# LaTeX2HTML 2002-2-1 (1.70)
# Associate images original text with physical files.


$key = q/displaystyleT;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$\displaystyle T$">|; 

$key = q/c_pmathcal{D}(Dvect{v});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img383.png"
 ALT="$c_p \mathcal{D}(\Dvect{v})$">|; 

$key = q/DP{Phi^*}{t}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img122.png"
 ALT="$\DP{\Phi^*}{t}=0$">|; 

$key = q/displaystylefrac{u^2+v^2}{2}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img325.png"
 ALT="$\displaystyle \frac{u^2 + v^2}{2}.$">|; 

$key = q/displaystyle-frac{1}{a}frac{R^dbar{T}_v}{a}frac{partial^2pi}{partiallambdapartiaa(1-mu^2)}DP{}{lambda}left[+frac{R^dT'_v}{a}(1-mu^2)DP{pi}{mu}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="373" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img362.png"
 ALT="$\displaystyle - \frac{1}{a} \frac{R^d \bar{T}_v}{a}
\frac{\partial^2 \pi}{\part...
...^2)} \DP{}{\lambda}
\left[ + \frac{R^d T'_v}{a} (1-\mu^2) \DP{\pi}{\mu} \right]$">|; 

$key = q/displaystylefrac{1}{c_p^drho}left{sigmaDP{p_s}{t}+sigmaDvect{v}_Hcdotnabla_{sigma}p_s+dot{sigma}p_sright};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="237" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img290.png"
 ALT="$\displaystyle \frac{1}{c_p^d \rho} \left\{ \sigma \DP{p_s}{t}
+ \sigma \Dvect{v}_H \cdot \nabla_{\sigma} p_s
+ \dot{\sigma} p_s \right\}$">|; 

$key = q/{displaymath}DD{rho}{t}=-rhoDdivDvect{v},{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img234.png"
 ALT="\begin{displaymath}
\DD{\rho}{t} = - \rho \Ddiv \Dvect{v},
\end{displaymath}">|; 

$key = q/bullet^v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="$\bullet^v$">|; 

$key = q/displaystyle+wbiggl{-frac{1}{rho}DP{p}{r}-g+underbrace{2Omegaucosvarphi}_{(2)}+uerbrace{frac{u^2}{r}}_{(4)}+underbrace{frac{v^2}{r}}_{(5)}+F_rbiggl};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="336" HEIGHT="84" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img227.png"
 ALT="$\displaystyle + w \biggl\{ - \frac{1}{\rho} \DP{p}{r} -g
+ \underbrace{ 2 \Omeg...
...race{ \frac{u^2}{r} }_{(4)}
+ \underbrace{ \frac{v^2}{r} }_{(5)}
+ F_r \biggl\}$">|; 

$key = q/displaystyle(Ddiv{Dvect{v}_H})_{sigma}+DP{dot{sigma}}{sigma}+DP{sigma}{z}left(DD{}{t}DP{z}{sigma}right)_{sigma}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img281.png"
 ALT="$\displaystyle ( \Ddiv{\Dvect{v}_H})_{\sigma} + \DP{\dot{\sigma}}{\sigma}
+ \DP{\sigma}{z}
\left( \DD{}{t} \DP{z}{\sigma} \right)_{\sigma}.$">|; 

$key = q/{displaymath}DdivDvect{A}=frac{1}{r^2cosvarphi}left[rDP{A_{lambda}}{lambda}+rDP{i}(cosvarphiA_{varphi})+cosvarphiDP{}{r}(r^2A_r)right],{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="417" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img195.png"
 ALT="\begin{displaymath}
\Ddiv \Dvect{A}
= \frac{1}{r^2 \cos \varphi}
\left[ r \...
...hi A_{\varphi})
+ \cos \varphi \DP{}{r} ( r^2 A_r )
\right],
\end{displaymath}">|; 

$key = q/{displaymath}Dgradbullet=Dvect{e}_{lambda}frac{1}{rcosvarphi}DP{bullet}{lambda}+i}frac{1}{r}DP{bullet}{varphi}+Dvect{e}_rDP{bullet}{r},{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="266" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img194.png"
 ALT="\begin{displaymath}
\Dgrad \bullet
= \Dvect{e}_{\lambda} \frac{1}{r \cos \varp...
...c{1}{r} \DP{\bullet}{\varphi}
+ \Dvect{e}_r \DP{\bullet}{r},
\end{displaymath}">|; 

