\left(
2\DP{q^{2}}{x_{k}} +
\DP{\overline{u^{\prime}_{j}u^{\prime}_{k}}}{x_{j}}\right)
- \nu \DP{q^{2}}{x_{k}}\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6876}%
$\displaystyle - 2\overline{u^{\prime}_{j}u^{\prime}_{k}}\DP{u_{j}}{x_{k}}
+ 2g_{j}\beta\overline{u^{\prime}_{j}\theta^{\prime}}
- 2\frac{q^{3}}{\Lambda _{1}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4808}%
\begin{displaymath}
  \DD{}{t} \equiv \DP{}{t} + u_{k}\DP{}{x_{k}}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4879}%
$C=1/3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4881}%
$\overline{u^{\prime}_{j}u^{\prime}_{k}}\sim q^{2}\delta_{jk}/3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6881}%
$\displaystyle \overline{u^{\prime}_{i}u^{\prime}_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6883}%
$\displaystyle \frac{\delta _{ij}}{3}q^{2}
- ql_{1}\left(\DP{u_{i}}{x_{j}} + \DP{u_{j}}{x_{i}}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6884}%
$\displaystyle \overline{u^{\prime}_{j}\theta^{\prime}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6886}%
$\displaystyle - ql_{2}\DP{\theta }{x_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6889}%
$\displaystyle - 2\overline{u^{\prime}_{j}u^{\prime}_{k}}\DP{u_{j}}{x_{k}}
+ 2g_{j}\beta\overline{u^{\prime}_{j}\theta^{\prime}}
+ \DP{}{x_{k}}\left[\nu \DP{q^{2}}{x_{k}}\right]
- 2\frac{q^{3}}{\Lambda _{1}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4883}%
$\overline{u^{\prime}_{i}u^{\prime}_{j}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4885}%
$\overline{u^{\prime}_{j}\theta^{\prime}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4887}%
$\overline{(\theta^{\prime})^{2}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4889}%
$q^{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4891}%
$ql_{1}=K_{m}, ql_{2}=K_{h}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6900}%
$\displaystyle \frac{2}{3}\delta _{ij}E
- K_{m}\left(\DP{u_{i}}{x_{j}} + \DP{u_{j}}{x_{i}}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6903}%
$\displaystyle - K_{h}\DP{\theta }{x_{k}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6906}%
$\displaystyle - \overline{u^{\prime}_{j}u^{\prime}_{k}}\DP{u_{j}}{x_{k}}
+ g_{j}\beta\overline{u^{\prime}_{j}\theta^{\prime}}
+ \DP{}{x_{k}}\left[K_{m} \DP{q^{2}}{x_{k}}\right]
- \frac{2^{3/2}}{\Lambda _{1}}E^{3/2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4897}%
$\beta = 1/\theta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6912}%
$\displaystyle \frac{g_{j}}{\overline{\theta}}
\overline{u^{\prime}_{j} \theta^{\prime}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6914}%
$\displaystyle - \frac{g}{\overline{\theta}}
\overline{w^{\prime}  \theta^{\prime}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6916}%
$\displaystyle - \frac{g}{\overline{\theta}}
\left( K_{h} \DP{\theta}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6921}%
$\displaystyle - \overline{(u_{i}^{\prime} u_{j}^{\prime})}
\DP{u_{i}}{x_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6923}%
$\displaystyle - \left\{
- K_{m} \left(\DP{u_{i}}{x_{j}} + \DP{u_{j}}{x_{i}}\right)
+ \frac{2}{3} \delta_{ij} E
\right\}
\DP{u_{i}}{x_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6925}%
$\displaystyle \left\{
K_{m} \left(\DP{u_{i}}{x_{j}} + \DP{u_{j}}{x_{i}}\right)
- \frac{2}{3} \delta_{ij} E
\right\}
\DP{u_{i}}{x_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6927}%
$\displaystyle \left\{
K_{m} \left(\DP{u}{x_{j}} + \DP{u_{j}}{x}\right)
- \frac{2}{3} \delta_{1j} E
\right\}
\DP{u}{x_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6928}%
$\displaystyle +
\left\{
K_{m} \left(\DP{w}{x_{j}} + \DP{u_{j}}{z}\right)
- \frac{2}{3} \delta_{3j} E
\right\}
\DP{w}{x_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6930}%
$\displaystyle \left\{
2 K_{m} \left(\DP{u}{x} \right)
- \frac{2}{3} E
\right\}
\DP{u}{x}
+
K_{m} \left( \DP{w}{x} + \DP{u}{z} \right)
\DP{u}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6931}%
$\displaystyle +
K_{m} \left(\DP{w}{x} + \DP{u}{z}\right)
\DP{w}{x}
+
\left\{
