<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;"># LaTeX2HTML 2002-2-1 (1.70)
# Associate images original text with physical files.


$key = q/{c_{p}}_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="28" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="${c_{p}}_{d}$"&gt;|; 

$key = q/{displaymath}mbox{dcstaff@gfd-dennou.org}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="190" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img460.png"
 ALT="\begin{displaymath}
\mbox{dcstaff@gfd-dennou.org}
\end{displaymath}"&gt;|; 

$key = q/displaystyletheta_{v}equivfrac{theta}{f};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="62" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img144.png"
 ALT="$\displaystyle \theta_{v} \equiv \frac{\theta}{f}$"&gt;|; 

$key = q/displaystyle3K_{m}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="48" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img274.png"
 ALT="$\displaystyle 3 K_{m}.$"&gt;|; 

$key = q/displaystyleDP{}{x}left(K_{m}DP{E}{x}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="118" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img359.png"
 ALT="$\displaystyle \DP{}{x} \left(K_{m} \DP{E}{x}\right)$"&gt;|; 

$key = q/C_{varepsilon}=C_{m}=0.2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="125" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="$C_{\varepsilon} = C_{m} = 0.2$"&gt;|; 

$key = q/displaystyle-left(uDP{theta}{x}+wDP{theta}{z}right)-wDP{bar{theta}}{x}+Dinv{bar{pi}}left(Q_{cnd}+Q_{rad}+Q_{dis}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="418" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$\displaystyle - \left( u \DP{\theta}{x} + w \DP{\theta}{z} \right)
- w\DP{\bar{\theta}}{x}
+ \Dinv{\bar{\pi}} \left(Q_{cnd} + Q_{rad} + Q_{dis}\right)$"&gt;|; 

$key = q/Q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img108.png"
 ALT="$Q$"&gt;|; 

$key = q/rho_{v}=rho_{v,s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="75" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img418.png"
 ALT="$\rho_{v} = \rho_{v,s}$"&gt;|; 

$key = q/j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="13" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img292.png"
 ALT="$j$"&gt;|; 

$key = q/D+dD;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="69" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img377.png"
 ALT="$D+dD$"&gt;|; 

$key = q/displaystyleoverline{(u_{i}^{prime}u_{j}^{prime})};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="53" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img267.png"
 ALT="$\displaystyle \overline{(u_{i}^{\prime} u_{j}^{\prime})}$"&gt;|; 

$key = q/displaystyle{theta_{v}}^{'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="26" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img205.png"
 ALT="$\displaystyle {\theta_{v}}^{'}$"&gt;|; 

$key = q/g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img447.png"
 ALT="$g$"&gt;|; 

$key = q/gamma=L_{v}slash({c_{p}}_{d}pi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="120" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$\gamma = L_{v}/ ({c_{p}}_{d} \pi)$"&gt;|; 

$key = q/{displaymath}=-frac{q}{3l_{1}}(overline{u^{prime}_{i}u^{prime}_{j}}-frac{delta_{{2}left(DP{u_{i}}{x_{j}}+DP{u_{j}}{x_{i}}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="351" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img294.png"
 ALT="\begin{displaymath}
= - \frac{q}{3l_{1}}(\overline{u^{\prime}_{i}u^{\prime}_{j}...
...+ Cq^{2}\left(\DP{u_{i}}{x_{j}}
+ \DP{u_{j}}{x_{i}}\right),
\end{displaymath}"&gt;|; 

$key = q/displaystyleint^{T_{0}}_{T}Dinv{T}dT;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="80" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img134.png"
 ALT="$\displaystyle \int^{T_{0}}_{T} \Dinv{T}dT$"&gt;|; 

$key = q/displaystyle-overline{u^{prime}_{k}u^{prime}_{i}}DP{u_{j}}{x_{k}}-overline{u^{pr_{i}theta^{prime}}+g_{i}overline{u^{prime}_{j}theta^{prime}});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="347" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img318.png"
 ALT="$\displaystyle - \overline{u^{\prime}_{k}u^{\prime}_{i}}\DP{u_{j}}{x_{k}}
- \ove...
...{\prime}_{i}\theta^{\prime} }
+ g_{i}\overline{u^{\prime}_{j}\theta^{\prime} })$"&gt;|; 

$key = q/displaystyletheta_{v}=bar{theta_{v}}(z)+{theta_{v}}^{'}(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="190" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img186.png"
 ALT="$\displaystyle \theta_{v} = \bar{\theta_{v}}(z) + {\theta_{v}}^{'}(x,z,t)$"&gt;|; 

$key = q/displaystylefequivleft(frac{1slashM_{d}}{1slashM_{d}+sumq_{v}slashM_{v}}right)(1+sumq_{v}+sumq_{x});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="366" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img123.png"
 ALT="$\displaystyle f \equiv
\left(\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v} }\right)
(1 + \sum q_{v} + \sum q_{x} )$"&gt;|; 

$key = q/displaystyle-DP{}{x_{j}}left[-K_{m}left(DP{u_{i}}{x_{j}}+DP{u_{j}}{x_{i}}right)+frac{2}{3}delta_{ij}Eright].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="315" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$\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].$"&gt;|; 

$key = q/displaystyleK_{d}frac{rho_{v,s}-rho_{v,infty}}{r_{d}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="118" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img424.png"
 ALT="$\displaystyle K_{d}\frac{\rho_{v,s} - \rho _{v,\infty}}{r_{d}}$"&gt;|; 

$key = q/K_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img414.png"
 ALT="$K_{d}$"&gt;|; 

$key = q/textstyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$\textstyle =$"&gt;|; 

$key = q/overline{theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="14" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img455.png"
 ALT="$\overline{\theta}$"&gt;|; 

$key = q/displaystylec_{p}dT-alphadp=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="133" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img128.png"
 ALT="$\displaystyle c_{p}dT - \alpha dp = 0$"&gt;|; 

$key = q/PR_{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$PR_{r}$"&gt;|; 

$key = q/theta^{'}slashbar{theta}ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="77" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img234.png"
 ALT="$\theta^{'}/\bar{\theta} \ll 1$"&gt;|; 

$key = q/displaystyleDD{q_{v}}{t}=Src.q_{v}+Turb.q_{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="197" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img103.png"
 ALT="$\displaystyle \DD{q_{v}}{t} = Src.q_{v} + Turb.q_{v}$"&gt;|; 

$key = q/displaystyleB+S+D_{E}-left(frac{C_{varepsilon}}{l}right)E^{frac{3}{2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="205" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img256.png"
 ALT="$\displaystyle B + S + D_{E}
- \left(\frac{C_{\varepsilon}}{l}\right)
E^{\frac{3}{2}}$"&gt;|; 

$key = q/C_{varepsilon},C_{m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="60" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img275.png"
 ALT="$C_{\varepsilon}, C_{m}$"&gt;|; 

$key = q/displaystyleU_{r}=12.2(q_{r})^{0.125};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="145" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$\displaystyle U_{r} = 12.2 (q_{r})^{0.125}$"&gt;|; 

$key = q/C_{s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img145.png"
 ALT="$C_{s}$"&gt;|; 

$key = q/displaystyle{C_{s}}^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="33" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img228.png"
 ALT="$\displaystyle {C_{s}}^{2}$"&gt;|; 

$key = q/l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="11" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img257.png"
 ALT="$l$"&gt;|; 

$key = q/displaystylefrac{R_{d}pi(thetaslashf)}{p}left(frac{{c_{p}}_{d}}{R_{d}}ppi^{-1}right)dpi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="203" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img169.png"
 ALT="$\displaystyle \frac{R_{d} \pi (\theta/f) }{p}
\left(
\frac{{c_{p}}_{d}}{R_{d}} p \pi^{-1}
\right)d\pi$"&gt;|; 

$key = q/displaystyle+left(C_{m}^{2}l^{2}right)left{left(DP{u}{x}right)^{2}+left(DP{w}{z}right)^{2}right};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="257" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="$\displaystyle + \left( C_{m}^{2} l^{2} \right) \left\{
\left( \DP{u}{x} \right)^{2}
+ \left( \DP{w}{z} \right)^{2}
\right\}$"&gt;|; 

$key = q/displaystyle-left(uDP{theta}{x}+wDP{theta}{z}right)-wDP{bar{theta}}{x}+frac{L}{{c_{p}}_{d}bar{pi}}left(CN_{vc}-EV_{cv}-EV_{rv}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="459" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$\displaystyle - \left( u \DP{\theta}{x} + w \DP{\theta}{z} \right)
- w\DP{\bar{...
...x}
+ \frac{L}{{c_{p}}_{d} \bar{\pi}} \left( CN_{vc} - EV_{cv} - EV_{rv} \right)$"&gt;|; 

$key = q/displaystyleCL_{cr}=2.2q_{c}(bar{rho}q_{r})^{0.875}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="186" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$\displaystyle CL_{cr} = 2.2 q_{c} (\bar{\rho} q_{r})^{0.875} .$"&gt;|; 

$key = q/l_{1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="18" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img295.png"
 ALT="$l_{1}$"&gt;|; 

$key = q/displaystyle-left{-K_{m}left(DP{u_{i}}{x_{j}}+DP{u_{j}}{x_{i}}right)+frac{2}{3}delta_{ij}Eright}DP{u_{i}}{x_{j}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="317" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img347.png"
 ALT="$\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}}$"&gt;|; 

$key = q/displaystyleDD{p}{t}=rho{C_{s}}^{2}left{-Ddiv{Dvect{u}}+Dinv{theta}DD{theta}{t}-f}{q_{c}}DD{q_{c}}{t}+sumDP{f}{q_{r}}DD{q_{r}}{t}right)right};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="600" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img140.png"
 ALT="$\displaystyle \DD{p}{t} = \rho {C_{s}}^{2}
\left\{
- \Ddiv{\Dvect{u}}
+ \Dinv{\...
...\DP{f}{q_{c}} \DD{q_{c}}{t}
+ \sum \DP{f}{q_{r}} \DD{q_{r}}{t}
\right)
\right\}$"&gt;|; 

$key = q/2nuoverline{DP{u^{prime}_{i}}{x_{k}}DP{u^{prime}_{j}}{x_{k}}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="79" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img300.png"
 ALT="$2\nu \overline{\DP{u^{\prime}_{i}}{x_{k}}\DP{u^{\prime}_{j}}{x_{k}}}$"&gt;|; 

$key = q/displaystyle-overline{u^{prime}_{k}u^{prime}_{i}}DP{u_{j}}{x_{k}}-overline{u^{prerline{u^{prime}_{i}theta}+g_{i}overline{u^{prime}_{j}theta});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="338" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img280.png"
 ALT="$\displaystyle -\overline{u^{\prime}_{k}u^{\prime}_{i}}\DP{u_{j}}{x_{k}}
-\overl...
...(g_{j}\overline{u^{\prime}_{i}\theta }
+ g_{i}\overline{u^{\prime}_{j}\theta })$"&gt;|; 

$key = q/displaystyleC_{m}E^{frac{1}{2}}l,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="67" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img272.png"
 ALT="$\displaystyle C_{m} E^{\frac{1}{2}} l,$"&gt;|; 

$key = q/displaystyleDP{u}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="31" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$\displaystyle \DP{u}{t}$"&gt;|; 

$key = q/textstyle-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img316.png"
 ALT="$\textstyle -$"&gt;|; 

$key = q/displaystyleoverline{u^{prime}_{j}theta^{prime}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="36" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img331.png"
 ALT="$\displaystyle \overline{u^{\prime}_{j}\theta^{\prime}}$"&gt;|; 

$key = q/displaystyleDP{}{x}left(K_{m}DP{E}{x}right)+DP{}{x}left(K_{m}DP{E}{x}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="255" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img356.png"
 ALT="$\displaystyle \DP{}{x} \left(K_{m} \DP{E}{x} \right)
+ \DP{}{x} \left(K_{m} \DP{E}{x} \right)$"&gt;|; 

$key = q/displaystyle{C_{s}}^{2}equivfrac{{c_{p}}_{d}}{{c_{v}}_{d}}R_{d}pitheta_{v}=frac{{c_{p}}_{d}}{{c_{v}}_{d}}R_{d}pileft(frac{theta}{f}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="265" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img165.png"
 ALT="$\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)$"&gt;|; 

$key = q/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};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="379" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="$\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}$"&gt;|; 

$key = q/displaystyleDD{overline{u^{prime}_{j}theta^{prime}}}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="50" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img320.png"
 ALT="$\displaystyle \DD{\overline{u^{\prime}_{j}\theta^{\prime} }}{t}$"&gt;|; 

$key = q/displaystyle2.2q_{c}(rho_{d}q_{r})^{0.875};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="123" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img404.png"
 ALT="$\displaystyle 2.2 q_{c}(\rho _{d}q_{r})^{0.875}$"&gt;|; 

$key = q/displaystylefrac{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};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="350" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img361.png"
 ALT="$\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\}$"&gt;|; 

$key = q/q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img301.png"
 ALT="$q$"&gt;|; 

$key = q/B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img258.png"
 ALT="$B$"&gt;|; 

$key = q/displaystyle-left(uDP{q_{v}}{x}+wDP{q_{v}}{z}right)-wDP{bar{q_{v}}}{x}-left(CN_{vc}-EV_{cv}-EV_{rv}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="435" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$\displaystyle - \left( u \DP{q_{v}}{x} + w \DP{q_{v}}{z} \right)
- w\DP{\bar{q_{v}}}{x}
- \left( CN_{vc} - EV_{cv} - EV_{rv} \right)$"&gt;|; 

$key = q/displaystylefrac{piN_{0}rho_{w}}{rho_{d}}lambda^{-4}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="97" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img398.png"
 ALT="$\displaystyle \frac{\pi N_{0}\rho_{w}}{\rho_{d}}\lambda ^{-4}.$"&gt;|; 

$key = q/nu,alpha,beta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="54" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img290.png"
 ALT="$\nu, \alpha, \beta$"&gt;|; 

$key = q/{displaymath}left(DD{m}{t}right)_{cr}=frac{pi}{4}D^{2}VErho_{d}q_{c}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="191" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img380.png"
 ALT="\begin{displaymath}
\left(\DD{m}{t}\right)_{cr} = \frac{\pi}{4}D^{2}VE\rho _{d}q_{c}
\end{displaymath}"&gt;|; 

$key = q/w;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img220.png"
 ALT="$w$"&gt;|; 

$key = q/displaystyle-left(uDP{q_{c}}{x}+wDP{q_{c}}{z}right)+(CN_{cr}+CL_{cr}-EV_{rv})+PR_{r}+Turb.q_{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="508" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$\displaystyle - \left( u \DP{q_{c}}{x} + w \DP{q_{c}}{z} \right)
+ (CN_{cr} + CL_{cr} - EV_{rv} ) + PR_{r} + Turb.q_{r}$"&gt;|; 

$key = q/displaystyleEV_{rv};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="45" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img430.png"
 ALT="$\displaystyle EV_{rv}$"&gt;|; 

$key = q/displaystylealpha=frac{RT}{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="74" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img131.png"
 ALT="$\displaystyle \alpha = \frac{RT}{p}$"&gt;|; 

$key = q/displaystylefrac{p_{0}pi^{{c_{v}}_{d}slashR_{d}}}{R_{d}(thetaslashf)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="81" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img126.png"
 ALT="$\displaystyle \frac{p_{0} \pi^{{c_{v}}_{d}/R_{d}}}{R_{d} (\theta/f)}$"&gt;|; 

$key = q/t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="11" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$t$"&gt;|; 

$key = q/overline{pleft(DP{u^{prime}_{i}}{x_{j}}+DP{u^{prime}_{i}}{x_{j}}right)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="112" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img293.png"
 ALT="$\overline{p\left(\DP{u^{\prime}_{i}}{x_{j}} + \DP{u^{\prime}_{i}}{x_{j}}\right)}$"&gt;|; 