$key = q/displaystyleleft(DD{bullet}{t}right)_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img258.png"
 ALT="$\displaystyle \left( \DD{\bullet}{t} \right)_z$">|; 

$key = q/displaystylercosvarphicoslambda,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img184.png"
 ALT="$\displaystyle r \cos \varphi \cos \lambda,$">|; 

$key = q/displaystylefrac{1}{a(1-mu^2)}DP{V}{lambda}-frac{1}{a}DP{U}{mu},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img333.png"
 ALT="$\displaystyle \frac{1}{a ( 1- \mu^2 )} \DP{V}{\lambda}
- \frac{1}{a} \DP{U}{\mu},$">|; 

$key = q/displaystylenabla^{2}_{sigma};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$\displaystyle \nabla^{2}_{\sigma}$">|; 

$key = q/Dvect{v};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img159.png"
 ALT="$\Dvect{v}$">|; 

$key = q/displaystylefrac{1}{rho}left(DD{rho}{t}right)_{sigma}+left(Ddiv{Dvect{v}_H}rightigma}}{sigma}+frac{rho}{p_s}left(DD{}{t}frac{p_s}{rho}right)_{sigma};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="305" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img285.png"
 ALT="$\displaystyle \frac{1}{\rho} \left( \DD{\rho}{t} \right)_{\sigma}
+ \left( \Ddi...
...}}{\sigma}
+ \frac{\rho}{p_s} \left( \DD{}{t} \frac{p_s}{\rho} \right)_{\sigma}$">|; 

$key = q/{displaymath}DdivDvect{A}=frac{1}{h_1h_2h_3}left[DP{}{xi_1}(h_2h_3A_1)+DP{}{xi_2}(h_1h_3A_2)+DP{}{xi_3}(h_1h_2A_3)right],{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="446" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img175.png"
 ALT="\begin{displaymath}
\Ddiv \Dvect{A}
= \frac{1}{h_1 h_2 h_3}
\left[ \DP{}{\x...
...\xi_2} ( h_1 h_3 A_2)
+ \DP{}{\xi_3} ( h_1 h_2 A_3)
\right],
\end{displaymath}">|; 

$key = q/displaystylefrac{u}{acosvarphi}left(frac{partial}{partiallambda}right)_{sigma}+frac{v}{a}left(frac{partial}{partialvarphi}right)_{sigma};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$\displaystyle \frac{u}{a \cos \varphi}
\left( \frac{\partial }{\partial \lambda...
...sigma}
+ \frac{v}{a}
\left( \frac{\partial }{\partial \varphi} \right)_{\sigma}$">|; 

$key = q/displaystylerho^{d}R^dT,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="$\displaystyle \rho^{d} R^d T,$">|; 

$key = q/displaystyleDvect{e}_{lambda}left[DP{A_{lambda}}{t}+frac{u}{rcosvarphi}DP{A_{lamwDP{A_{lambda}}{r}+frac{u}{r}A_r-frac{utanvarphi}{r}A_{varphi}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="452" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img203.png"
 ALT="$\displaystyle \Dvect{e}_{\lambda} \left[
\DP{A_{\lambda}}{t} + \frac{u}{r \cos ...
..._{\lambda}}{r}
+ \frac{u}{r} A_r - \frac{u \tan \varphi}{r} A_{\varphi} \right]$">|; 

$key = q/(Dvect{e}_{lambda},Dvect{e}_{varphi},Dvect{e}_{r});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img190.png"
 ALT="$(\Dvect{e}_{\lambda}, \Dvect{e}_{\varphi},
\Dvect{e}_{r})$">|; 

$key = q/displaystyleDP{zeta}{t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img313.png"
 ALT="$\displaystyle \DP{\zeta}{t}$">|; 

$key = q/u;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img309.png"
 ALT="$u$">|; 

$key = q/T_vequivT(1+epsilon_vq);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img102.png"
 ALT="$T_v \equiv T ( 1 + \epsilon_v q )$">|; 

$key = q/displaystyleDD{u}{t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img209.png"
 ALT="$\displaystyle \DD{u}{t}$">|; 

$key = q/displaystylefrac{1}{acos^2varphi}DP{vcosphi}{lambda}-frac{1}{acosvarphi}DP{}{varphi}(ucosvarphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img332.png"
 ALT="$\displaystyle \frac{1}{a \cos^2 \varphi} \DP{v \cos \phi}{\lambda}
- \frac{1}{a \cos \varphi} \DP{}{\varphi} ( u \cos \varphi)$">|; 