2 K_{m} \left(\DP{w}{z}  \right)
- \frac{2}{3} E
\right\}
\DP{w}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6933}%
$\displaystyle 2 K_{m} \left\{
\left( \DP{u}{x} \right)^{2}
+ \left( \DP{w}{z} \right)^{2}
\right\}
+  K_{m}
\left(\DP{u}{z} + \DP{w}{x}\right)^{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6934}%
$\displaystyle - \frac{2}{3} E \left( \DP{u}{x} + \DP{w}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6939}%
$\displaystyle \DP{}{x_{j}} \left(K_{m} \DP{E}{x_{j}} \right),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6941}%
$\displaystyle \DP{}{x} \left(K_{m} \DP{E}{x} \right)
+ \DP{}{x} \left(K_{m} \DP{E}{x} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6946}%
$\displaystyle + 2 K_{m} \left\{
\left( \DP{u}{x} \right)^{2}
+ \left( \DP{w}{z} \right)^{2}
\right\}
+  K_{m}
\left(\DP{u}{z} + \DP{w}{x}\right)^{2}
- \frac{2}{3} E \left( \DP{u}{x} + \DP{w}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6947}%
$\displaystyle + \DP{}{x} \left(K_{m} \DP{E}{x} \right)
+ \DP{}{x} \left(K_{m} \DP{E}{x} \right)
- \left(\frac{C_{\varepsilon}}{l}\right)
E^{\frac{3}{2}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6951}%
$\displaystyle \DP{}{x} \left(K_{m} \DP{E}{x}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6953}%
$\displaystyle \DP{}{z} \left(K_{m} \DP{E}{z}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6955}%
$\displaystyle \frac{1}{C_{m}^{2} l^{2}}
\Biggl\{\DP{}{x}
\left(K_{m} \DP{K_{m}^{2}}{x}\right)
+ \DP{}{z}
\left(K_{m} \DP{K_{m}^{2}}{z}\right)
\Biggr\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6957}%
$\displaystyle \frac{1}{C_{m}^{2} l^{2}}
\Biggl\{K_{m} \DP[2]{K_{m}^{2}}{x}
+ \DP{K_{m}}{x}
\DP{K_{m}^{2}}{x}
+ K_{m} \DP[2]{K_{m}^{2}}{z}
+ \DP{K_{m}}{z}
\DP{K_{m}^{2}}{z}
\Biggr\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6959}%
$\displaystyle \frac{K_{m}}{C_{m}^{2} l^{2}}
\left(\DP[2]{K_{m}^{2}}{x}
+ \DP[2]{K_{m}^{2}}{z}
\right)
+ \frac{2 K_{m}}{C_{m}^{2} l^{2}}
\Biggl\{\left(\DP{K_{m}}{x}\right)^{2}
+ \left(\DP{K_{m}}{z}\right)^{2}
\Biggr\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6961}%
$\displaystyle \frac{2 K_{m}}{C_{m}^{2} l^{2}}  \DD{K_{m}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6963}%
$\displaystyle - \frac{g}{\overline{\theta}}
\left( K_{h} \DP{\theta}{z} \right)
+ 2 K_{m} \left\{
\left( \DP{u}{x} \right)^{2}
+ \left( \DP{w}{z} \right)^{2}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6964}%
$\displaystyle +  K_{m}
\left(\DP{u}{z} + \DP{w}{z}\right)^{2}
- \frac{2}{3} \frac{K_{m}^{2}}{C_{m}^{2} l^{2}} \left( \DP{u}{x} + \DP{w}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6965}%
$\displaystyle + \frac{K_{m}}{C_{m}^{2} l^{2}}
\left(\DP[2]{K_{m}^{2}}{x}
+ \DP[2]{K_{m}^{2}}{z}
\right)
+ \frac{2 K_{m}}{C_{m}^{2} l^{2}}
\Biggl\{\left(\DP{K_{m}}{x}\right)^{2}
+ \left(\DP{K_{m}}{z}\right)^{2}
\Biggr\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6966}%
$\displaystyle - \frac{C_{\varepsilon}}{C_{m}^{3} {l}^{4}}
K_{m}^{3}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6970}%
$\displaystyle - \left(
u \DP{K_{m}}{x} + w \DP{K_{m}}{z}
\right)
- \frac{g C_{m}^{2} l^{2}}{ 2 \overline{\theta}} \frac{K_{h}}{K_{m}}
\left(\DP{\theta}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6972}%
$\displaystyle +  \frac{ C_{m}^{2} l^{2} }{2}
\left( \DP{u}{z} + \DP{w}{z}\right)^{2}
- \frac{K_{m}}{3}
\left( \DP{u}{x} + \DP{w}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6974}%
$\displaystyle - \frac{C_{\varepsilon}}{2 C_{m} l^{2}} K_{m}^{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4905}%
$C_{m} = C_{\varepsilon} = 0.2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4907}%
$K_{h} = 3 K_{m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6980}%
$\displaystyle - \left(
u \DP{K_{m}}{x} + w \DP{K_{m}}{z}
\right)
- \frac{3 g C_{m}^{2} l^{2}}{ 2 \overline{\theta}}
\left(\DP{\theta}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5316}%
$D$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5318}%
$(dm(D)/dt)_{cr}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5322}%