$key = q/{eqnarraystar}4pir_{d}left(1+frac{Fr}{s}right)&amp;sim&amp;2.24times10^{3}D^{1.6},K_{d}(})&amp;sim&amp;10^{-5}(rho_{v,s}-rho_{v,infty}).{eqnarraystar};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="311" HEIGHT="74" BORDER="0"
 SRC="|."$dir".q|img428.png"
 ALT="\begin{eqnarray*}
4\pi r_{d}\left(1+\frac{Fr}{s}\right) &amp;amp;\sim&amp;amp; 2.24\times 10^{3...
...} - \rho_{v,\infty}) &amp;amp;\sim&amp;amp; 10^{-5}(\rho_{v,s}-\rho_{v,\infty}).
\end{eqnarray*}"&gt;|; 

$key = q/{displaymath}F=-K_{d}DD{rho_{v}}{r}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="107" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img412.png"
 ALT="\begin{displaymath}
F = - K_{d}\DD{\rho_{v}}{r}
\end{displaymath}"&gt;|; 

$key = q/c_{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img442.png"
 ALT="$c_{v}$"&gt;|; 

$key = q/C;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img296.png"
 ALT="$C$"&gt;|; 

$key = q/r=r_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="55" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img417.png"
 ALT="$r=r_{d}$"&gt;|; 

$key = q/rho_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img107.png"
 ALT="$\rho_{d}$"&gt;|; 

$key = q/displaystyleDD{q^{2}}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="36" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img323.png"
 ALT="$\displaystyle \DD{q^{2}}{t}$"&gt;|; 

$key = q/z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$z$"&gt;|; 

$key = q/displaystyle-2overline{u^{prime}_{j}u^{prime}_{k}}DP{u_{j}}{x_{k}}+2g_{j}betaove{x_{k}}left[nuDP{q^{2}}{x_{k}}right]-2frac{q^{3}}{Lambda_{1}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="372" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img333.png"
 ALT="$\displaystyle - 2\overline{u^{\prime}_{j}u^{\prime}_{k}}\DP{u_{j}}{x_{k}}
+ 2g_...
...
+ \DP{}{x_{k}}\left[\nu \DP{q^{2}}{x_{k}}\right]
- 2\frac{q^{3}}{\Lambda _{1}}$"&gt;|; 

$key = q/displaystylerho_{d}+sumrho_{v}+sumrho_{c}+sumrho_{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="220" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img111.png"
 ALT="$\displaystyle \rho_{d} + \sum \rho_{v} + \sum \rho_{c} + \sum \rho_{r}$"&gt;|; 

$key = q/displaystylefrac{p}{R_{d}(Tslashf)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="79" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img124.png"
 ALT="$\displaystyle \frac{p}{R_{d} (T/f)}$"&gt;|; 

$key = q/displaystyle{C_{s}}^{2}equivfrac{{c_{p}}_{d}}{{c_{v}}_{d}}R_{d}T_{v}=frac{{c_{p}}_{d}}{{c_{v}}_{d}}R_{d}frac{T}{f};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="218" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img146.png"
 ALT="$\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}$"&gt;|; 

$key = q/displaystyle+2K_{m}left{left(DP{u}{x}right)^{2}+left(DP{w}{z}right)^{2}right}+K_z}+DP{w}{x}right)^{2}-frac{2}{3}Eleft(DP{u}{x}+DP{w}{z}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="557" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img357.png"
 ALT="$\displaystyle + 2 K_{m} \left\{
\left( \DP{u}{x} \right)^{2}
+ \left( \DP{w}{z}...
...{z} + \DP{w}{x}\right)^{2}
- \frac{2}{3} E \left( \DP{u}{x} + \DP{w}{z} \right)$"&gt;|; 

$key = q/1slashf=1slashbar{f};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="90" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img225.png"
 ALT="$1/f = 1/\bar{f}$"&gt;|; 

$key = q/overline{pDP{theta^{prime}}{x_{k}}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="41" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img297.png"
 ALT="$\overline{p\DP{\theta^{\prime} }{x_{k}}}$"&gt;|; 

$key = q/{displaymath}=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="28" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img305.png"
 ALT="\begin{displaymath}
= 0
\end{displaymath}"&gt;|; 

$key = q/q_{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$q_{v}$"&gt;|; 

$key = q/displaystyledleft[frac{p_{0}pi^{c_{vslashR_{d}}}}{R_{d}(thetaslashf)}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="106" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img174.png"
 ALT="$\displaystyle d \left[
\frac{p_{0} \pi^{c_{v/R_{d}}}}{R_{d} (\theta/f)}
\right]$"&gt;|; 

$key = q/displaystylefrac{R_{d}pi(thetaslashf)}{p}left(frac{p_{0}{c_{p}}_{d}}{R_{d}}pi^{{c_{p}}_{d}slashR-1}right)dpi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="247" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img168.png"
 ALT="$\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$"&gt;|; 

$key = q/displaystyle-overline{(u_{i}^{prime}u_{j}^{prime})}DP{u_{i}}{x_{j}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="101" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img346.png"
 ALT="$\displaystyle - \overline{(u_{i}^{\prime} u_{j}^{\prime})}
\DP{u_{i}}{x_{j}}$"&gt;|; 

$key = q/U_{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$U_{r}$"&gt;|; 

$key = q/displaystyle-frac{g}{overline{theta}}left(K_{h}DP{theta}{z}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="111" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img345.png"
 ALT="$\displaystyle - \frac{g}{\overline{\theta}}
\left( K_{h} \DP{\theta}{z} \right)$"&gt;|; 

$key = q/displaystyleDP{w^{'}}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="39" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img201.png"
 ALT="$\displaystyle \DP{w^{'}}{t}$"&gt;|; 

$key = q/bar{f};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="16" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img197.png"
 ALT="$\bar{f}$"&gt;|; 

$key = q/displaystyleDP{}{x_{k}}left[qlambda_{1}left(2DP{q^{2}}{x_{k}}+DP{overline{u^{prime}_{j}u^{prime}_{k}}}{x_{j}}right)-nuDP{q^{2}}{x_{k}}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="303" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img324.png"
 ALT="$\displaystyle \DP{}{x_{k}}\left[
q\lambda _{1}\left(
2\DP{q^{2}}{x_{k}} +
\DP{\...
...ine{u^{\prime}_{j}u^{\prime}_{k}}}{x_{j}}\right)
- \nu \DP{q^{2}}{x_{k}}\right]$"&gt;|; 

$key = q/Q_{cnd};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$Q_{cnd}$"&gt;|; 

$key = q/T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$T$"&gt;|; 

$key = q/displaystyleq_{v}=bar{q_{v}}(z)+q_{v}^{'}(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="183" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img188.png"
 ALT="$\displaystyle q_{v} = \bar{q_{v}}(z) + q_{v}^{'}(x,z,t)$"&gt;|; 

$key = q/displaystyleDP{u^{'}}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="36" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img194.png"
 ALT="$\displaystyle \DP{u^{'}}{t}$"&gt;|; 

$key = q/displaystylefrac{{c_{p}}_{d}}{{c_{v}}_{d}}R_{d}(bar{pi}+pi^{'})left(frac{(bar{theta}+theta^{'})}{bar{f}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="213" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img229.png"
 ALT="$\displaystyle \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d} (\bar{\pi} + \pi^{'})
\left( \frac{(\bar{\theta} + \theta^{'})}{\bar{f}} \right)$"&gt;|; 

$key = q/Q_{dis};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="38" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="$Q_{dis}$"&gt;|; 

$key = q/displaystyleDP{}{x_{j}}left(K_{m}DP{E}{x_{j}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="136" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img355.png"
 ALT="$\displaystyle \DP{}{x_{j}} \left(K_{m} \DP{E}{x_{j}} \right),$"&gt;|; 

$key = q/rho=rho(theta,p,q_{v},q_{x});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="140" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img149.png"
 ALT="$\rho= \rho(\theta,p,q_{v},q_{x})$"&gt;|; 

$key = q/s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img427.png"
 ALT="$s$"&gt;|; 

$key = q/displaystyle-left(uDP{u}{x}+wDP{u}{z}right)-{c_{p}}_{d}bar{theta_{v}}DP{pi}{z}+Turb.w;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="321" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$\displaystyle - \left( u \DP{u}{x} + w \DP{u}{z} \right)
- {c_{p}}_{d} \bar{\theta_{v}} \DP{\pi}{z}
+ Turb.w$"&gt;|; 

$key = q/displaystyleDP{pi^{'}}{t}=-frac{overline{{C_{s}}^{2}}}{{c_{p}}_{d}bar{rho}(bar{t2}}Ddivleft{bar{rho}(bar{theta}slashbar{f})Dvect{u^{'}}right};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="284" HEIGHT="73" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img242.png"
 ALT="$\displaystyle \DP{\pi^{'}}{t}=
- \frac{\overline{{C_{s}}^{2}}}{{c_{p}}_{d} \bar...
...f})^{2}}
\Ddiv \left\{
\bar{\rho} (\bar{\theta}/\bar{f}) \Dvect{u^{'}}
\right\}$"&gt;|; 

$key = q/displaystyleDP{bar{pi}+pi^{'}}{t}+u^{'}DP{bar{pi}+pi^{'}}{x}+w^{'}DP{bar{pi}+pi^s}}^{2}}}{{c_{p}}_{d}(bar{theta}slashbar{f})}DdivDvect{u^{'}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="436" HEIGHT="73" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img226.png"
 ALT="$\displaystyle \DP{\bar{\pi} + \pi^{'}}{t}
+ u^{'} \DP{\bar{\pi}+\pi^{'}}{x}
+ w...
...verline{{C_{s}}^{2} }}{ {c_{p}}_{d} (\bar{\theta}/\bar{f})}
\Ddiv \Dvect{u^{'}}$"&gt;|; 

$key = q/{eqnarraystar}q&amp;equiv&amp;sqrt{overline{(u^{prime}_{i})^{2}}}&amp;=&amp;sqrt{2E}{eqnarraystar};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="109" HEIGHT="64" BORDER="0"
 SRC="|."$dir".q|img289.png"
 ALT="\begin{eqnarray*}
q &amp;amp;\equiv&amp;amp; \sqrt{\overline{(u^{\prime}_{i})^{2}}} \\\\
&amp;amp; = &amp;amp; \sqrt{2E}
\end{eqnarray*}"&gt;|; 

$key = q/displaystyle-frac{overline{{C_{s}}^{2}}}{{c_{p}}_{d}bar{rho}(bar{theta}slashbar{{theta}slashbar{f})left(DP{u^{'}}{x}+DP{w^{'}}{z}right)right};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="420" HEIGHT="73" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img240.png"
 ALT="$\displaystyle - \frac{\overline{{C_{s}}^{2}}}{{c_{p}}_{d} \bar{\rho} (\bar{\the...
...o} (\bar{\theta}/\bar{f})
\left( \DP{u^{'}}{x} + \DP{w^{'}}{z} \right)
\right\}$"&gt;|; 

$key = q/displaystyleDP{theta^{'}}{t}=-left(u^{'}DP{theta^{'}}{x}+w^{'}DP{theta^{'}}{x}right)-w^{'}DP{bar{theta}}{x}+Q+Turb.bar{theta}+Turb.theta^{'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="489" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img244.png"
 ALT="$\displaystyle \DP{\theta^{'}}{t}
=
- \left(
u^{'}\DP{\theta^{'}}{x}
+ w^{'}\DP{...
...}
\right)
- w^{'}\DP{\bar{\theta}}{x}
+ Q + Turb.\bar{\theta} + Turb.\theta^{'}$"&gt;|; 

$key = q/displaystyle-frac{g}{overline{theta}}left(K_{h}DP{theta}{z}right)+2K_{m}left{left(DP{u}{x}right)^{2}+left(DP{w}{z}right)^{2}right};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="347" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img365.png"
 ALT="$\displaystyle - \frac{g}{\overline{\theta}}
\left( K_{h} \DP{\theta}{z} \right)...
...m} \left\{
\left( \DP{u}{x} \right)^{2}
+ \left( \DP{w}{z} \right)^{2}
\right\}$"&gt;|; 

$key = q/displaystyle-2.24times10^{-2}Gamma(2.6)(pirho_{w})^{-0.65}N_{0}^{0.35}(q_{v,s}-q_{v,infty})(rho_{d}q_{r})^{0.65};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="456" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img434.png"
 ALT="$\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}$"&gt;|; 

$key = q/displaystyleCL_{cr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="45" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img388.png"
 ALT="$\displaystyle CL_{cr}$"&gt;|; 

$key = q/displaystyleDP{pi}{t}=-frac{overline{{C_{s}}^{2}}}{{c_{p}}_{d}bar{rho}(bar{theta})^{2}}Ddivleft{bar{rho}(bar{theta}slashbar{f})Dvect{u}right};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="273" HEIGHT="73" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img250.png"
 ALT="$\displaystyle \DP{\pi}{t}=
- \frac{\overline{{C_{s}}^{2}}}{{c_{p}}_{d} \bar{\rh...
...bar{f})^{2}}
\Ddiv \left\{
\bar{\rho} (\bar{\theta}/\bar{f}) \Dvect{u}
\right\}$"&gt;|; 

$key = q/q_v=rho_vslashrho_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="90" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img113.png"
 ALT="$q_v = \rho_v/\rho_{d}$"&gt;|; 

$key = q/theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$\theta $"&gt;|; 

$key = q/displaystyleV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img384.png"
 ALT="$\displaystyle V$"&gt;|; 

$key = q/K_{h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="29" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="$K_{h}$"&gt;|; 

$key = q/displaystyle+K_{m}left(DP{w}{x}+DP{u}{z}right)DP{w}{x}+left{2K_{m}left(DP{w}{z}right)-frac{2}{3}Eright}DP{w}{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="416" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img352.png"
 ALT="$\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}$"&gt;|; 

$key = q/L_{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$L_{v}$"&gt;|; 

$key = q/textstyle+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img277.png"
 ALT="$\textstyle +$"&gt;|; 

$key = q/displaystyleoverline{theta_{v}}+theta_{v}^{'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="61" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="$\displaystyle \overline{\theta_{v}} + \theta_{v}^{'}$"&gt;|; 

$key = q/{displaymath}Q_{rad}=-frac{1}{overline{rho}c_{p_{d}}}DD{F_{net}}{z}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="157" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="\begin{displaymath}
Q_{rad} = - \frac{1}{\overline{\rho}c_{p_{d}}}\DD{F_{net}}{z}
\end{displaymath}"&gt;|; 

$key = q/C_{m}=C_{varepsilon}=0.2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="125" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img372.png"
 ALT="$C_{m} = C_{\varepsilon} = 0.2$"&gt;|; 

$key = q/displaystylefrac{g_{j}}{overline{theta}}overline{u^{prime}_{j}theta^{prime}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="61" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img262.png"
 ALT="$\displaystyle \frac{g_{j}}{\overline{\theta}}
\overline{u^{\prime}_{j} \theta^{\prime}} ,$"&gt;|; 

$key = q/i=1,3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="63" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img457.png"
 ALT="$i = 1, 3$"&gt;|; 

$key = q/displaystyle+g_{j}betaoverline{u^{prime}_{j}theta^{prime}}-2nuoverline{left(DP{u^{prime}_{j}}{x_{k}}right)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="181" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img288.png"
 ALT="$\displaystyle + g_{j}\beta\overline{u^{\prime}_{j}\theta^{\prime}}
- 2\nu \overline{\left(\DP{u^{\prime}_{j}}{x_{k}}\right)}$"&gt;|; 

$key = q/(u_{1},u_{3})=(u,w);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="137" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img458.png"
 ALT="$(u_{1}, u_{3}) = (u, w)$"&gt;|; 

$key = q/overline{u^{prime}_{j}theta^{prime}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="36" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img335.png"
 ALT="$\overline{u^{\prime}_{j}\theta^{\prime}}$"&gt;|; 