$key = q/displaystyle-frac{1}{a}DP{}{mu}left[frac{R^dbar{T}_v}{a}(1-mu^2)DP{pi}{mu}right]-frac{1}{a}DP{}{mu}left[frac{R^dT'_v}{a}(1-mu^2)DP{pi}{mu}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="387" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img367.png"
 ALT="$\displaystyle - \frac{1}{a} \DP{}{\mu}
\left[ \frac{R^d \bar{T}_v}{a} ( 1-\mu^2...
...ac{1}{a} \DP{}{\mu}
\left[ \frac{R^d T'_v}{a} ( 1-\mu^2 ) \DP{\pi}{\mu} \right]$">|; 

$key = q/r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$r$">|; 

$key = q/displaystyle-frac{1}{rho}Dvect{v}Dgrad{p}-gw-Dvect{v}cdotDvect{F}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img228.png"
 ALT="$\displaystyle - \frac{1}{\rho} \Dvect{v} \Dgrad{p} - g w
- \Dvect{v} \cdot \Dvect{F}.$">|; 

$key = q/Dvect{g}equivDgradPhi^*-Dvect{Omega}times(Dvect{Omega}timesDvect{v});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img165.png"
 ALT="$\Dvect{g} \equiv \Dgrad \Phi^* - \Dvect{\Omega}
\times ( \Dvect{\Omega} \times \Dvect{v})$">|; 

$key = q/(x_1,x_2,x_3);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img182.png"
 ALT="$(x_1, x_2, x_3)$">|; 

$key = q/displaystyle-frac{1}{acosvarphi}DP{}{varphi}left[-cosvarphidot{sigma}DP{u}{sigma{R^dT_v}{ap_s}DP{p_s}{lambda}+F_{lambda}cosvarphi+fvcosvarphiright].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="436" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img316.png"
 ALT="$\displaystyle - \frac{1}{a \cos \varphi} \DP{}{\varphi}
\left[ - \cos \varphi \...
...a p_s} \DP{p_s}{\lambda}
+ F_{\lambda} \cos \varphi + f v \cos \varphi \right].$">|; 

$key = q/displaystyleDP{D}{t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img317.png"
 ALT="$\displaystyle \DP{D}{t}$">|; 

$key = q/displaystylesinvarphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$\displaystyle \sin \varphi$">|; 

$key = q/displaystyleleft(DP{bullet}{lambda}right)_{sigma}+frac{gsigma}{R^dT_v}DP{bullet}{sigma}left(DP{z}{lambda}right)_{sigma},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="208" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img251.png"
 ALT="$\displaystyle \left( \DP{\bullet}{\lambda} \right)_{\sigma}
+ \frac{g \sigma}{R^d T_v} \DP{\bullet}{\sigma}
\left( \DP{z}{\lambda} \right)_{\sigma},$">|; 

$key = q/displaystyle(2Omegacosvarphiw-2Omegasinvarphiv)Dvect{e}_{lambda}+2OmegasinvarphiuDvect{e}_{varphi}-2OmegacosvarphiuDvect{e}_r.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="390" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img208.png"
 ALT="$\displaystyle ( 2 \Omega \cos \varphi w - 2 \Omega \sin \varphi v) \Dvect{e}_{\...
...Omega \sin \varphi u \Dvect{e}_{\varphi}
- 2 \Omega \cos \varphi u \Dvect{e}_r.$">|; 

$key = q/displaystylefrac{dsigma}{dt};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$\displaystyle \frac{d \sigma}{d t}$">|; 

$key = q/displaystyleDrotDvect{A};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img197.png"
 ALT="$\displaystyle \Drot \Dvect{A}$">|; 

$key = q/sim;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="$\sim$">|; 

$key = q/%latex2htmlidmarker4906setcounter{footnote}{2}fnsymbol{footnote};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="6" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="% latex2html id marker 4906
\setcounter{footnote}{2}\fnsymbol{footnote}">|; 