$D+dD$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5324}%
$N_{D}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4983}%
\begin{displaymath}
  CL_{cr} = \frac{1}{\rho_{d}}\int _{0}^{\infty}\left(\DD{m}{t}\right)_{cr}
   N_{D}\Dd D
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4996}%
\begin{displaymath}
  \left(\DD{m}{t}\right)_{cr} = \frac{\pi}{4}D^{2}VE\rho _{d}q_{c}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5328}%
$V$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7004}%
$\displaystyle N_{D}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7006}%
$\displaystyle N_{0}\exp (-\lambda D),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7007}%
$\displaystyle V$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7009}%
$\displaystyle 130D^{0.5}.$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5334}%
$N_{0}, \lambda $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5336}%
$N_{0}=10^{7}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7013}%
$\displaystyle CL_{cr}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7015}%
$\displaystyle \frac{130\pi}{4}E N_{0} q_{c}
\int_{0}^{\infty}D^{2.5}\exp(-\lambda D)\Dd D$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7017}%
$\displaystyle 32.5 \pi E N_{0} q_{c} \frac{3.75}{\lambda ^{3}}\frac{1}{2}
\sqrt{\frac{\pi}{\lambda}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7019}%
$\displaystyle 60.9375 \pi^{3/2} E N_{0} q_{c} \lambda ^{-3.5}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5342}%
$E=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5344}%
$\lambda$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7026}%
$\displaystyle q_{r}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7028}%
$\displaystyle \frac{1}{\rho_{d}}\int _{0}^{\infty} \rho_{w}
\frac{\pi}{6} D^{3}
N_{D}\Dd D$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7030}%
$\displaystyle \frac{\pi N_{0}\rho_{w}}{6\rho_{d}}\int _{0}^{\infty}
D^{3}\exp(-\lambda D)\Dd D$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7032}%
$\displaystyle \frac{\pi N_{0}\rho_{w}}{6\rho_{d}}\frac{6}{\lambda ^{4}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7034}%
$\displaystyle \frac{\pi N_{0}\rho_{w}}{\rho_{d}}\lambda ^{-4}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5348}%
$\rho_{w}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5350}%
$10^{3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5352}%
${}^{3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7042}%
$\displaystyle 60.9375 \pi ^{\frac{5}{8}}\rho_{w}^{-\frac{7}{8}}
EN_{0}^{\frac{1}{8}}q_{c}(\rho _{d}q_{r})^{\frac{7}{8}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7044}%
$\displaystyle 0.295 \times 10^{-4}E N_{0}^{0.125}
q_{c}(\rho _{d}q_{r})^{0.875}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7046}%
$\displaystyle 2.2 q_{c}(\rho _{d}q_{r})^{0.875}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5356}%
$N_{0}=10^{7}, E=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmldisplayA{displaymath5107}%
\begin{displaymath}
  EV_{rv} = \frac{1}{\rho_{d}}\int _{0}^{\infty}\left(\DD{m}{t}\right)_{ev}
  N_{D}\Dd D
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5360}%
$(dm(D)/dt)_{ev}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5364}%
$F$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5120}%
\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_inline5366}%
$r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5368}%
$r_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5300}%
\begin{displaymath}
   F = - K_{d}\DD{\rho_{v}}{r}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5372}%
$\rho_{v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5374}%
$K_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5301}%
\begin{displaymath}
  \frac{1}{r^{2}}\DP{}{r}\left(r^{2}F\right) = 0
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5302}%
\begin{displaymath}
   \rho _{v} = -\frac{C_{1}}{r} + C_{2}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5376}%
$r=r_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5378}%