$key = q/{eqnarraystar}overline{u^{prime}_{k}u^{prime}_{i}u^{prime}_{j}}&amp;=&amp;-qlambda_{1}leP{overline{(theta^{prime})^{2}}}{x_{k}}.{eqnarraystar};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="375" HEIGHT="165" BORDER="0"
 SRC="|."$dir".q|img307.png"
 ALT="\begin{eqnarray*}
\overline{u^{\prime}_{k}u^{\prime}_{i}u^{\prime}_{j}}
&amp;amp;=&amp;amp; -...
... -q\lambda _{3}
\DP{\overline{(\theta^{\prime})^{2}}}{x_{k}}.
\end{eqnarray*}"&gt;|; 

$key = q/CN_{vc};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="48" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$CN_{vc}$"&gt;|; 

$key = q/{displaymath}piequivleft(frac{p}{p_{0}}right)^{R_{d}slash{c_{p}}_{d}}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="126" HEIGHT="59" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="\begin{displaymath}
\pi \equiv \left(\frac{p}{p_{0}}\right)^{R_{d}/{c_{p}}_{d}}
\end{displaymath}"&gt;|; 

$key = q/displaystyle-left(u^{'}DP{u^{'}}{x}+w^{'}DP{u^{'}}{z}right)-{c_{p}}_{d}bar{theta_{v}}DP{pi^{'}}{x}+Turb.u;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="343" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img195.png"
 ALT="$\displaystyle - \left(
u^{'} \DP{u^{'}}{x}
+ w^{'} \DP{u^{'}}{z}
\right)
- {c_{p}}_{d} \bar{\theta_{v}} \DP{\pi^{'}}{x} + Turb.u$"&gt;|; 

$key = q/displaystyle-left(u^{'}DP{w^{'}}{x}+w^{'}DP{w^{'}}{z}right)+{c_{p}}_{d}bar{thetav}}^{'}left(frac{g}{{c_{p}}_{d}bar{theta_{v}}}right)-g+Turb.w;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="659" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img202.png"
 ALT="$\displaystyle - \left(
u^{'} \DP{w^{'}}{x}
+ w^{'} \DP{w^{'}}{z}
\right)
+ {c_{...
...eta_{v}}^{'}
\left( \frac{g}{{c_{p}}_{d} \bar{\theta_{v}}} \right)
- g + Turb.w$"&gt;|; 

$key = q/displaystyleDP{}{x_{k}}left[qlambda_{1}left(DP{overline{u^{prime}_{i}u^{prime}_{ight)-nuDP{}{x_{k}}overline{u^{prime}_{i}u^{prime}_{j}}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="413" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img317.png"
 ALT="$\displaystyle \DP{}{x_{k}}\left[
q\lambda _{1}\left(
\DP{\overline{u^{\prime}_{...
...}}{x_{i}}\right)
-\nu\DP{}{x_{k}}\overline{u^{\prime}_{i}u^{\prime}_{j}}\right]$"&gt;|; 

$key = q/D;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="21" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img375.png"
 ALT="$D$"&gt;|; 

$key = q/displaystyleE=frac{1}{2}overline{(u^{prime})^{2}+(w^{prime})^{2}}=frac{{K_{m}}^{2}}{C_{m}^{2}l^{2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="227" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="$\displaystyle E = \frac{1}{2}
\overline{(u^{\prime})^{2} + (w^{\prime})^{2}}
= \frac{{K_{m}}^{2}}{C_{m}^{2} l^{2}}$"&gt;|; 

$key = q/displaystylew=w^{'}(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="121" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img184.png"
 ALT="$\displaystyle w = w^{'}(x,z,t)$"&gt;|; 

$key = q/displaystyleDP{q_{c}^{'}}{t}=-left(u^{'}DP{q_{c}^{'}}{x}+w^{'}DP{q_{c}^{'}}{x}right)+Src.q_{c}^{'}+Turb.q_{c}^{'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="384" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img246.png"
 ALT="$\displaystyle \DP{q_{c}^{'}}{t}
=
- \left(
u^{'}\DP{q_{c}^{'}}{x}
+ w^{'}\DP{q_{c}^{'}}{x}
\right)
+ Src.q_{c}^{'} + Turb.q_{c}^{'},$"&gt;|; 

$key = q/displaystyleDP{}{x_{j}}left(K_{m}DP{E}{x_{j}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="128" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img266.png"
 ALT="$\displaystyle \DP{}{x_{j}} \left(K_{m} \DP{E}{x_{j}} \right)$"&gt;|; 

$key = q/displaystyle{c_{p}}_{d}DD{T}{t}-Dinv{rho_{d}}DD{p}{t}=Q+Turb.T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="247" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img102.png"
 ALT="$\displaystyle {c_{p}}_{d}\DD{T}{t} - \Dinv{\rho_{d}} \DD{p}{t} = Q + Turb.T$"&gt;|; 

$key = q/displaystyle-frac{q}{3l_{1}}(overline{u^{prime}_{i}u^{prime}_{j}}-frac{delta_{ijj}}{x_{i}}right)-frac{2}{3}frac{q^{3}}{Lambda_{1}}delta_{ij},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="416" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img319.png"
 ALT="$\displaystyle - \frac{q}{3l_{1}}(\overline{u^{\prime}_{i}u^{\prime}_{j}}
- \fra...
...+ \DP{u_{j}}{x_{i}}\right)
- \frac{2}{3}\frac{q^{3}}{\Lambda _{1}}\delta _{ij},$"&gt;|; 

$key = q/displaystyleDinv{f}left{frac{theta^{'}}{theta}-sumDinv{f}DP{f}{q_{v}}q_{v}^{'}-sf}DP{f}{q_{c}}q_{c}^{'}-sumDinv{f}DP{f}{q_{r}}q_{r}^{'}right};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="400" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img207.png"
 ALT="$\displaystyle \Dinv{f}
\left\{
\frac{\theta^{'}}{\theta}
- \sum \Dinv{f} \DP{f}...
...inv{f} \DP{f}{q_{c}} q_{c}^{'}
- \sum \Dinv{f} \DP{f}{q_{r}} q_{r}^{'}
\right\}$"&gt;|; 

$key = q/D_{u_{i}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img443.png"
 ALT="$D_{u_{i}}$"&gt;|; 

$key = q/l=(DeltaxDeltaz)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="123" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="$l=(\Delta x\Delta z)^{1/2}$"&gt;|; 

$key = q/displaystylerho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$\displaystyle \rho$"&gt;|; 

$key = q/N_{D};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img378.png"
 ALT="$N_{D}$"&gt;|; 

$key = q/rho_{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img413.png"
 ALT="$\rho_{v}$"&gt;|; 

$key = q/u,w;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="38" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$u, w$"&gt;|; 

$key = q/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;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="373" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img196.png"
 ALT="$\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$"&gt;|; 

$key = q/displaystylefrac{piN_{0}rho_{w}}{6rho_{d}}int_{0}^{infty}D^{3}exp(-lambdaD)DdD;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="240" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img396.png"
 ALT="$\displaystyle \frac{\pi N_{0}\rho_{w}}{6\rho_{d}}\int _{0}^{\infty}
D^{3}\exp(-\lambda D)\Dd D$"&gt;|; 

$key = q/rho_{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img453.png"
 ALT="$\rho_{0}$"&gt;|; 

$key = q/displaystyle+Turb.q_{v}+Turb.bar{q_{v}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="172" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$\displaystyle + Turb.q_{v} + Turb.\bar{q_{v}},$"&gt;|; 

$key = q/displaystyleDD{q_{x}}{t}=Src.q_{r}+Fall.q_{x}+Turb.q_{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="277" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img163.png"
 ALT="$\displaystyle \DD{q_{x}}{t} = Src.q_{r} + Fall.q_{x} + Turb.q_{r}$"&gt;|; 

$key = q/displaystyleoverline{u_{j}^{prime}theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="32" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img269.png"
 ALT="$\displaystyle \overline{u_{j}^{\prime} \theta }$"&gt;|; 

$key = q/{displaymath}left(DD{m}{t}right)_{ev}sim-2.24times10^{-2}(rho_{v,s}-rho_{v,infty})D^{1.6}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="332" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img429.png"
 ALT="\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}"&gt;|; 

$key = q/displaystylethetaequivTleft(frac{p_{0}}{p}right)^{R_{d}slash{c_{p}}_{d}}=frac{T}{pi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="189" HEIGHT="75" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$\displaystyle \theta \equiv T \left(\frac{p_{0}}{p}\right)^{R_{d}/{c_{p}}_{d}}
= \frac{T}{\pi}$"&gt;|; 

$key = q/displaystylepiequivfrac{T}{theta}=left(frac{p}{p_{0}}right)^{R_{d}slash{c_{p}}_{d}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="174" HEIGHT="75" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img164.png"
 ALT="$\displaystyle \pi \equiv \frac{T}{\theta}
= \left( \frac{p}{p_{0}} \right)^{R_{d}/{c_{p}}_{d}}$"&gt;|; 

$key = q/{displaymath}overline{pu^{prime}_{i}}=overline{ptheta^{prime}}=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="109" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img310.png"
 ALT="\begin{displaymath}
\overline{pu^{\prime}_{i}} = \overline{p\theta^{\prime} } = 0
\end{displaymath}"&gt;|; 

$key = q/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}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="179" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img306.png"
 ALT="$\overline{u^{\prime}_{k}u^{\prime}_{i}u^{\prime}_{j}},
\overline{u^{\prime}_{...
...{\prime}_{j}\theta^{\prime} },
\overline{u^{\prime}_{k}(\theta^{\prime})^{2}}$"&gt;|; 

$key = q/displaystylepleft(1-frac{sump_{v}}{p_{d}+sump_{v}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="156" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img117.png"
 ALT="$\displaystyle p \left( 1 - \frac{\sum p_{v}}{p_{d} + \sum p_{v} }\right)$"&gt;|; 

$key = q/displaystyle-frac{1}{rho_{d}}2.24times10^{-2}(q_{v,s}-q_{v,infty})int_{0}^{infty}D^{1.6}N_{D}DdD,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="364" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img431.png"
 ALT="$\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,$"&gt;|; 

$key = q/displaystyleDD{pi}{t}=frac{{C_{s}}^{2}}{{c_{p}}_{d}rhotheta_{v}}left{Dinv{rho}DDq_{v}+sumDP{f}{q_{c}}dq_{c}+sumDP{f}{q_{r}}dq_{r}right)right};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="592" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img181.png"
 ALT="$\displaystyle \DD{\pi}{t}
=
\frac{{C_{s}}^{2} }{{c_{p}}_{d} \rho \theta_{v} }
\...
...dq_{v}
+ \sum \DP{f}{q_{c}} dq_{c}
+ \sum \DP{f}{q_{r}} dq_{r}
\right)
\right\}$"&gt;|; 

$key = q/displaystyleDP{}{x_{k}}left[u_{k}overline{u^{prime}_{i}u^{prime}_{j}}+overline{u_{j}}-nuDP{}{x_{k}}overline{u^{prime}_{i}u^{prime}_{j}}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="291" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img278.png"
 ALT="$\displaystyle \DP{}{x_{k}}\left[
u_{k}\overline{u^{\prime}_{i}u^{\prime}_{j}}
+...
...^{\prime}_{j}}
- \nu \DP{}{x_{k}}\overline{u^{\prime}_{i}u^{\prime}_{j}}\right]$"&gt;|; 

$key = q/{displaymath}=-frac{q}{3l_{2}}overline{u^{prime}_{i}theta^{prime}}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="90" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img298.png"
 ALT="\begin{displaymath}
= -\frac{q}{3l_{2}}\overline{u^{\prime}_{i}\theta^{\prime} }
\end{displaymath}"&gt;|; 

$key = q/displaystyleDD{u}{t}+Dinv{rho}DP{p}{x}=Turb.u;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="174" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img98.png"
 ALT="$\displaystyle \DD{u}{t} + \Dinv{\rho}\DP{p}{x} = Turb.u$"&gt;|; 

$key = q/displaystyleDP{theta}{t}=-left(uDP{theta}{x}+wDP{theta}{x}right)-wDP{bar{theta}}{x}+Q+Turb.bar{theta}+Turb.theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="456" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img251.png"
 ALT="$\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$"&gt;|; 

$key = q/rho_{v}=rho_{v,infty};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="82" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img420.png"
 ALT="$\rho_{v}=\rho_{v,\infty}$"&gt;|; 

$key = q/CL_{cr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="45" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$CL_{cr}$"&gt;|; 

$key = q/displaystylefrac{{c_{p}}_{d}}{{c_{v}}_{d}}R_{d}bar{pi}frac{bar{theta}}{bar{f}}equivoverline{{C_{s}}^{2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="134" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img233.png"
 ALT="$\displaystyle \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d}
\bar{\pi} \frac{\bar{\theta}}{\bar{f}}
\equiv \overline{{C_{s}}^{2}}$"&gt;|; 

$key = q/10^{3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="31" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img400.png"
 ALT="$10^{3}$"&gt;|; 

$key = q/{displaymath}DD{}{t}equivDP{}{t}+u_{k}DP{}{x_{k}}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="142" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img326.png"
 ALT="\begin{displaymath}
\DD{}{t} \equiv \DP{}{t} + u_{k}\DP{}{x_{k}}
\end{displaymath}"&gt;|; 

$key = q/displaystyle+frac{p_{0}pi^{c_{vslashR_{d}}}}{R_{d}theta}left(sumDP{f}{q_{v}}dq_{v}+sumDP{f}{q_{c}}dq_{c}+sumDP{f}{q_{r}}dq_{r}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="409" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img176.png"
 ALT="$\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)$"&gt;|; 

$key = q/displaystylefrac{2K_{m}}{C_{m}^{2}l^{2}}DD{K_{m}}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="91" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img364.png"
 ALT="$\displaystyle \frac{2 K_{m}}{C_{m}^{2} l^{2}} \DD{K_{m}}{t}$"&gt;|; 

$key = q/displaystyleoverline{theta_{v}}+theta_{v}^{'};;;(for;;q_{c}=0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="180" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="$\displaystyle \overline{ \theta_{v}} + \theta_{v}^{'} \;\;\; (for \;\; q_{c} = 0)$"&gt;|; 

$key = q/{displaymath}f_{k}varepsilon_{jkl}overline{u_{l}^{prime}theta^{prime}}=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="107" HEIGHT="37" BORDER="0"
 SRC="|."$dir".q|img313.png"
 ALT="\begin{displaymath}
f_{k}\varepsilon _{jkl}\overline{u_{l}^{\prime}\theta^{\prime}} = 0
\end{displaymath}"&gt;|; 

$key = q/displaystyleS;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="17" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img263.png"
 ALT="$\displaystyle S$"&gt;|; 

$key = q/displaystyleTurb.{u_{i}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="67" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="$\displaystyle Turb.{u_{i}}$"&gt;|; 

$key = q/rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$\rho $"&gt;|; 

$key = q/D_{E};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img260.png"
 ALT="$D_{E}$"&gt;|; 

$key = q/displaystylefrac{1}{rho_{d}}int_{0}^{infty}rho_{w}frac{pi}{6}D^{3}N_{D}DdD;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="178" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img395.png"
 ALT="$\displaystyle \frac{1}{\rho_{d}}\int _{0}^{\infty} \rho_{w}
\frac{\pi}{6} D^{3}
N_{D}\Dd D$"&gt;|; 

$key = q/displaystyle-4.81times10^{-2}(q_{v,s}-q_{v,infty})(rho_{d}q_{r})^{0.65};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="283" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img436.png"
 ALT="$\displaystyle - 4.81\times 10^{-2}(q_{v,s} -q_{v,\infty})
(\rho_{d}q_{r})^{0.65}$"&gt;|; 

$key = q/displaystylep_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img115.png"
 ALT="$\displaystyle p_{d}$"&gt;|; 

$key = q/displaystylefrac{{c_{p}}_{d}rhotheta_{v}}{{C_{s}}^{2}}dpi-frac{rho}{theta}dtheta_{v}}dq_{v}+sumDP{f}{q_{c}}dq_{c}+sumDP{f}{q_{r}}dq_{r}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="504" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img180.png"
 ALT="$\displaystyle \frac{ {c_{p}}_{d} \rho \theta_{v}}{{C_{s}}^{2} } d\pi
- \frac{\r...
...}{q_{v}} dq_{v}
+ \sum \DP{f}{q_{c}} dq_{c}
+ \sum \DP{f}{q_{r}} dq_{r}
\right)$"&gt;|; 