$key = q/{displaymath}Dgradbullet=left(frac{1}{h_1}DP{bullet}{xi_1},frac{1}{h_2}DP{bullet}{xi_2},frac{1}{h_3}DP{bullet}{xi_3}right),{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="231" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img174.png"
 ALT="\begin{displaymath}
\Dgrad \bullet
= \left( \frac{1}{h_1} \DP{\bullet}{\xi_1},...
...{\bullet}{\xi_2},
\frac{1}{h_3} \DP{\bullet}{\xi_3} \right),
\end{displaymath}">|; 

$key = q/displaystylex_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img185.png"
 ALT="$\displaystyle x_2$">|; 

$key = q/q=rho^vslashrho;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img109.png"
 ALT="$q=\rho^v/\rho$">|; 

$key = q/displaystylefrac{uvtanvarphi}{r}+fv-frac{1}{rhorcosvarphi}DP{p}{lambda}+F_{lambda};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="239" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img229.png"
 ALT="$\displaystyle \frac{uv \tan \varphi}{r}
+ fv - \frac{1}{\rho r \cos \varphi} \DP{p}{\lambda}
+ F_{\lambda}$">|; 

$key = q/displaystyle-dot{sigma}frac{partialq}{partialsigma}+S_{q}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img356.png"
 ALT="$\displaystyle - \dot{\sigma} \frac{\partial q }{\partial \sigma}
+ S_{q}.$">|; 

$key = q/displaystylefrac{1}{a^2cos^2varphi}DP[2]{}{lambda}+frac{1}{a^2cosvarphi}DP{}{varphi}(cosvarphiDP{}{varphi}),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="273" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img323.png"
 ALT="$\displaystyle \frac{1}{a^2 \cos^2 \varphi} \DP[2]{}{\lambda}
+ \frac{1}{a^2 \cos \varphi} \DP{}{\varphi} ( \cos
\varphi \DP{}{\varphi} ),$">|; 

$key = q/displaystylefrac{1}{rho}left(DD{rho}{t}right)_z+left(Ddiv{Dvect{v}}right)_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img283.png"
 ALT="$\displaystyle \frac{1}{\rho} \left( \DD{\rho}{t} \right)_z
+ \left( \Ddiv{\Dvect{v}} \right)_z$">|; 

$key = q/displaystylefrac{1}{acos^2varphi}DP{ucosphi}{lambda}+frac{1}{acosvarphi}DP{}{varphi}(vcosvarphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img335.png"
 ALT="$\displaystyle \frac{1}{a \cos^2 \varphi} \DP{u \cos \phi}{\lambda}
+ \frac{1}{a \cos \varphi} \DP{}{\varphi} ( v \cos \varphi)$">|; 

$key = q/Dvect{A};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img146.png"
 ALT="$\Dvect{A}$">|; 

$key = q/displaystyle-nabla^2_{sigma}(Phi+KE).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img321.png"
 ALT="$\displaystyle - \nabla^2_{\sigma} ( \Phi + KE).$">|; 

$key = q/displaystyleDD{}{t}left(frac{1}{2}Dvect{v}^2right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img223.png"
 ALT="$\displaystyle \DD{}{t} \left( \frac{1}{2} \Dvect{v}^2 \right)$">|; 

$key = q/displaystyleleft(DP{bullet}{varphi}right)_{sigma}+frac{gsigma}{R^dT_v}DP{bullet}{sigma}left(DP{z}{varphi}right)_{sigma}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img254.png"
 ALT="$\displaystyle \left( \DP{\bullet}{\varphi} \right)_{\sigma}
+ \frac{g \sigma}{R^d T_v} \DP{\bullet}{\sigma}
\left( \DP{z}{\varphi} \right)_{\sigma}.$">|; 

$key = q/mathcal{D}(D);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img386.png"
 ALT="$\mathcal{D}(D)$">|; 

$key = q/{displaymath}DP{Phi}{sigma}=-frac{R^dT_v}{sigma}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img265.png"
 ALT="\begin{displaymath}
\DP{\Phi}{\sigma}=-\frac{R^d T_v}{\sigma}.
\end{displaymath}">|; 

$key = q/displaystyleleft(DD{Dvect{A}}{t}right)_{{rm{r}+Dvect{Omega}timesDvect{A}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img155.png"
 ALT="$\displaystyle \left( \DD{\Dvect{A}}{t} \right)_{\rm r}
+ \Dvect{\Omega} \times \Dvect{A}.$">|; 