$\rho_{v} = \rho_{v,s}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5380}%
$r=\infty$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5382}%
$\rho_{v}=\rho_{v,\infty}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5303}%
\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_indisplay7069}%
$\displaystyle F(r_{d})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7071}%
$\displaystyle - K_{d}\left.\DD{\rho_{v}}{r}\right|_{r=r_{d}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7073}%
$\displaystyle K_{d}\frac{\rho_{v,s} - \rho _{v,\infty}}{r_{d}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5165}%
\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{displaymath5175}%
\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})
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5388}%
$s$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{eqnarraystar5189}%
\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{displaymath5203}%
\begin{displaymath}
  \left(\DD{m}{t}\right)_{ev} \sim 
     - 2.24\times 10^{-2}(\rho_{v,s}-\rho_{v,\infty})D^{1.6}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7084}%
$\displaystyle EV_{rv}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7086}%
$\displaystyle - \frac{1}{\rho_{d}}2.24\times 10^{-2}(q_{v,s} -q_{v,\infty})\int _{0}^{\infty}
D^{1.6}N_{D}\Dd D,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7088}%
$\displaystyle - 2.24\times 10^{-2}(q_{v,s} -q_{v,\infty})\int _{0}^{\infty}
D^{1.6}N_{0}\exp(-\lambda D)\Dd D$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7090}%
$\displaystyle - 2.24\times 10^{-2}(q_{v,s} -q_{v,\infty})
N_{0}\frac{\Gamma(2.6)}{\lambda ^{13/5}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7092}%
$\displaystyle - 2.24\times 10^{-2}
\Gamma(2.6) (\pi \rho_{w})^{-0.65}
N_{0}^{0.35}
(q_{v,s} -q_{v,\infty})
(\rho_{d}q_{r})^{0.65}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7094}%
$\displaystyle - 1.7\times 10^{-4}N_{0}^{0.35}(q_{v,s} -q_{v,\infty})
(\rho_{d}q_{r})^{0.65}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7096}%
$\displaystyle - 4.81\times 10^{-2}(q_{v,s} -q_{v,\infty})
(\rho_{d}q_{r})^{0.65}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5392}%
$\Gamma(2.6)=1.4296245$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5304}%
\begin{displaymath}
  EV_{rv} = 4.85\times 10^{-2}(q_{v,s} -q_{v,\infty})(\rho_{d}q_{r})^{0.65}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5474}%
$C_{\varepsilon}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5476}%
$C_{m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5480}%
$\bar{c}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5484}%
$c_{v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5486}%
$D_{u_{i}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5488}%
$x_{i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5490}%
$D_{\theta}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5494}%
$f$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5496}%
$g$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5506}%
$\overline{p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5508}%
$p_{0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5510}%
$\Pi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5512}%
$\overline{\Pi}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5524}%
$\overline{\rho}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5526}%
$\rho_{0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5530}%
$\overline{T}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5532}%
$\overline{\theta}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5536}%
$u_{i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5538}%
$i = 1, 3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5540}%
$(u_{1}, u_{3}) = (u, w)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5546}%
$(x_{1}, x_{3}) = (x, z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5472}%
\begin{displaymath}
  \mbox{dcstaff@gfd-dennou.org}
 \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}


\end{document}