$key = q/displaystyleDP{(bar{theta}+theta^{'})}{t}=-u^{'}DP{(bar{theta}+theta^{'})}{x}-w^'}DP{(bar{theta}+theta^{'})}{x}+Q+Turb.(bar{theta}+theta^{'});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="501" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img243.png"
 ALT="$\displaystyle \DP{(\bar{\theta} + \theta^{'})}{t}
=
- u^{'}\DP{(\bar{\theta} + ...
...w^{'}\DP{(\bar{\theta} + \theta^{'})}{x}
+ Q + Turb.(\bar{\theta} + \theta^{'})$"&gt;|; 

$key = q/N_{0}=10^{7},E=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="136" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img405.png"
 ALT="$N_{0}=10^{7}, E=1$"&gt;|; 

$key = q/displaystyleDinv{1+sumq_{v}+sumq_{c}+sumq_{r}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="193" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img215.png"
 ALT="$\displaystyle \Dinv{1 + \sum q_{v} + \sum q_{c} + \sum q_{r}}$"&gt;|; 

$key = q/mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="16" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$\mu$"&gt;|; 

$key = q/displaystyleDinv{{C_{s}}^{2}}dp-frac{rho}{theta}dtheta+sumfrac{rho}{f}DP{f}{q_{vc{rho}{f}DP{f}{q_{c}}dq_{c}+sumfrac{rho}{f}DP{f}{q_{r}}dq_{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="473" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img155.png"
 ALT="$\displaystyle \Dinv{{C_{s}}^{2}} dp
- \frac{\rho}{\theta} d\theta
+ \sum \frac{...
... \frac{\rho}{f} \DP{f}{q_{c}} dq_{c}
+ \sum \frac{\rho}{f} \DP{f}{q_{r}} dq_{r}$"&gt;|; 

$key = q/g_{j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img291.png"
 ALT="$g_{j}$"&gt;|; 

$key = q/displaystyle{c_{p}}_{d}(thetaslashf)dpi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="93" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img170.png"
 ALT="$\displaystyle {c_{p}}_{d} (\theta/f) d\pi$"&gt;|; 

$key = q/overline{rho};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img452.png"
 ALT="$\overline{\rho}$"&gt;|; 

$key = q/{displaymath}rho_{v}=-frac{C_{1}}{r}+C_{2}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="124" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img416.png"
 ALT="\begin{displaymath}
\rho _{v} = -\frac{C_{1}}{r} + C_{2}
\end{displaymath}"&gt;|; 

$key = q/displaystyle+frac{K_{m}}{C_{m}^{2}l^{2}}left(DP[2]{K_{m}^{2}}{x}+DP[2]{K_{m}^{2}left(DP{K_{m}}{x}right)^{2}+left(DP{K_{m}}{z}right)^{2}Biggr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="479" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img367.png"
 ALT="$\displaystyle + \frac{K_{m}}{C_{m}^{2} l^{2}}
\left(\DP[2]{K_{m}^{2}}{x}
+ \DP[...
...Biggl\{\left(\DP{K_{m}}{x}\right)^{2}
+ \left(\DP{K_{m}}{z}\right)^{2}
\Biggr\}$"&gt;|; 

$key = q/displaystyleDD{q_{r}}{t}=Src.q_{r}+Fall.q_{r}+Turb.q_{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="275" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img105.png"
 ALT="$\displaystyle \DD{q_{r}}{t} = Src.q_{r} + Fall.q_{r} + Turb.q_{r}$"&gt;|; 

$key = q/displaystyleDP{}{x_{k}}left[qlambda_{2}left(DP{overline{u^{prime}_{k}theta^{prim}+DP{overline{u^{prime}_{j}theta^{prime}}}{x_{k}}right)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="234" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img321.png"
 ALT="$\displaystyle \DP{}{x_{k}}\left[q\lambda _{2}\left(
\DP{\overline{u^{\prime}_{k...
...}}{x_{j}}
+ \DP{\overline{u^{\prime}_{j}\theta^{\prime} }}{x_{k}}\right)\right]$"&gt;|; 

$key = q/displaystylefrac{p}{R_{d}T_{v}}=frac{p_{0}pi^{{c_{v}}_{d}slashR_{d}}}{R_{d}theta_{v}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="151" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$\displaystyle \frac{p}{R_{d}T_{v} }
=
\frac{p_{0} \pi^{{c_{v}}_{d}/R_{d}}}{R_{d} \theta_{v}}$"&gt;|; 

$key = q/displaystyleDP{q_{r}}{t}=-left(uDP{q_{r}}{x}+wDP{q_{r}}{x}right)+Src.q_{r}+Fall.q_{r}+Turb.q_{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="452" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img254.png"
 ALT="$\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}$"&gt;|; 

$key = q/displaystylerho_{d}=frac{p_{d}}{R_{d}T}=frac{p}{R_{d}T}left(frac{1slashM_{d}}{1slashM_{d}+sumq_{v}slashM_{v}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="320" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img120.png"
 ALT="$\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)$"&gt;|; 

$key = q/Q_{rad};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="$Q_{rad}$"&gt;|; 

$key = q/{}^{3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="12" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img401.png"
 ALT="${}^{3}$"&gt;|; 

$key = q/r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img410.png"
 ALT="$r$"&gt;|; 

$key = q/displaystyle+left(frac{theta^{'}}{bar{theta}}+frac{sumq_{v}^{'}slashM_{v}}{1slas{'}+sumq_{c}^{'}+sumq_{r}^{'}}{1+sumbar{q_{v}}}right)g+Turb.w;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="505" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img222.png"
 ALT="$\displaystyle +
\left(
\frac{\theta^{'}}{\bar{\theta}}
+ \frac{\sum q_{v}^{'}/M...
...'} + \sum q_{c}^{'} + \sum q_{r}^{'}}
{1 + \sum \bar{q_{v}}}
\right) g
+ Turb.w$"&gt;|; 

$key = q/displaystyle-K_{m}left(DP{u_{i}}{x_{j}}+DP{u_{j}}{x_{i}}right)+frac{2}{3}delta_{ij}E,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="242" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img268.png"
 ALT="$\displaystyle - K_{m} \left(\DP{u_{i}}{x_{j}}
+ \DP{u_{j}}{x_{i}}\right)
+ \frac{2}{3} \delta_{ij} E,$"&gt;|; 

$key = q/K_{h}=3K_{m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="92" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img373.png"
 ALT="$K_{h} = 3 K_{m}$"&gt;|; 

$key = q/displaystyle-left(uDP{q_{c}}{x}+wDP{q_{c}}{z}right)+(CN_{vc}-EV_{cv}-CN_{cr}-CL_{cr})+Turb.q_{c},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="520" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$\displaystyle - \left( u \DP{q_{c}}{x} + w \DP{q_{c}}{z} \right)
+ ( CN_{vc} - EV_{cv} - CN_{cr} - CL_{cr}) + Turb.q_{c},$"&gt;|; 

$key = q/displaystyleoverline{pleft(DP{u^{prime}_{i}}{x_{j}}+DP{u^{prime}_{j}}{x_{i}}righnuoverline{DP{u^{prime}_{i}}{x_{k}}DP{u^{prime}_{j}}{x_{k}}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="249" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img281.png"
 ALT="$\displaystyle \overline{p\left(\DP{u^{\prime}_{i}}{x_{j}}
+ \DP{u^{\prime}_{j}}...
...right)}
- 2\nu \overline{\DP{u^{\prime}_{i}}{x_{k}}\DP{u^{\prime}_{j}}{x_{k}}},$"&gt;|; 

$key = q/displaystyleD_{E};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img265.png"
 ALT="$\displaystyle D_{E}$"&gt;|; 

$key = q/displaystylerho=bar{rho}(z)+rho^{'}(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="169" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img187.png"
 ALT="$\displaystyle \rho = \bar{\rho}(z) + \rho^{'}(x,z,t)$"&gt;|; 

$key = q/displaystyle-2overline{u^{prime}_{j}u^{prime}_{k}}DP{u_{j}}{x_{k}}+2g_{j}betaoverline{u^{prime}_{j}theta^{prime}}-2frac{q^{3}}{Lambda_{1}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="248" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img325.png"
 ALT="$\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}}$"&gt;|; 

$key = q/r=infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="58" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img419.png"
 ALT="$r=\infty$"&gt;|; 

$key = q/displaystyleTurb.{theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="60" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="$\displaystyle Turb.{\theta}$"&gt;|; 

$key = q/displaystylefrac{K_{m}}{C_{m}^{2}l^{2}}left(DP[2]{K_{m}^{2}}{x}+DP[2]{K_{m}^{2}}left(DP{K_{m}}{x}right)^{2}+left(DP{K_{m}}{z}right)^{2}Biggr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="464" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img363.png"
 ALT="$\displaystyle \frac{K_{m}}{C_{m}^{2} l^{2}}
\left(\DP[2]{K_{m}^{2}}{x}
+ \DP[2]...
...Biggl\{\left(\DP{K_{m}}{x}\right)^{2}
+ \left(\DP{K_{m}}{z}\right)^{2}
\Biggr\}$"&gt;|; 

$key = q/displaystyleDD{rho}{t}+rholeft(DP{u}{x}+DP{w}{z}right)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="203" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img100.png"
 ALT="$\displaystyle \DD{\rho}{t} + \rho\left( \DP{u}{x} + \DP{w}{z}\right) = 0$"&gt;|; 

$key = q/{c_{v}}_{d}+R_{d}={c_{p}}_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="122" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img148.png"
 ALT="${c_{v}}_{d} + R_{d} = {c_{p}}_{d}$"&gt;|; 

$key = q/i=j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="45" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img285.png"
 ALT="$i=j$"&gt;|; 

$key = q/displaystyledrho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img150.png"
 ALT="$\displaystyle d\rho$"&gt;|; 

$key = q/~^{'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="16" HEIGHT="22" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img248.png"
 ALT="$&amp;nbsp;^{'}$"&gt;|; 

$key = q/{displaymath}left(DD{m}{t}right)_{ev}=-4pir_{d}left(1+frac{Fr}{s}right)K_{d}(rho_{v,s}-rho_{v,infty}){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="354" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img426.png"
 ALT="\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}"&gt;|; 

$key = q/rho=rho(theta,pi,q_{v},q_{x});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="142" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img172.png"
 ALT="$\rho= \rho(\theta, \pi, q_{v}, q_{x})$"&gt;|; 

$key = q/displaystylefrac{R}{c_{p}}ln{(p_{0}slashp)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="96" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img137.png"
 ALT="$\displaystyle \frac{R}{c_{p}} \ln{(p_{0}/p)}$"&gt;|; 

$key = q/displaystyleDP{w^{'}}{t}=-left(u^{'}DP{w^{'}}{x}+w^{'}DP{w^{'}}{z}right)-{c_{p}}}}DP{pi^{'}}{z}+{theta_{v}}^{'}DP{bar{pi}}{z}right)-g+Turb.w.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="614" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img200.png"
 ALT="$\displaystyle \DP{w^{'}}{t} =
- \left(
u^{'} \DP{w^{'}}{x}
+ w^{'} \DP{w^{'}}{z...
...v}} \DP{\pi^{'}}{z}
+ {\theta_{v}}^{'} \DP{\bar{\pi}}{z}
\right)
- g
+ Turb.w .$"&gt;|; 

$key = q/displaystyleN_{0}exp(-lambdaD),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="120" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img383.png"
 ALT="$\displaystyle N_{0}\exp (-\lambda D),$"&gt;|; 

$key = q/EV_{rv};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="45" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$EV_{rv}$"&gt;|; 

$key = q/displaystyleoverline{theta_{v}}+theta_{v}^{'}+frac{sumLq_{v}}{{c_p}_{d}bar{pi}};;;(for;;q_{c}&gt;0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="256" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="$\displaystyle \overline{\theta_{v}} + \theta_{v}^{'} + \frac{ \sum L
q_{v}}{{c_p}_{d} \bar{\pi}}
\;\;\; (for \;\; q_{c} &amp;gt; 0)$"&gt;|; 

$key = q/displaystylefrac{p}{R_{d}T}left(frac{1slashM_{d}}{1slashM_{d}+sumq_{v}slashM_{v}}right)(1+sumq_{v}+sumq_{c}+sumq_{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="434" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img122.png"
 ALT="$\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} )$"&gt;|; 

$key = q/displaystyle-left(uDP{K_{m}}{x}+wDP{K_{m}}{z}right)-frac{3gC_{m}^{2}l^{2}}{2overline{theta}}left(DP{theta}{z}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="323" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img374.png"
 ALT="$\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)$"&gt;|; 

$key = q/displaystyle-left(uDP{q_{v}}{x}+wDP{q_{v}}{z}right)-wDP{bar{q_{v}}}{x}+Src.q_{v}+Turb.q_{v}+Turb.bar{q_{v}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="478" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$\displaystyle - \left( u \DP{q_{v}}{x} + w \DP{q_{v}}{z} \right)
- w\DP{\bar{q_{v}}}{x}
+ Src.q_{v} + Turb.q_{v} + Turb.\bar{q_{v}},$"&gt;|; 

$key = q/displaystyleq_{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img394.png"
 ALT="$\displaystyle q_{r}$"&gt;|; 

$key = q/displaystyleDinv{frac{1slashM_{d}}{1slashM_{d}+sumq_{v}slashM_{v}}(1+sumq_{v}+sumq_{c}+sumq_{r})};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="313" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img210.png"
 ALT="$\displaystyle \Dinv{\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}}
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r})}$"&gt;|; 

$key = q/displaystyle-overline{u^{prime}_{j}u^{prime}_{k}}DP{u_{j}}{x_{k}}-DP{}{x_{k}}overline{pu^{prime}_{j}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="175" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img287.png"
 ALT="$\displaystyle - \overline{u^{\prime}_{j}u^{\prime}_{k}}\DP{u_{j}}{x_{k}}
- \DP{}{x_{k}}\overline{pu^{\prime}_{j}}$"&gt;|; 

$key = q/displaystyle2K_{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};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="384" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img353.png"
 ALT="$\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}$"&gt;|; 

$key = q/displaystylepleft(1-frac{sumrho_{v}R_{v}T}{rho_{d}R_{d}T+sumrho_{v}R_{v}T}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="228" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img118.png"
 ALT="$\displaystyle p \left( 1 - \frac{\sum \rho_{v} R_{v} T}{\rho_{d} R_{d}T + \sum
\rho_{v} R_{v} T }\right)$"&gt;|; 

$key = q/displaystyle-1.7times10^{-4}N_{0}^{0.35}(q_{v,s}-q_{v,infty})(rho_{d}q_{r})^{0.65};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="315" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img435.png"
 ALT="$\displaystyle - 1.7\times 10^{-4}N_{0}^{0.35}(q_{v,s} -q_{v,\infty})
(\rho_{d}q_{r})^{0.65}$"&gt;|; 

$key = q/overline{u^{prime}_{i}u^{prime}_{j}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="38" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img334.png"
 ALT="$\overline{u^{\prime}_{i}u^{\prime}_{j}}$"&gt;|; 

$key = q/displaystyle-K_{h}DP{theta}{x_{j}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="82" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img270.png"
 ALT="$\displaystyle - K_{h}\DP{\theta}{x_{j}}.$"&gt;|; 

$key = q/{c_{v}}_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="28" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img147.png"
 ALT="${c_{v}}_{d}$"&gt;|; 

$key = q/displaystyle-overline{(u_{i}^{prime}u_{j}^{prime})}DP{u_{i}}{x_{j}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="106" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img264.png"
 ALT="$\displaystyle - \overline{(u_{i}^{\prime} u_{j}^{\prime})}
\DP{u_{i}}{x_{j}} ,$"&gt;|; 