$key = q/displaystyleleft(DD{lnp_s}{t}right)_{sigma}+left(Ddiv{Dvect{v}_H}right)_{sigma}+DP{dot{sigma}}{sigma}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img286.png"
 ALT="$\displaystyle \left( \DD{\ln p_s}{t} \right)_{\sigma}
+ \left( \Ddiv{\Dvect{v}_H} \right)_{\sigma}
+ \DP{\dot{\sigma}}{\sigma}.$">|; 

$key = q/Phi=gz;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img264.png"
 ALT="$\Phi=gz$">|; 

$key = q/{displaymath}dot{sigma}equivfrac{gsigma}{R^dT_v}left{left(DP{z}{t}right)_{sigma}ma}+frac{v}{a}left(DP{z}{varphi}right)_{sigma}-wright}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="405" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img263.png"
 ALT="\begin{displaymath}
\dot{\sigma} \equiv
\frac{g \sigma}{R^d T_v} \left\{
\le...
...ac{v}{a} \left( \DP{z}{\varphi} \right)_{\sigma}
-w \right\}.
\end{displaymath}">|; 

$key = q/{displaymath}frac{1}{rho}left(DP{p}{varphi}right)_z=R^dT_vDP[][sigma]{pi}{varphi}+DP{Phi}{varphi}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img270.png"
 ALT="\begin{displaymath}
\frac{1}{\rho} \left( \DP{p}{\varphi} \right)_z
= R^d T_v \DP[][\sigma]{\pi}{\varphi} + \DP{\Phi}{\varphi}.
\end{displaymath}">|; 

$key = q/displaystyleU;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$\displaystyle U$">|; 

$key = q/{displaymath}frac{partialpi}{partialt}=-int_{0}^{1}Dvect{v}_{H}cdotnabla_{sigma}pidsigma-int_{0}^{1}Ddsigma,{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="\begin{displaymath}
\frac{\partial \pi}{\partial t}
= - \int_{0}^{1} \Dvect{v}...
...cdot \nabla_{\sigma} \pi d \sigma
- \int_{0}^{1} D d \sigma ,
\end{displaymath}">|; 

$key = q/displaystylercosvarphisinlambda,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img186.png"
 ALT="$\displaystyle r \cos \varphi \sin \lambda,$">|; 

$key = q/(r,lambda,phi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$(r,\lambda,\phi)$">|; 

$key = q/p_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$p_s$">|; 

$key = q/{displaymath}DP{rho}{t}+DP{}{x_j}(rhov_j)=0.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img104.png"
 ALT="\begin{displaymath}
\DP{\rho}{t}
+ \DP{}{x_j}( \rho v_j )
= 0.
\end{displaymath}">|; 

$key = q/displaystylembox{{sl{KE};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$\displaystyle \mbox{\sl KE}$">|; 

$key = q/Dvect{v}_aequiv(dDvect{r}slashdt)_{{rm{a};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img158.png"
 ALT="$\Dvect{v}_a \equiv (d\Dvect{r}/dt)_{\rm a}$">|; 

$key = q/{displaymath}dot{sigma}=-sigmafrac{partialpi}{partialt}-int_{0}^{sigma}Ddsigma-int_{0}^{sigma}Dvect{v}_{H}cdotnabla_{sigma}pidsigma.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="284" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img304.png"
 ALT="\begin{displaymath}
\dot{\sigma}
= - \sigma
\frac{\partial \pi}{\partial t}...
...}^{\sigma}
\Dvect{v}_{H} \cdot \nabla_{\sigma} \pi d \sigma.
\end{displaymath}">|; 

$key = q/displaystyleDP{}{t}(rhoPhi^*)+DP{}{x_i}(rhoPhi^*v_i).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img131.png"
 ALT="$\displaystyle \DP{}{t} ( \rho \Phi^* )
+ \DP{}{x_i} ( \rho \Phi^* v_i ).$">|; 

$key = q/displaystylebar{T}(sigma)+T^{prime};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$\displaystyle \bar{T}(\sigma) + T^{\prime}$">|; 

$key = q/displaystylex_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img183.png"
 ALT="$\displaystyle x_1$">|; 

$key = q/displaystylefrac{1}{acosvarphi}DP{v}{lambda}-frac{1}{acosvarphi}DP{}{varphi}(ucosvarphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="228" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img331.png"
 ALT="$\displaystyle \frac{1}{a \cos \varphi} \DP{v}{\lambda}
- \frac{1}{a \cos \varphi} \DP{}{\varphi} ( u \cos \varphi)$">|; 