$key = q/displaystyleDP{pi^{'}}{t}=-w^{'}DP{bar{pi}}{z}-frac{overline{{C_{s}}^{2}}}{{c_{p}}_{d}(bar{theta}slashbar{f})}DdivDvect{u^{'}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="257" HEIGHT="73" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img236.png"
 ALT="$\displaystyle \DP{\pi^{'}}{t}
=
- w^{'} \DP{\bar{\pi}}{z}
- \frac{\overline{{C_{s}}^{2}} }{ {c_{p}}_{d} (\bar{\theta} /\bar{f})}
\Ddiv \Dvect{u^{'}}$"&gt;|; 

$key = q/displaystyleq_{c}=q_{c}^{'}(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="118" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img190.png"
 ALT="$\displaystyle q_{c} = q_{c}^{'}(x,z,t)$"&gt;|; 

$key = q/displaystyleDP{q_{v}}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="36" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$\displaystyle \DP{q_{v}}{t}$"&gt;|; 

$key = q/displaystyleDinv{f}left{theta^{'}-sumfrac{theta}{f}DP{f}{q_{v}}q_{v}^{'}-sumfrac{q_{c}}q_{c}^{'}-sumfrac{theta}{f}DP{f}{q_{r}}q_{r}^{'}right};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="396" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img206.png"
 ALT="$\displaystyle \Dinv{f}
\left\{
\theta^{'}
- \sum \frac{\theta}{f} \DP{f}{q_{v}}...
...DP{f}{q_{c}} q_{c}^{'}
- \sum \frac{\theta}{f} \DP{f}{q_{r}} q_{r}^{'}
\right\}$"&gt;|; 

$key = q/E=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="54" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img392.png"
 ALT="$E=1$"&gt;|; 

$key = q/pi^{'}slashbar{pi}ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="81" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img235.png"
 ALT="$\pi^{'}/\bar{\pi} \ll 1$"&gt;|; 

$key = q/q_{c};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$q_{c}$"&gt;|; 

$key = q/E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="$E$"&gt;|; 

$key = q/1slashtheta=1slashbar{theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="86" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img224.png"
 ALT="$1/\theta = 1/\bar{\theta}$"&gt;|; 

$key = q/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);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="349" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img366.png"
 ALT="$\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)$"&gt;|; 

$key = q/overline{(theta^{prime})^{2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="40" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img336.png"
 ALT="$\overline{(\theta^{\prime})^{2}}$"&gt;|; 

$key = q/theta_{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="21" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$\theta_{v}$"&gt;|; 

$key = q/alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img130.png"
 ALT="$\alpha$"&gt;|; 

$key = q/R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img132.png"
 ALT="$R$"&gt;|; 

$key = q/overline{u^{prime}_{j}u^{prime}_{k}}simq^{2}delta_{jk}slash3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="124" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img328.png"
 ALT="$\overline{u^{\prime}_{j}u^{\prime}_{k}}\sim q^{2}\delta_{jk}/3$"&gt;|; 

$key = q/{displaymath}EV_{rv}=frac{1}{rho_{d}}int_{0}^{infty}left(DD{m}{t}right)_{ev}N_{D}DdD{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="250" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img406.png"
 ALT="\begin{displaymath}
EV_{rv} = \frac{1}{\rho_{d}}\int _{0}^{\infty}\left(\DD{m}{t}\right)_{ev}
N_{D}\Dd D
\end{displaymath}"&gt;|; 

$key = q/displaystyle-overline{u^{prime}_{j}u^{prime}_{k}}DP{theta}{x_{k}}-overline{thetae})^{2}}-frac{q}{3l_{2}}overline{u^{prime}_{j}theta^{prime}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="353" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img322.png"
 ALT="$\displaystyle - \overline{u^{\prime}_{j}u^{\prime}_{k}}\DP{\theta }{x_{k}}
- \o...
...eta^{\prime})^{2}}
- \frac{q}{3l_{2}}\overline{u^{\prime}_{j}\theta^{\prime} },$"&gt;|; 

$key = q/displaystyleDP{q_{c}}{t}=-left(uDP{q_{c}}{x}+wDP{q_{c}}{x}right)+Src.q_{c}+Turb.q_{c},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="374" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img253.png"
 ALT="$\displaystyle \DP{q_{c}}{t}
=
- \left(
u\DP{q_{c}}{x}
+ w\DP{q_{c}}{x}
\right)
+ Src.q_{c} + Turb.q_{c},$"&gt;|; 

$key = q/displaystyle130D^{0.5}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="72" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img385.png"
 ALT="$\displaystyle 130D^{0.5}.$"&gt;|; 

$key = q/displaystyle-left(uDP{q_{c}}{x}+wDP{q_{c}}{z}right)+Src.q_{c}+Turb.q_{c};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="313" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$\displaystyle - \left( u \DP{q_{c}}{x} + w \DP{q_{c}}{z} \right)
+ Src.q_{c} + Turb.q_{c}$"&gt;|; 

$key = q/displaystyleDD{pi}{t}=frac{{C_{s}}^{2}}{{c_{p}}_{d}rhotheta_{v}}left{-DdivDvect{q_{v}+sumDP{f}{q_{c}}dq_{c}+sumDP{f}{q_{r}}dq_{r}right)right};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="603" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img182.png"
 ALT="$\displaystyle \DD{\pi}{t}
= \frac{{C_{s}}^{2} }{{c_{p}}_{d} \rho \theta_{v} }
\...
...dq_{v}
+ \sum \DP{f}{q_{c}} dq_{c}
+ \sum \DP{f}{q_{r}} dq_{r}
\right)
\right\}$"&gt;|; 

$key = q/p_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img114.png"
 ALT="$p_{d}$"&gt;|; 

$key = q/displaystyle-K_{d}left.DD{rho_{v}}{r}right|_{r=r_{d}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="116" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img423.png"
 ALT="$\displaystyle - K_{d}\left.\DD{\rho_{v}}{r}\right\vert _{r=r_{d}}$"&gt;|; 

$key = q/displaystyleleft[frac{1slashM_{d}}{1slashM_{d}+sumq_{v}slashM_{v}}-left{frac{sum{v}slashM_{v})^{2}}(1+sumq_{v}+sumq_{c}+sumq_{r})right}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="588" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img211.png"
 ALT="$\displaystyle \left[
\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}}
-
\left\{
\frac...
...m q_{v}/M_{v})^{2}}
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r})
\right\}
\right]$"&gt;|; 

$key = q/u_{i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img456.png"
 ALT="$u_{i}$"&gt;|; 

$key = q/displaystyleDP{}{x_{j}}overline{pu^{prime}_{i}}+DP{}{x_{i}}overline{pu^{prime}_{e}_{i}}+varepsilon_{ikl}overline{u_{l}^{prime}u^{prime}_{j}});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="341" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img279.png"
 ALT="$\displaystyle \DP{}{x_{j}}\overline{pu^{\prime}_{i}}
+ \DP{}{x_{i}}\overline{pu...
...me}u^{\prime}_{i}}
+ \varepsilon _{ikl}\overline{u_{l}^{\prime}u^{\prime}_{j}})$"&gt;|; 

$key = q/r_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img411.png"
 ALT="$r_{d}$"&gt;|; 

$key = q/displaystyle{c_{p}}_{d}theta_{v}dpi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="66" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img171.png"
 ALT="$\displaystyle {c_{p}}_{d} \theta_{v} d\pi$"&gt;|; 

$key = q/p_{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img449.png"
 ALT="$p_{0}$"&gt;|; 

$key = q/D_{theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img445.png"
 ALT="$D_{\theta}$"&gt;|; 

$key = q/overline{T};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img454.png"
 ALT="$\overline{T}$"&gt;|; 

$key = q/overline{Pi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="19" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img451.png"
 ALT="$\overline{\Pi}$"&gt;|; 

$key = q/{C_{s}}^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="33" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="${C_{s}}^{2}$"&gt;|; 

$key = q/textstyleapprox;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img230.png"
 ALT="$\textstyle \approx$"&gt;|; 

$key = q/EV_{cv};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="44" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$EV_{cv}$"&gt;|; 

$key = q/displaystyleln{(T_{0}slashT)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="79" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img136.png"
 ALT="$\displaystyle \ln{(T_{0}/T)}$"&gt;|; 

$key = q/displaystylebar{f}={left(1-frac{sumbar{q_{v}}slashM_{v}}{1slashM_{d}+sumbar{q_{v}}slashM_{v}}right)(1+sumbar{q_{v}})};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="332" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img198.png"
 ALT="$\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}} )}$"&gt;|; 

$key = q/displaystyle-2.24times10^{-2}(q_{v,s}-q_{v,infty})int_{0}^{infty}D^{1.6}N_{0}exp(-lambdaD)DdD;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="421" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img432.png"
 ALT="$\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$"&gt;|; 

$key = q/{displaymath}C_{1}=(rho_{v,infty}-rho_{v,s})r_{d},quadC_{2}=rho_{v,infty}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="268" HEIGHT="37" BORDER="0"
 SRC="|."$dir".q|img421.png"
 ALT="\begin{displaymath}
C_{1} = (\rho _{v,\infty}-\rho_{v,s})r_{d},
\quad C_{2} = \rho _{v,\infty}
\end{displaymath}"&gt;|; 

$key = q/displaystyle+Dinv{f}left(frac{p_{0}pi^{c_{vslashR_{d}}}}{R_{d}(thetaslashf)}righ_{v}}dq_{v}+sumDP{f}{q_{c}}dq_{c}+sumDP{f}{q_{r}}dq_{r}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="455" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img178.png"
 ALT="$\displaystyle +
\Dinv{f}
\left(
\frac{p_{0} \pi^{c_{v/R_{d}}} }{R_{d} (\theta /...
...}{q_{v}} dq_{v}
+ \sum \DP{f}{q_{c}} dq_{c}
+ \sum \DP{f}{q_{r}} dq_{r}
\right)$"&gt;|; 

$key = q/displaystyletheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="14" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img138.png"
 ALT="$\displaystyle \theta$"&gt;|; 

$key = q/displaystyleDD{u}{t}+{{c_{p}}_{d}}theta_{v}DP{pi}{x}=Turb.u;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="201" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img158.png"
 ALT="$\displaystyle \DD{u}{t} + {{c_{p}}_{d}} \theta_{v} \DP{\pi}{x} = Turb.u$"&gt;|; 

$key = q/displaystylesumDinv{f}DP{f}{q_{c}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="76" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img213.png"
 ALT="$\displaystyle \sum \Dinv{f}\DP{f}{q_{c}}$"&gt;|; 

$key = q/displaystyleDD{p}{t}={C_{s}}^{2}left(DD{rho}{t}+frac{rho}{theta}DD{theta}{t}-sum{f}DP{f}{q_{c}}dq_{c}-sumfrac{rho}{f}DP{f}{q_{r}}dq_{r}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="557" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img156.png"
 ALT="$\displaystyle \DD{p}{t}
= {C_{s}}^{2}
\left(
\DD{\rho}{t}
+ \frac{\rho}{\theta}...
...rho}{f} \DP{f}{q_{c}} dq_{c}
- \sum \frac{\rho}{f} \DP{f}{q_{r}} dq_{r}
\right)$"&gt;|; 

$key = q/overline{{C_{s}}^{2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="33" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img227.png"
 ALT="$\overline{{C_{s}}^{2}}$"&gt;|; 

$key = q/displaystylepleft(1-frac{sump_{v}}{p}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="116" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img116.png"
 ALT="$\displaystyle p \left( 1 - \frac{\sum p_{v}}{p} \right)$"&gt;|; 

$key = q/(x_{1},x_{3})=(x,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="132" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img459.png"
 ALT="$(x_{1}, x_{3}) = (x, z)$"&gt;|; 

$key = q/displaystyle-left(u^{'}DP{w^{'}}{x}+w^{'}DP{w^{'}}{z}right)-{c_{p}}_{d}bar{theta_{v}}DP{pi^{'}}{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="270" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img221.png"
 ALT="$\displaystyle - \left(
u^{'} \DP{w^{'}}{x}
+ w^{'} \DP{w^{'}}{z}
\right)
- {c_{p}}_{d} \bar{\theta_{v}} \DP{\pi^{'}}{z}$"&gt;|; 

$key = q/displaystyle-left(uDP{q_{c}}{x}+wDP{q_{c}}{z}right)+Src.q_{r}+Fall.q_{r}+Turb.q_{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="395" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$\displaystyle - \left( u \DP{q_{c}}{x} + w \DP{q_{c}}{z} \right)
+ Src.q_{r} + Fall.q_{r} + Turb.q_{r}$"&gt;|; 

$key = q/displaystyleDD{q_{c}}{t}=Src.q_{c}+Turb.q_{c};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="193" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img104.png"
 ALT="$\displaystyle \DD{q_{c}}{t} = Src.q_{c} + Turb.q_{c}$"&gt;|; 

$key = q/theta_{el};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="$\theta_{el}$"&gt;|; 

$key = q/displaystyle-overline{u^{prime}_{j}u^{prime}_{k}}DP{u_{j}}{x_{k}}+g_{j}betaoverl{q^{2}}{x_{k}}right]-frac{2^{3slash2}}{Lambda_{1}}E^{3slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="408" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img341.png"
 ALT="$\displaystyle - \overline{u^{\prime}_{j}u^{\prime}_{k}}\DP{u_{j}}{x_{k}}
+ g_{j...
..._{k}}\left[K_{m} \DP{q^{2}}{x_{k}}\right]
- \frac{2^{3/2}}{\Lambda _{1}}E^{3/2}$"&gt;|; 

$key = q/f_{k}(varepsilon_{jkl}overline{u_{l}^{prime}u^{prime}_{i}}+varepsilon_{ikl}overl}),;f_{k}varepsilon_{jkl}overline{u_{l}^{prime}theta^{prime}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="265" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img311.png"
 ALT="$f_{k}(\varepsilon _{jkl}\overline{u_{l}^{\prime}u^{\prime}_{i}}
+ \varepsilon ...
...me}_{j}}), \;
f_{k}\varepsilon _{jkl}\overline{u_{l}^{\prime}\theta^{\prime} }$"&gt;|; 

$key = q/N_{0}=10^{7};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="79" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img387.png"
 ALT="$N_{0}=10^{7}$"&gt;|; 

$key = q/C=1slash3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="73" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img327.png"
 ALT="$C=1/3$"&gt;|; 

$key = q/displaystyledleft[frac{p_{0}}{R_{d}(thetaslashf)}left(frac{p}{p_{0}}right)^{{c_{v}}_{d}slash{c_{p}}_{d}}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="205" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img152.png"
 ALT="$\displaystyle d \left[
\frac{p_{0}}{R_{d} (\theta / f) }
\left( \frac{p}{p_{0}} \right)^{{c_{v}}_{d}/{c_{p}}_{d}}
\right]$"&gt;|; 

$key = q/displaystyleN_{D};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img382.png"
 ALT="$\displaystyle N_{D}$"&gt;|; 

$key = q/theta_{v}=thetaslashf;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="76" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img191.png"
 ALT="$\theta_{v} = \theta/f$"&gt;|; 

$key = q/{displaymath}Q_{dis}=frac{1}{overline{c_{p}}}frac{C_{varepsilon}}{l}frac{K_{m}^{3}}{(C_{m}l)^{3}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="163" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="\begin{displaymath}
Q_{dis} = \frac{1}{\overline{c_{p}}}\frac{C_{\varepsilon}}{l}
\frac{K_{m}^{3}}{(C_{m}l)^{3}}.
\end{displaymath}"&gt;|; 

$key = q/(dm(D)slashdt)_{cr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="115" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img376.png"
 ALT="$(dm(D)/dt)_{cr}$"&gt;|; 

$key = q/displaystyleDinv{1+sumq_{v}+sumq_{c}+sumq_{r}}-frac{sum1slashM_{v}}{1slashM_{d}+sumq_{v}slashM_{v}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="358" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img212.png"
 ALT="$\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}}$"&gt;|; 

$key = q/displaystylefrac{p}{R_{d}pi(thetaslashf)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="86" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img125.png"
 ALT="$\displaystyle \frac{p}{R_{d} \pi (\theta /f )}$"&gt;|; 