$key = q/c_p;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="$c_p$">|; 

$key = q/Dvect{v}equiv(dDvect{r}slashdt)_{{rm{r};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img160.png"
 ALT="$\Dvect{v} \equiv (d\Dvect{r}/dt)_{\rm
r}$">|; 

$key = q/{displaymath}frac{partialD}{partialt}=frac{1}{a(1-mu^{2})}frac{partialmbox{{sl{Unabla^{2}_{sigma}(Phi+Rbar{T}pi+mbox{{sl{KE})+{calD}(D){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="436" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="\begin{displaymath}
\frac{\partial D}{\partial t}
= \frac{1}{a(1-\mu^{2})}
\...
...ma}
( \Phi + R \bar{T} \pi + \mbox{\sl KE} )
+ {\cal D}(D)
\end{displaymath}">|; 

$key = q/displaystyleleft(DP{bullet}{lambda}right)_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img249.png"
 ALT="$\displaystyle \left( \DP{\bullet}{\lambda} \right)_z$">|; 

$key = q/epsilon_vequiv1slashepsilon-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img98.png"
 ALT="$\epsilon_v \equiv
1/\epsilon -1$">|; 

$key = q/displaystylev_iDP{}{t}(rhov_i)+v_iDP{}{x_j}(rhov_jv_i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img123.png"
 ALT="$\displaystyle v_i \DP{}{t} ( \rho v_i )
+ v_i \DP{}{x_j} ( \rho v_j v_i )$">|; 

$key = q/{displaymath}DD{Dvect{v}}{t}=sum^3_{k=1}Dvect{e}_kleft[DP{v_k}{t}+sum^3_{j=1}frafrac{v_k}{h_k}frac{1}{h_j}DP{h_k}{xi_j}right)v_jright].{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="473" HEIGHT="64" BORDER="0"
 SRC="|."$dir".q|img179.png"
 ALT="\begin{displaymath}
\DD{\Dvect{v}}{t}
= \sum^3_{k=1} \Dvect{e}_k
\left[ \DP{v...
...{v_k}{h_k} \frac{1}{h_j} \DP{h_k}{\xi_j} \right) v_j
\right].
\end{displaymath}">|; 

$key = q/displaystylefrac{R^dT_v}{p_s}DP{p_s}{lambda}+frac{R^dT_v}{p}frac{gsigma}{R^dT_v}p_sDP[][sigma]{z}{lambda};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="245" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img268.png"
 ALT="$\displaystyle \frac{R^d T_v}{p_s} \DP{p_s}{\lambda}
+ \frac{R^d T_v}{p} \frac{g \sigma}{R^d T_v} p_s \DP[][\sigma]{z}{\lambda}$">|; 

$key = q/RequivR^d(1+epsilon_vq);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img101.png"
 ALT="$R \equiv R^d ( 1+\epsilon_v q )$">|; 

$key = q/u,v,w;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img222.png"
 ALT="$u,
v, w$">|; 

$key = q/^{-4};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img402.png"
 ALT="$^{-4}$">|; 

$key = q/displaystylefrac{1}{c_p^drho}DD{p}{t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img288.png"
 ALT="$\displaystyle \frac{1}{c_p^d \rho} \DD{p}{t}$">|; 

$key = q/{displaystylesigma=frac{p}{p_s}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="${\displaystyle
\sigma= \frac{p}{p_s} }$">|; 

$key = q/varphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img189.png"
 ALT="$\varphi$">|; 

$key = q/delta_v=epsilon_v^{-1}-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img406.png"
 ALT="$\delta_v = \epsilon_v^{-1} - 1$">|; 

$key = q/displaystyle+frac{1}{acosvarphi}left[left(DP{}{varphi}(vcosvarphi)right)_{sigma}da}right]-frac{gsigma}{R^dT_v}DP{}{sigma}left(DD{z}{t}right)_{sigma};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="536" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img276.png"
 ALT="$\displaystyle + \frac{1}{a \cos \varphi}
\left[ \left( \DP{}{\varphi} (v \cos \...
...ght]
- \frac{g \sigma}{R^d T_v} \DP{}{\sigma} \left( \DD{z}{t}
\right)_{\sigma}$">|; 