$key = q/displaystyle-frac{g}{overline{theta}}overline{w^{prime}theta^{prime}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="65" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img344.png"
 ALT="$\displaystyle - \frac{g}{\overline{\theta}}
\overline{w^{\prime} \theta^{\prime}}$"&gt;|; 

$key = q/displaystyle-left(uDP{w}{x}+wDP{w}{z}right)-{c_{p}}_{d}bar{theta_{v}}DP{pi}{x}+Turb.w;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="328" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img249.png"
 ALT="$\displaystyle - \left(
u \DP{w}{x}
+ w \DP{w}{z}
\right)
- {c_{p}}_{d} \bar{\theta_{v}} \DP{\pi}{x}
+ Turb.w$"&gt;|; 

$key = q/{theta_{v}}^{'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="26" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img204.png"
 ALT="${\theta_{v}}^{'}$"&gt;|; 

$key = q/displaystyleDP{q_{v}}{t}=-left(uDP{q_{v}}{x}+wDP{q_{v}}{x}right)-wDP{bar{q_{v}}}{x}+Src.q_{v}+Turb.bar{q_{v}}+Turb.q_{v},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="534" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img252.png"
 ALT="$\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},$"&gt;|; 

$key = q/displaystyleDP{q_{r}^{'}}{t}=-left(u^{'}DP{q_{r}^{'}}{x}+w^{'}DP{q_{r}^{'}}{x}right)+Src.q_{r}^{'}+Fall.q_{r}^{'}+Turb.q_{r}^{'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="463" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img247.png"
 ALT="$\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}^{'}$"&gt;|; 

$key = q/displaystyle-Dinv{2l^{2}}K_{m}^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="75" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="$\displaystyle - \Dinv{2 l^{2}} K_{m}^{2}$"&gt;|; 

$key = q/displaystyleDD{p}{t}=rho{C_{s}}^{2}left(-DdivDvect{u}+Dinv{theta}DD{theta}{t}-sumDinv{f}DP{f}{q_{c}}dq_{c}-sumDinv{f}DP{f}{q_{r}}dq_{r}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="586" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img157.png"
 ALT="$\displaystyle \DD{p}{t}
= \rho {C_{s}}^{2}
\left(
- \Ddiv \Dvect{u}
+ \Dinv{\th...
...\sum \Dinv{f} \DP{f}{q_{c}} dq_{c}
- \sum \Dinv{f} \DP{f}{q_{r}} dq_{r}
\right)$"&gt;|; 

$key = q/alphaoverline{u^{prime}_{j}DP{theta^{prime}}{x_{k}}},;nuoverline{theta^{prime}DP{u^{prime}_{j}}{x_{k}}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="127" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img314.png"
 ALT="$\alpha \overline{u^{\prime}_{j}\DP{\theta^{\prime} }{x_{k}}}, \;
\nu \overline{\theta^{\prime} \DP{u^{\prime}_{j}}{x_{k}}}$"&gt;|; 

$key = q/displaystyleDD{overline{u^{prime}_{i}u^{prime}_{j}}}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="53" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img315.png"
 ALT="$\displaystyle \DD{\overline{u^{\prime}_{i}u^{\prime}_{j}}}{t}$"&gt;|; 

$key = q/displaystyle-2.24times10^{-2}(q_{v,s}-q_{v,infty})N_{0}frac{Gamma(2.6)}{lambda^{13slash5}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="287" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img433.png"
 ALT="$\displaystyle - 2.24\times 10^{-2}(q_{v,s} -q_{v,\infty})
N_{0}\frac{\Gamma(2.6)}{\lambda ^{13/5}}$"&gt;|; 

$key = q/Pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img450.png"
 ALT="$\Pi$"&gt;|; 

$key = q/displaystylePR_{r}=Dinv{bar{rho}}DP{}{z}(bar{rho}U_{r}q_{r}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="169" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$\displaystyle PR_{r} = \Dinv{\bar{\rho}} \DP{}{z}(\bar{\rho} U_{r} q_{r}).$"&gt;|; 

$key = q/displaystyleK_{m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="33" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img271.png"
 ALT="$\displaystyle K_{m}$"&gt;|; 

$key = q/displaystyle+left{K_{m}left(DP{w}{x_{j}}+DP{u_{j}}{z}right)-frac{2}{3}delta_{3j}Eright}DP{w}{x_{j}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="304" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img350.png"
 ALT="$\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}}$"&gt;|; 

$key = q/S;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img259.png"
 ALT="$S$"&gt;|; 

$key = q/displaystyle-left(uDP{K_{m}}{x}+wDP{K_{m}}{z}right)-frac{3gC_{m}^{2}l^{2}}{2overline{theta_{v}}}left(DP{theta_{el}}{z}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="333" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="$\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)$"&gt;|; 

$key = q/displaystylefrac{piN_{0}rho_{w}}{6rho_{d}}frac{6}{lambda^{4}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="85" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img397.png"
 ALT="$\displaystyle \frac{\pi N_{0}\rho_{w}}{6\rho_{d}}\frac{6}{\lambda ^{4}}$"&gt;|; 

$key = q/displaystyle0.295times10^{-4}EN_{0}^{0.125}q_{c}(rho_{d}q_{r})^{0.875};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="265" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img403.png"
 ALT="$\displaystyle 0.295 \times 10^{-4}E N_{0}^{0.125}
q_{c}(\rho _{d}q_{r})^{0.875}$"&gt;|; 

$key = q/displaystylepleft(1-frac{sumq_{v}slashM_{v}}{1slashM_{d}+sumq_{v}slashM_{v}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="216" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img119.png"
 ALT="$\displaystyle p \left( 1 - \frac{\sum q_{v}/M_{v}}{1/M_{d} + \sum q_{v}/M_{v}
}\right)$"&gt;|; 

$key = q/displaystyle+Dinv{bar{pi}}left(Q_{rad}+Q_{dis}right)+Turb.bar{theta}+Turb.theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="302" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$\displaystyle + \Dinv{\bar{\pi}} \left(Q_{rad} + Q_{dis}\right)
+ Turb.\bar{\theta}
+ Turb.\theta$"&gt;|; 

$key = q/displaystyleF(r_{d});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="50" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img422.png"
 ALT="$\displaystyle F(r_{d})$"&gt;|; 

$key = q/displaystylefrac{g_{j}}{overline{theta}}overline{u^{prime}_{j}theta^{prime}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="56" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img343.png"
 ALT="$\displaystyle \frac{g_{j}}{\overline{\theta}}
\overline{u^{\prime}_{j} \theta^{\prime}}$"&gt;|; 

$key = q/displaystyleDinv{rho}dp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="37" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img166.png"
 ALT="$\displaystyle \Dinv{\rho} dp$"&gt;|; 

$key = q/displaystylerho_{d}(1+sumq_{v}+sumq_{c}+sumq_{r}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="245" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img112.png"
 ALT="$\displaystyle \rho_{d} (1 + \sum q_{v} + \sum q_{c} + \sum q_{r} ).$"&gt;|; 

$key = q/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}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="374" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img358.png"
 ALT="$\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}}.$"&gt;|; 

$key = q/displaystyledleft[frac{p_{0}}{R_{d}theta_{v}}left(frac{p}{p_{0}}right)^{{c_{v}}_{d}slash{c_{p}}_{d}}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="177" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img151.png"
 ALT="$\displaystyle d \left[
\frac{p_{0}}{R_{d} \theta_{v}}
\left( \frac{p}{p_{0}} \right)^{{c_{v}}_{d}/{c_{p}}_{d}}
\right]$"&gt;|; 

$key = q/displaystyle-w^{'}frac{R_{d}}{{c_{v}}_{d}}bar{pi}Dinv{left(frac{bar{rho}R_{d}(ba}(bar{theta}slashbar{f})}left(DP{u^{'}}{x}+DP{w^{'}}{z}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="467" HEIGHT="73" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img239.png"
 ALT="$\displaystyle - w^{'}
\frac{R_{d}}{{c_{v}}_{d}} \bar{\pi}
\Dinv{\left( \frac{\b...
...c_{p}}_{d} (\bar{\theta}/\bar{f})}
\left( \DP{u^{'}}{x} + \DP{w^{'}}{z} \right)$"&gt;|; 

$key = q/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);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="340" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="$\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)$"&gt;|; 

$key = q/Gamma(2.6)=1.4296245;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="160" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img437.png"
 ALT="$\Gamma(2.6)=1.4296245$"&gt;|; 

$key = q/displaystyleDP{w}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="34" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$\displaystyle \DP{w}{t}$"&gt;|; 

$key = q/displaystyle{C_{s}}^{2}=frac{{c_{p}}_{d}}{{c_{v}}_{d}}R_{d}pitheta_{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="135" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$\displaystyle {C_{s}}^{2}
= \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d} \pi \theta_{v}$"&gt;|; 

$key = q/bar{~};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="11" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$\bar{&amp;nbsp;}$"&gt;|; 

$key = q/lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img393.png"
 ALT="$\lambda$"&gt;|; 

$key = q/displaystyle+frac{p_{0}}{R_{d}theta}left(frac{p}{p_{0}}right)^{{c_{v}}_{d}slash{_{v}}dq_{v}+sumDP{f}{q_{c}}dq_{c}+sumDP{f}{q_{r}}dq_{r}right};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="473" HEIGHT="75" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img154.png"
 ALT="$\displaystyle +
\frac{p_{0}}{R_{d} \theta}
\left( \frac{p}{p_{0}} \right)^{{c_{...
...{q_{v}} dq_{v}
+ \sum \DP{f}{q_{c}} dq_{c}
+ \sum \DP{f}{q_{r}} dq_{r}
\right\}$"&gt;|; 

$key = q/F_{net};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="37" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$F_{net}$"&gt;|; 

$key = q/Deltax,Deltaz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="64" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="$\Delta x, \Delta z$"&gt;|; 

$key = q/displaystyle+left(frac{theta}{bar{theta}}+frac{sumq_{v}slashM_{v}}{1slashM_{d}+s{v}}-frac{sumq_{v}+sumq_{c}+sumq_{r}}{1+sumbar{q_{v}}}right)g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="417" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$\displaystyle + \left(
\frac{\theta}{\bar{\theta}}
+ \frac{\sum q_{v}/M_{v}}{1/...
...
- \frac{\sum q_{v} + \sum q_{c} + \sum q_{r}}
{1 + \sum \bar{q_{v}}}
\right) g$"&gt;|; 

$key = q/displaystylefrac{R_{d}pi(thetaslashf)}{p}dleft(p_{0}pi^{{c_{p}}_{d}slashR_{d}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="191" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img167.png"
 ALT="$\displaystyle \frac{R_{d} \pi (\theta/f)}{p}
d \left(
p_{0} \pi^{{c_{p}}_{d}/R_{d}}
\right)$"&gt;|; 

$key = q/ql_{1}=K_{m},ql_{2}=K_{h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="161" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img338.png"
 ALT="$ql_{1}=K_{m}, ql_{2}=K_{h}$"&gt;|; 

$key = q/displaystyleDP{overline{u^{prime}_{j}theta^{prime}}}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="52" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img282.png"
 ALT="$\displaystyle \DP{\overline{u^{\prime}_{j}\theta^{\prime}}}{t}$"&gt;|; 

$key = q/displaystyleDP{q_{r}}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="36" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$\displaystyle \DP{q_{r}}{t}$"&gt;|; 

$key = q/displaystyle-DP{}{x_{j}}left(K_{h}DP{theta}{x_{j}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="147" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="$\displaystyle - \DP{}{x_{j}} \left(K_{h}\DP{\theta}{x_{j}}\right)
.$"&gt;|; 

$key = q/V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img381.png"
 ALT="$V$"&gt;|; 

$key = q/displaystyletheta_{v}=frac{theta}{left(frac{1slashM_{d}}{1slashM_{d}+sum{{q_{v}}slash{M_{v}}}}right)left(1+sumq_{v}+sumq_{c}+sumq_{r}right)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="382" HEIGHT="80" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$\displaystyle \theta_{v} =
\frac{\theta}{
\left( \frac{1/M_{d}}
{1/M_{d} + \sum...
...v}}/{M_{v}}}} \right)
\left( 1 + \sum q_{v} + \sum q_{c} + \sum q_{r} \right) }$"&gt;|; 

$key = q/displaystyle-DP{}{x_{j}}overline{u_{i}^{prime}theta^{prime}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="82" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="$\displaystyle - \DP{}{x_{j}} \overline{u_{i}^{\prime} \theta^{\prime}}$"&gt;|; 

$key = q/displaystyleDinv{frac{1slashM_{d}}{1slashM_{d}+sumq_{v}slashM_{v}}(1+sumq_{v}+su{d}+sumq_{v}slashM_{v}}(1+sumq_{v}+sumq_{c}+sumq_{r})}{q_{c}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="631" HEIGHT="84" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img214.png"
 ALT="$\displaystyle \Dinv{\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}}
(1 + \sum q_{v} ...
...{1/M_{d} + \sum q_{v}/M_{v}}
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r})}{q_{c}}$"&gt;|; 

$key = q/displaystyleDP{theta}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="29" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$\displaystyle \DP{\theta}{t}$"&gt;|; 

$key = q/displaystylefrac{2}{3}delta_{ij}E-K_{m}left(DP{u_{i}}{x_{j}}+DP{u_{j}}{x_{i}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="222" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img339.png"
 ALT="$\displaystyle \frac{2}{3}\delta _{ij}E
- K_{m}\left(\DP{u_{i}}{x_{j}} + \DP{u_{j}}{x_{i}}\right)$"&gt;|; 

$key = q/displaystyleleft{K_{m}left(DP{u}{x_{j}}+DP{u_{j}}{x}right)-frac{2}{3}delta_{1j}Eright}DP{u}{x_{j}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="287" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img349.png"
 ALT="$\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}}$"&gt;|; 

$key = q/{displaymath}left(DD{m}{t}right)_{ev}=-4pir_{d}K_{d}(rho_{v,s}-rho_{v,infty}){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="264" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img425.png"
 ALT="\begin{displaymath}
\left(\DD{m}{t}\right)_{ev} = - 4\pi r_{d}K_{d}(\rho_{v,s}-\rho_{v,\infty})
\end{displaymath}"&gt;|; 

$key = q/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);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="340" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img370.png"
 ALT="$\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)$"&gt;|; 

$key = q/displaystyleDD{w}{t}+{{c_{p}}_{d}}theta_{v}DP{pi}{z}=-g+Turb.w;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="255" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img159.png"
 ALT="$\displaystyle \DD{w}{t} + {{c_{p}}_{d}} \theta_{v} \DP{\pi}{z} = -g + Turb.w$"&gt;|; 

$key = q/displaystyleDP{w^{'}}{t}=-left(u^{'}DP{w^{'}}{x}+w^{'}DP{w^{'}}{z}right)-{c_{p}}{'}DP{bar{pi}}{z}+{theta_{v}}^{'}DP{pi^{'}}{z}right)-g+Turb.w;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="686" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img199.png"
 ALT="$\displaystyle \DP{w^{'}}{t} =
- \left(
u^{'} \DP{w^{'}}{x}
+ w^{'} \DP{w^{'}}{z...
...}^{'} \DP{\bar{\pi}}{z}
+ {\theta_{v}}^{'} \DP{\pi^{'}}{z}
\right)
- g
+ Turb.w$"&gt;|; 

$key = q/displaystylerho=frac{p}{R_{d}T_{v}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="84" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img101.png"
 ALT="$\displaystyle \rho = \frac{p}{R_{d} T_{v}}$"&gt;|; 

$key = q/displaystyle{c_{p}}_{d}(thetaslashf)left(frac{{c_{v}}_{d}}{{c_{p}}_{d}R_{d}pi(th}pi^{c_{vslashR_{d}}}}{R_{d}(thetaslashf)}frac{dtheta}{theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="445" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img177.png"
 ALT="$\displaystyle {c_{p}}_{d} (\theta/f)
\left( \frac{{c_{v}}_{d}}{{c_{p}}_{d} R_{d...
...d\pi
-
\frac{p_{0} \pi^{c_{v/R_{d}}} }{R_{d} (\theta/f)}
\frac{d\theta}{\theta}$"&gt;|; 

$key = q/displaystyleDP{bar{pi}}{z}=-frac{g}{{c_{p}}_{d}bar{theta_{v}}}=-frac{g}{{c_{p}}_{d}(bar{theta}slashbar{f})};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="227" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img192.png"
 ALT="$\displaystyle \DP{\bar{\pi}}{z}
= - \frac{g}{{c_{p}}_{d} \bar{\theta_{v}}}
= - \frac{g}{{c_{p}}_{d} (\bar{\theta}/\bar{f})}$"&gt;|; 

$key = q/displaystyle+Turb.bar{theta}+Turb.theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="153" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$\displaystyle + Turb.\bar{\theta}
+ Turb.\theta$"&gt;|; 

$key = q/rho_{w};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="25" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img399.png"
 ALT="$\rho_{w}$"&gt;|; 

$key = q/{displaymath}f_{k}varepsilon_{jkl}overline{u_{l}^{prime}u^{prime}_{i}}=f_{k}varelon_{ikl}overline{u_{l}^{prime}u^{prime}_{j}}=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="215" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img312.png"
 ALT="\begin{displaymath}
f_{k}\varepsilon _{jkl}\overline{u_{l}^{\prime}u^{\prime}_{...
...varepsilon _{ikl}\overline{u_{l}^{\prime}u^{\prime}_{j}} = 0,
\end{displaymath}"&gt;|; 

$key = q/(dm(D)slashdt)_{ev};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="116" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img407.png"
 ALT="$(dm(D)/dt)_{ev}$"&gt;|; 

$key = q/displaystyleDD{E}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="34" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img255.png"
 ALT="$\displaystyle \DD{E}{t}$"&gt;|; 

$key = q/displaystyle-frac{C_{varepsilon}}{2C_{m}l^{2}}K_{m}^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="101" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img371.png"
 ALT="$\displaystyle - \frac{C_{\varepsilon}}{2 C_{m} l^{2}} K_{m}^{2}$"&gt;|; 

$key = q/displaystylefrac{{c_{p}}_{d}}{{c_{v}}_{d}}R_{d}left(bar{pi}frac{bar{theta}}{bar{}frac{theta^{'}}{bar{f}}+pi^{'}frac{bar{theta}}{bar{f}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="216" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img231.png"
 ALT="$\displaystyle \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d}
\left(
\bar{\pi} \frac{\bar...
...{\pi} \frac{\theta^{'}}{\bar{f}}
+ \pi^{'} \frac{\bar{\theta}}{\bar{f}}
\right)$"&gt;|; 

$key = q/displaystyleDP{K_{m}}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="49" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="$\displaystyle \DP{K_{m}}{t}$"&gt;|; 

$key = q/M;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="25" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img121.png"
 ALT="$M$"&gt;|; 

$key = q/displaystyleDP{pi^{'}}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="37" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img237.png"
 ALT="$\displaystyle \DP{\pi^{'}}{t}$"&gt;|; 

$key = q/displaystylebar{theta_{v}}left{1+frac{theta}{bar{theta}}+frac{sumq_{v}slashM_{v}_{v}}-frac{sumq_{v}+sumq_{c}+sumq_{r}}{1+sumbar{q_{v}}}right};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="439" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="$\displaystyle \bar{\theta_{v}}
\left\{
1 + \frac{\theta}{\bar{\theta}}
+ \frac{...
...}
- \frac{\sum q_{v} + \sum q_{c} + \sum q_{r}}
{1 + \sum \bar{q_{v}}}
\right\}$"&gt;|; 

$key = q/displaystyle-frac{overline{{C_{s}}^{2}}}{{c_{p}}_{d}bar{rho}(bar{theta}slashbar{2}}Ddivleft{bar{rho}(bar{theta}slashbar{f})Dvect{u^{'}}right};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="227" HEIGHT="73" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img241.png"
 ALT="$\displaystyle - \frac{\overline{{C_{s}}^{2}}}{{c_{p}}_{d} \bar{\rho} (\bar{\the...
...f})^{2}}
\Ddiv \left\{
\bar{\rho} (\bar{\theta}/\bar{f}) \Dvect{u^{'}}
\right\}$"&gt;|; 

$key = q/pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$\pi $"&gt;|; 

$key = q/K_{m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="33" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="$K_{m}$"&gt;|; 

$key = q/c_{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img129.png"
 ALT="$c_{p}$"&gt;|; 

$key = q/displaystyle-left(uDP{K_{m}}{x}+wDP{K_{m}}{z}right)-frac{gC_{m}^{2}l^{2}}{2overline{theta}}frac{K_{h}}{K_{m}}left(DP{theta}{z}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="346" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img369.png"
 ALT="$\displaystyle - \left(
u \DP{K_{m}}{x} + w \DP{K_{m}}{z}
\right)
- \frac{g C_{m...
...} l^{2}}{ 2 \overline{\theta}} \frac{K_{h}}{K_{m}}
\left(\DP{\theta}{z} \right)$"&gt;|; 

$key = q/displaystyleDP{q_{c}}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="35" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$\displaystyle \DP{q_{c}}{t}$"&gt;|; 

$key = q/{displaymath}EV_{rv}=4.85times10^{-2}(q_{v,s}-q_{v,infty})(rho_{d}q_{r})^{0.65}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="325" HEIGHT="37" BORDER="0"
 SRC="|."$dir".q|img438.png"
 ALT="\begin{displaymath}
EV_{rv} = 4.85\times 10^{-2}(q_{v,s} -q_{v,\infty})(\rho_{d}q_{r})^{0.65}
\end{displaymath}"&gt;|; 

$key = q/displaystylefrac{p_{0}}{R_{d}(thetaslashf)}frac{{c_{v}}_{d}}{{c_{p}}_{d}}left(fr}}right)^{{c_{v}}_{d}slash{c_{p}}_{d}}frac{dtheta}{theta^{2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="427" HEIGHT="75" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img153.png"
 ALT="$\displaystyle \frac{p_{0} }{R_{d} (\theta/f)}
\frac{{c_{v}}_{d}}{{c_{p}}_{d}}
\...
...t( \frac{p}{p_{0}} \right)^{{c_{v}}_{d}/{c_{p}}_{d}}
\frac{d\theta}{\theta^{2}}$"&gt;|; 

$key = q/displaystyleDP{pi}{t}=-frac{overline{{C_{s}}^{2}}}{{c_{p}}_{d}bar{rho}bar{theta_{v}}^{2}}DP{}{x_{j}}(bar{rho}bar{theta_{v}}u_{j});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="224" HEIGHT="73" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$\displaystyle \DP{\pi}{t}
= - \frac{\overline{{C_{s}}^{2}}}{{c_{p}}_{d} \bar{\rho} \bar{\theta_{v}}^{2}}
\DP{}{x_{j}}(\bar{\rho} \bar{\theta_{v}} u_{j})$"&gt;|; 

$key = q/F;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img408.png"
 ALT="$F$"&gt;|; 

$key = q/displaystyle32.5piEN_{0}q_{c}frac{3.75}{lambda^{3}}frac{1}{2}sqrt{frac{pi}{lambda}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="183" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img390.png"
 ALT="$\displaystyle 32.5 \pi E N_{0} q_{c} \frac{3.75}{\lambda ^{3}}\frac{1}{2}
\sqrt{\frac{\pi}{\lambda}}$"&gt;|; 

$key = q/displaystyle{theta_{v}}^{'}=frac{bar{theta}}{bar{f}}left{frac{theta^{'}}{bar{theumq_{v}^{'}+sumq_{c}^{'}+sumq_{r}^{'}}{1+sumbar{q_{v}}}right};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="457" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img219.png"
 ALT="$\displaystyle {\theta_{v}}^{'}
= \frac{\bar{\theta}}{\bar{f}}
\left\{
\frac{\th...
...um q_{v}^{'} + \sum q_{c}^{'} + \sum q_{r}^{'}}
{1 + \sum \bar{q_{v}}}
\right\}$"&gt;|; 

$key = q/displaystylefrac{c_{p}}{T}dT-frac{R}{p}dp=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="143" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img133.png"
 ALT="$\displaystyle \frac{c_{p}}{T}dT - \frac{R}{p} dp = 0$"&gt;|; 

$key = q/C_{m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img440.png"
 ALT="$C_{m}$"&gt;|; 

$key = q/displaystyle{theta_{v}}^{'}=Dinv{f}left{frac{theta^{'}}{theta}+frac{sumq_{v}^{'}umq_{c}^{'}+sumq_{r}^{'}}{1+sumq_{v}+sumq_{c}+sumq_{r}}right};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="489" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img218.png"
 ALT="$\displaystyle {\theta_{v}}^{'}
= \Dinv{f}
\left\{
\frac{\theta^{'}}{\theta}
+ \...
...q_{c}^{'} + \sum q_{r}^{'}}
{1 + \sum q_{v} + \sum q_{c} + \sum q_{r}}
\right\}$"&gt;|; 

$key = q/displaystyletheta_{el};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="$\displaystyle \theta_{el}$"&gt;|; 

$key = q/-CN_{vc}+EV_{cv};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="125" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$-CN_{vc} + EV_{cv}$"&gt;|; 

$key = q/displaystylerho=frac{p_{0}pi^{{c_{v}}_{d}slashR_{d}}}{R_{d}theta_{v}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="116" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img161.png"
 ALT="$\displaystyle \rho = \frac{p_{0} \pi^{{c_{v}}_{d}/R_{d}}}{R_{d} \theta_{v}}$"&gt;|; 

$key = q/displaystylefrac{p_{0}}{R_{d}(thetaslashf)}pi^{(c_{vslashR_{d}}-1)}frac{{c_{v}}_rac{p_{0}pi^{c_{vslashR_{d}}}f}{R_{d}}frac{dtheta}{theta^{2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="323" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img175.png"
 ALT="$\displaystyle \frac{p_{0}}{R_{d} (\theta/f) }
\pi^{(c_{v/R_{d}}-1)}
\frac{{c_{v...
..._{d}}
d\pi
-
\frac{p_{0} \pi^{c_{v/R_{d}}} f}{R_{d}}
\frac{d\theta}{\theta^{2}}$"&gt;|; 

$key = q/displaystyle-left(uDP{u}{x}+wDP{u}{z}right)-{c_{p}}_{d}bar{theta_{v}}DP{pi}{x}+Turb.u;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="318" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$\displaystyle - \left( u \DP{u}{x} + w \DP{u}{z} \right)
- {c_{p}}_{d} \bar{\theta_{v}} \DP{\pi}{x}
+ Turb.u$"&gt;|; 

$key = q/displaystyleDD{w}{t}+Dinv{rho}DP{p}{z}=-g+Turb.w;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="227" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img99.png"
 ALT="$\displaystyle \DD{w}{t} + \Dinv{\rho}\DP{p}{z} = -g + Turb.w$"&gt;|; 

$key = q/{displaymath}=frac{2}{3}frac{q^{3}}{Lambda_{1}}delta_{ij}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="80" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img302.png"
 ALT="\begin{displaymath}
= \frac{2}{3}\frac{q^{3}}{\Lambda _{1}}\delta _{ij}.
\end{displaymath}"&gt;|; 

$key = q/displaystyleDD{q_{x}}{t}=Src.q_{c}+Turb.q_{c};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="195" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img162.png"
 ALT="$\displaystyle \DD{q_{x}}{t} = Src.q_{c} + Turb.q_{c}$"&gt;|; 

$key = q/displaystyleleft{2K_{m}left(DP{u}{x}right)-frac{2}{3}Eright}DP{u}{x}+K_{m}left(DP{w}{x}+DP{u}{z}right)DP{u}{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="392" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img351.png"
 ALT="$\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}$"&gt;|; 

$key = q/displaystyleEV_{rv}=4.85times10^{-2}(q_{vsw}-q_{v})(bar{rho}q_{r})^{0.65};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="314" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$\displaystyle EV_{rv} =
4.85 \times 10^{-2} (q_{vsw} - q_{v}) (\bar{\rho} q_{r})^{0.65}$"&gt;|; 

$key = q/x_{i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img444.png"
 ALT="$x_{i}$"&gt;|; 

$key = q/{displaymath}CL_{cr}=frac{1}{rho_{d}}int_{0}^{infty}left(DD{m}{t}right)_{cr}N_{D}DdD{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="250" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img379.png"
 ALT="\begin{displaymath}
CL_{cr} = \frac{1}{\rho_{d}}\int _{0}^{\infty}\left(\DD{m}{t}\right)_{cr}
N_{D}\Dd D
\end{displaymath}"&gt;|; 

$key = q/displaystyleDinv{frac{1slashM_{d}}{1slashM_{d}+sumq_{v}slashM_{v}}(1+sumq_{v}+su{d}+sumq_{v}slashM_{v}}(1+sumq_{v}+sumq_{c}+sumq_{r})}{q_{r}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="631" HEIGHT="84" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img217.png"
 ALT="$\displaystyle \Dinv{\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}}
(1 + \sum q_{v} ...
...{1/M_{d} + \sum q_{v}/M_{v}}
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r})}{q_{r}}$"&gt;|; 

$key = q/displaystylepi=bar{pi}(z)+pi^{'}(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="174" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img185.png"
 ALT="$\displaystyle \pi = \bar{\pi}(z) + \pi^{'}(x,z,t)$"&gt;|; 

$key = q/displaystyleq_{r}=q_{r}^{'}(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="119" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img189.png"
 ALT="$\displaystyle q_{r} = q_{r}^{'}(x,z,t)$"&gt;|; 

$key = q/q_{v},q_{r},q_{c};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="68" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img109.png"
 ALT="$q_{v}, q_{r}, q_{c}$"&gt;|; 

$key = q/displaystyleDP{u^{'}}{t}=-left(u^{'}DP{u^{'}}{x}+w^{'}DP{u^{'}}{z}right)-{c_{p}}}^{'}DP{bar{pi}}{x}+{theta_{v}}^{'}DP{pi^{'}}{x}right)+Turb.u;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="640" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img193.png"
 ALT="$\displaystyle \DP{u^{'}}{t} =
- \left(
u^{'} \DP{u^{'}}{x}
+ w^{'} \DP{u^{'}}{z...
..._{v}}^{'} \DP{\bar{\pi}}{x}
+ {\theta_{v}}^{'} \DP{\pi^{'}}{x}
\right)
+ Turb.u$"&gt;|; 

$key = q/displaystyle-overline{u^{prime}_{j}u^{prime}_{k}}DP{theta}{x_{k}}-overline{thetau)overline{DP{u^{prime}_{j}}{x_{k}}DP{theta^{prime}}{x_{k}}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="491" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img284.png"
 ALT="$\displaystyle -\overline{u^{\prime}_{j}u^{\prime}_{k}}\DP{\theta }{x_{k}}
-\ove...
...lpha + \nu )
\overline{\DP{u^{\prime}_{j}}{x_{k}}\DP{\theta^{\prime} }{x_{k}}}.$"&gt;|; 

$key = q/displaystyleleft{K_{m}left(DP{u_{i}}{x_{j}}+DP{u_{j}}{x_{i}}right)-frac{2}{3}delta_{ij}Eright}DP{u_{i}}{x_{j}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="284" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img348.png"
 ALT="$\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}}$"&gt;|; 

$key = q/displaystyleB;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img261.png"
 ALT="$\displaystyle B$"&gt;|; 

$key = q/lambda_{i}(i=1,2,3);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="112" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img308.png"
 ALT="$\lambda _{i}(i=1,2,3)$"&gt;|; 

$key = q/displaystyle-DP{}{x_{j}}overline{(u_{i}^{prime}u_{j}^{prime})};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="101" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$\displaystyle - \DP{}{x_{j}} \overline{(u_{i}^{\prime} u_{j}^{\prime})}$"&gt;|; 

$key = q/l_{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="18" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img299.png"
 ALT="$l_{2}$"&gt;|; 

$key = q/beta=1slashtheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="69" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img342.png"
 ALT="$\beta = 1/\theta$"&gt;|; 

$key = q/displaystyle-K_{h}DP{theta}{x_{k}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="78" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img340.png"
 ALT="$\displaystyle - K_{h}\DP{\theta }{x_{k}}$"&gt;|; 

$key = q/displaystylefrac{{c_{p}}_{d}rho(thetaslashf)}{{C_{s}}^{2}}dpi-frac{rho}{theta}dt_{v}}dq_{v}+sumDP{f}{q_{c}}dq_{c}+sumDP{f}{q_{r}}dq_{r}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="532" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img179.png"
 ALT="$\displaystyle \frac{ {c_{p}}_{d} \rho (\theta/f)}{{C_{s}}^{2} } d\pi
- \frac{\r...
...}{q_{v}} dq_{v}
+ \sum \DP{f}{q_{c}} dq_{c}
+ \sum \DP{f}{q_{r}} dq_{r}
\right)$"&gt;|; 

$key = q/R_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img106.png"
 ALT="$R_{d}$"&gt;|; 

$key = q/displaystyle-frac{C_{varepsilon}}{C_{m}^{3}{l}^{4}}K_{m}^{3}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="97" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img368.png"
 ALT="$\displaystyle - \frac{C_{\varepsilon}}{C_{m}^{3} {l}^{4}}
K_{m}^{3}.$"&gt;|; 

$key = q/displaystyleu=u^{'}(x,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="114" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img183.png"
 ALT="$\displaystyle u = u^{'}(x,z,t)$"&gt;|; 

$key = q/C_{varepsilon};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img439.png"
 ALT="$C_{\varepsilon}$"&gt;|; 

$key = q/displaystylefrac{130pi}{4}EN_{0}q_{c}int_{0}^{infty}D^{2.5}exp(-lambdaD)DdD;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="288" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img389.png"
 ALT="$\displaystyle \frac{130\pi}{4}E N_{0} q_{c}
\int_{0}^{\infty}D^{2.5}\exp(-\lambda D)\Dd D$"&gt;|; 

$key = q/p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$p$"&gt;|; 

$key = q/displaystylefrac{R}{c_{p}}int^{p_{0}}_{p}Dinv{p}dp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="93" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img135.png"
 ALT="$\displaystyle \frac{R}{c_{p}} \int^{p_{0}}_{p} \Dinv{p} dp$"&gt;|; 

$key = q/displaystyleDinv{frac{1slashM_{d}}{1slashM_{d}+sumq_{v}slashM_{v}}(1+sumq_{v}+su{d}+sumq_{v}slashM_{v}}(1+sumq_{v}+sumq_{c}+sumq_{r})}{q_{v}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="631" HEIGHT="84" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img209.png"
 ALT="$\displaystyle \Dinv{\frac{1/M_{d}}{1/M_{d} + \sum q_{v}/M_{v}}
(1 + \sum q_{v} ...
...{1/M_{d} + \sum q_{v}/M_{v}}
(1 + \sum q_{v} + \sum q_{c} + \sum q_{r})}{q_{v}}$"&gt;|; 

$key = q/bar{c};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img441.png"
 ALT="$\bar{c}$"&gt;|; 

$key = q/displaystyle-left(u^{'}DP{w^{'}}{x}+w^{'}DP{w^{'}}{z}right)-{c_{p}}_{d}bar{theta}}DP{pi^{'}}{z}+frac{{theta_{v}}^{'}}{bar{theta_{v}}}g+Turb.w;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="411" HEIGHT="71" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img203.png"
 ALT="$\displaystyle - \left(
u^{'} \DP{w^{'}}{x}
+ w^{'} \DP{w^{'}}{z}
\right)
- {c_{...
...eta_{v}} \DP{\pi^{'}}{z}
+ \frac{{\theta_{v}}^{'}}{\bar{\theta_{v}}} g
+ Turb.w$"&gt;|; 

$key = q/f;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="16" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img446.png"
 ALT="$f$"&gt;|; 

$key = q/displaystyle-ql_{2}DP{theta}{x_{j}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="75" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img332.png"
 ALT="$\displaystyle - ql_{2}\DP{\theta }{x_{j}}$"&gt;|; 

$key = q/Lambda_{1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img303.png"
 ALT="$\Lambda _{1}$"&gt;|; 

$key = q/displaystyleCN_{cr}=(q_{c}-q_{c0})slashtau_{ac};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="178" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$\displaystyle CN_{cr} = ( q_{c} - q_{c0} ) / \tau _{ac}$"&gt;|; 

$key = q/displaystylethetaequivTleft(frac{p_{0}}{p}right)^{R_{d}slash{c_{p}}_{d}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="146" HEIGHT="75" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img143.png"
 ALT="$\displaystyle \theta \equiv T \left(\frac{p_{0}}{p}\right)^{R_{d}/{c_{p}}_{d}}$"&gt;|; 

$key = q/displaystyle60.9375pi^{frac{5}{8}}rho_{w}^{-frac{7}{8}}EN_{0}^{frac{1}{8}}q_{c}(rho_{d}q_{r})^{frac{7}{8}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="234" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img402.png"
 ALT="$\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}}$"&gt;|; 

$key = q/c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$c$"&gt;|; 

$key = q/displaystyleDP{overline{u^{prime}_{i}u^{prime}_{j}}}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="54" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img276.png"
 ALT="$\displaystyle \DP{\overline{u^{\prime}_{i}u^{\prime}_{j}}}{t}$"&gt;|; 

$key = q/displaystyle60.9375pi^{3slash2}EN_{0}q_{c}lambda^{-3.5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="190" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img391.png"
 ALT="$\displaystyle 60.9375 \pi^{3/2} E N_{0} q_{c} \lambda ^{-3.5}$"&gt;|; 

$key = q/displaystyleDP{}{x_{k}}left[u_{k}overline{theta^{prime}u^{prime}_{j}}+overline{ue}}+varepsilon_{jkl}f_{k}overline{u^{prime}_{l}theta^{prime}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="530" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img283.png"
 ALT="$\displaystyle \DP{}{x_{k}}\left[
u_{k}\overline{\theta^{\prime} u^{\prime}_{j}}...
...a^{\prime} }
+ \varepsilon _{jkl}f_{k}\overline{u^{\prime}_{l}\theta^{\prime} }$"&gt;|; 

$key = q/Fall;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="41" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$Fall$"&gt;|; 

$key = q/x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$x$"&gt;|; 

$key = q/displaystyle-w^{'}DP{}{z}left(frac{bar{rho}R_{d}(bar{theta}slashbar{f})}{p_{0}}r}(bar{theta}slashbar{f})}left(DP{u^{'}}{x}+DP{w^{'}}{z}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="428" HEIGHT="75" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img238.png"
 ALT="$\displaystyle - w^{'} \DP{}{z}
\left( \frac{\bar{\rho} R_{d}(\bar{\theta}/\bar{...
...{p}}_{d} (\bar{\theta}/\bar{f})}
\left( \DP{ u^{'}}{x} + \DP{ w^{'}}{z} \right)$"&gt;|; 

$key = q/pi=Tslashtheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="73" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img127.png"
 ALT="$\pi = T/\theta$"&gt;|; 

$key = q/displaystylefrac{delta_{ij}}{3}q^{2}-ql_{1}left(DP{u_{i}}{x_{j}}+DP{u_{j}}{x_{i}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="208" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img330.png"
 ALT="$\displaystyle \frac{\delta _{ij}}{3}q^{2}
- ql_{1}\left(\DP{u_{i}}{x_{j}} + \DP{u_{j}}{x_{i}}\right)$"&gt;|; 

$key = q/overline{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img448.png"
 ALT="$\overline{p}$"&gt;|; 

$key = q/q^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="21" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img337.png"
 ALT="$q^{2}$"&gt;|; 

$key = q/displaystyledleft[frac{p_{0}pi^{c_{vslashR_{d}}}}{R_{d}theta_{v}}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="104" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img173.png"
 ALT="$\displaystyle d \left[
\frac{p_{0} \pi^{c_{v/R_{d}}}}{R_{d} \theta_{v}}
\right]$"&gt;|; 

$key = q/displaystyleTleft(frac{p_{0}}{p}right)^frac{R}{c_{p}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="84" HEIGHT="79" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img139.png"
 ALT="$\displaystyle T \left(\frac{p_{0}}{p}\right)^\frac{R}{c_{p}}$"&gt;|; 

$key = q/displaystylefrac{{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);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="203" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img232.png"
 ALT="$\displaystyle \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d}
\bar{\pi} \frac{\bar{\theta...
...left(
1 + \frac{\theta^{'}}{\bar{\theta}} + \frac{ \pi^{'} }{\bar{\pi}}
\right)$"&gt;|; 

$key = q/(alpha+nu)overline{DP{u^{prime}_{j}}{x_{k}}DP{theta^{prime}}{x_{k}}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="119" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img304.png"
 ALT="$(\alpha + \nu )
\overline{\DP{u^{\prime}_{j}}{x_{k}}\DP{\theta^{\prime} }{x_{k}}}$"&gt;|; 

$key = q/displaystylerho=frac{p_{0}}{R_{d}theta_{v}}left(frac{p}{p_{0}}right)^{{c_{v}}_{d}slash{c_{p}}_{d}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="178" HEIGHT="75" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img141.png"
 ALT="$\displaystyle \rho = \frac{p_{0}}{R_{d} \theta_{v}}
\left( \frac{p}{p_{0}}\right)^{{c_{v}}_{d}/{c_{p}}_{d}}$"&gt;|; 

$key = q/displaystyleK_{h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="29" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img273.png"
 ALT="$\displaystyle K_{h}$"&gt;|; 

$key = q/displaystyleDP{q^{2}}{t}+u_{k}DP{q^{2}}{x_{k}}+DP{}{x_{k}}left(overline{u^{prime}_{k}u^{prime}_{j}u^{prime}_{j}}-nuDP{q^{2}}{x_{k}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="321" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img286.png"
 ALT="$\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)$"&gt;|; 

$key = q/{displaymath}left(DD{m}{t}right)_{ev}=-4pir_{d}^{2}F(r_{d}){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="186" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img409.png"
 ALT="\begin{displaymath}
\left(\DD{m}{t}\right)_{ev} = - 4\pi r_{d}^{2}F(r_{d})
\end{displaymath}"&gt;|; 

$key = q/displaystylesumDinv{f}DP{f}{q_{r}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="77" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img216.png"
 ALT="$\displaystyle \sum \Dinv{f}\DP{f}{q_{r}}$"&gt;|; 

$key = q/{displaymath}frac{1}{r^{2}}DP{}{r}left(r^{2}Fright)=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="131" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img415.png"
 ALT="\begin{displaymath}
\frac{1}{r^{2}}\DP{}{r}\left(r^{2}F\right) = 0
\end{displaymath}"&gt;|; 

$key = q/displaystyleDP{q_{v}^{'}}{t}=-left(u^{'}DP{q_{v}^{'}}{x}+w^{'}DP{q_{v}^{'}}{x}ri{bar{q_{v}}}{x}+Src.q_{v}^{'}+Turb.bar{q_{v}}+Turb.q_{v}^{'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="550" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img245.png"
 ALT="$\displaystyle \DP{q_{v}^{'}}{t}
=
- \left(
u^{'}\DP{q_{v}^{'}}{x}
+ w^{'}\DP{q_...
...- w^{'}\DP{\bar{q_{v}}}{x}
+ Src.q_{v}^{'} + Turb.\bar{q_{v}} + Turb.q_{v}^{'},$"&gt;|; 

$key = q/Turb;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="46" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img110.png"
 ALT="$Turb$"&gt;|; 

$key = q/displaystyleoverline{u^{prime}_{i}u^{prime}_{j}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="38" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img329.png"
 ALT="$\displaystyle \overline{u^{\prime}_{i}u^{\prime}_{j}}$"&gt;|; 

$key = q/displaystyle-frac{2}{3}Eleft(DP{u}{x}+DP{w}{z}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="155" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img354.png"
 ALT="$\displaystyle - \frac{2}{3} E \left( \DP{u}{x} + \DP{w}{z} \right)$"&gt;|; 

$key = q/displaystylesumDinv{f}DP{f}{q_{v}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="78" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img208.png"
 ALT="$\displaystyle \sum \Dinv{f}\DP{f}{q_{v}}$"&gt;|; 

$key = q/CN_{cr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="47" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$CN_{cr}$"&gt;|; 

$key = q/displaystyleDP{}{z}left(K_{m}DP{E}{z}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="117" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img360.png"
 ALT="$\displaystyle \DP{}{z} \left(K_{m} \DP{E}{z}\right)$"&gt;|; 

$key = q/l=left(DeltaxDeltazright)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="123" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="$l = \left(\Delta x \Delta z \right)^{1/2}$"&gt;|; 

$key = q/displaystylefrac{1}{C_{m}^{2}l^{2}}Biggl{K_{m}DP[2]{K_{m}^{2}}{x}+DP{K_{m}}{x}DP}+K_{m}DP[2]{K_{m}^{2}}{z}+DP{K_{m}}{z}DP{K_{m}^{2}}{z}Biggr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="473" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img362.png"
 ALT="$\displaystyle \frac{1}{C_{m}^{2} l^{2}}
\Biggl\{K_{m} \DP[2]{K_{m}^{2}}{x}
+ \D...
...{2}}{x}
+ K_{m} \DP[2]{K_{m}^{2}}{z}
+ \DP{K_{m}}{z}
\DP{K_{m}^{2}}{z}
\Biggr\}$"&gt;|; 

$key = q/Src;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="34" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$Src$"&gt;|; 

$key = q/displaystyleDD{pi}{t}=frac{{C_{s}}^{2}}{{c_{p}}_{d}rhotheta_{v}}left{-DdivDvect{f}{q_{c}}DD{q_{c}}{t}+sumDP{f}{q_{r}}DD{q_{r}}{t}right)right};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="617" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img160.png"
 ALT="$\displaystyle \DD{\pi}{t}
= \frac{{C_{s}}^{2}}{ {c_{p}}_{d} \rho \theta_{v} }
\...
...\DP{f}{q_{c}} \DD{q_{c}}{t}
+ \sum \DP{f}{q_{r}} \DD{q_{r}}{t}
\right)
\right\}$"&gt;|; 

$key = q/displaystyleDD{theta}{t}=Q+Turb.theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="147" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img142.png"
 ALT="$\displaystyle \DD{\theta}{t} = Q + Turb.\theta$"&gt;|; 

$key = q/displaystylefrac{p}{R_{d}T}left(frac{1slash{M_{d}}}{1slashM_{d}+sum{{q_{v}}slash{M_{v}}}}right)left(1+sumq_{v}+sumq_{c}+sumq_{r}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="440" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$\displaystyle \frac{p}{R_{d}T}
\left(
\frac{1/{M_{d}}}
{1/M_{d} + \sum{{q_{v}}/{M_{v}}}} \right)
\left( 1 + \sum q_{v} + \sum q_{c} + \sum q_{r} \right)$"&gt;|; 

$key = q/q_{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$q_{r}$"&gt;|; 

$key = q/displaystyleDD{pi}{t}=-frac{{C_{s}}^{2}}{{c_{p}}_{d}(thetaslashf)}DdivDvect{u};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="176" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img223.png"
 ALT="$\displaystyle \DD{\pi}{t}
=
- \frac{{C_{s}}^{2}}{ {c_{p}}_{d} (\theta/f)}
\Ddiv \Dvect{u}$"&gt;|; 

$key = q/^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="23" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$^{-1}$"&gt;|; 

$key = q/overline{pu^{prime}_{i}},overline{ptheta^{prime}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="62" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img309.png"
 ALT="$\overline{pu^{\prime}_{i}}, \overline{p\theta^{\prime} }$"&gt;|; 

$key = q/N_{0},lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|&lt;IMG
 WIDTH="46" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img386.png"
 ALT="$N_{0}, \lambda $"&gt;|; 

1;

</pre></body></html>