$key = q/displaystylefrac{1}{a(1-mu^2)}DP{U}{lambda}+frac{1}{a}DP{V}{mu}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img336.png"
 ALT="$\displaystyle \frac{1}{a ( 1-\mu^2)} \DP{U}{\lambda}
+ \frac{1}{a} \DP{V}{\mu}.$">|; 

$key = q/mathcal{D}(zeta);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img385.png"
 ALT="$\mathcal{D}(\zeta)$">|; 

$key = q/displaystylefrac{U^{2}+V^{2}}{2(1-mu^{2})};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$\displaystyle \frac{U^{2}+V^{2}}{2(1-\mu^{2}) }$">|; 

$key = q/displaystylefrac{1}{rho}left(DD{rho}{t}right)_{sigma}+left(Ddiv{Dvect{v}_H}rightot{sigma}}{sigma}+DP{sigma}{z}left(DD{}{t}DP{z}{sigma}right)_{sigma};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="314" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img284.png"
 ALT="$\displaystyle \frac{1}{\rho} \left( \DD{\rho}{t} \right)_{\sigma}
+ \left( \Ddi...
...igma}}{\sigma}
+ \DP{\sigma}{z} \left( \DD{}{t} \DP{z}{\sigma} \right)_{\sigma}$">|; 

$key = q/textstyleDvect{A}=;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img148.png"
 ALT="$\textstyle \Dvect{A} =$">|; 

$key = q/zeta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img330.png"
 ALT="$\zeta$">|; 

$key = q/%latex2htmlidmarker4923setcounter{footnote}{3}fnsymbol{footnote};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="6" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="% latex2html id marker 4923
\setcounter{footnote}{3}\fnsymbol{footnote}">|; 

$key = q/Dvect{g};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img180.png"
 ALT="$\Dvect{g}$">|; 

$key = q/piequivlnp_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img271.png"
 ALT="$\pi \equiv \ln p_s$">|; 

$key = q/q=rho_vslashrho;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="$q=\rho_v/\rho$">|; 

$key = q/displaystyleDD{v}{t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img211.png"
 ALT="$\displaystyle \DD{v}{t}$">|; 

$key = q/v_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img121.png"
 ALT="$v_i$">|; 

$key = q/{displaymath}rhoDD{varepsilon}{t}=frac{p}{rho}left(DD{rho}{t}right)+rhoQ.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img134.png"
 ALT="\begin{displaymath}
\rho \DD{\varepsilon}{t}
= \frac{p}{\rho} \left( \DD{\rho}{t} \right)
+ \rho Q.
\end{displaymath}">|; 

$key = q/Dvect{v}slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img118.png"
 ALT="$\Dvect{v}/2$">|; 

$key = q/displaystyleleft(DP{bullet}{lambda}right)_{sigma}-DP{sigma}{z}DP{bullet}{sigma}left(DP{z}{lambda}right)_{sigma};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img250.png"
 ALT="$\displaystyle \left( \DP{\bullet}{\lambda} \right)_{\sigma}
- \DP{\sigma}{z} \DP{\bullet}{\sigma}
\left( \DP{z}{\lambda} \right)_{\sigma}$">|; 

$key = q/z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$z$">|; 

$key = q/displaystyle-frac{gsigma}{R^dT_v}DP{bullet}{sigma}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img248.png"
 ALT="$\displaystyle - \frac{g \sigma}{R^d T_v} \DP{\bullet}{\sigma}.$">|; 

$key = q/{displaymath}DD{u}{t}=frac{uvtanvarphi}{a}+fv-frac{1}{rhoacosvarphi}DP{p}{lambda}+F_{lambda},{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="281" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img236.png"
 ALT="\begin{displaymath}
\DD{u}{t} = \frac{uv \tan \varphi}{a}
+ fv - \frac{1}{\rho a \cos \varphi} \DP{p}{\lambda}
+ F_{\lambda},
\end{displaymath}">|; 

$key = q/displaystyle-frac{bar{T}}{a(1-mu^{2})}DP{U}{lambda}-frac{1}{a(1-mu^{2})}DP{UT'}{frac{1}{a(1-mu^{2})}DP{U}{lambda}+frac{bar{1}}{a}DP{V}{mu}right]+T'D;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="629" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img372.png"
 ALT="$\displaystyle - \frac{\bar{T}}{a(1-\mu^{2})} \DP{U}{\lambda}
- \frac{1}{a(1-\mu...
...1}{a(1-\mu^{2})} \DP{U}{\lambda}
+ \frac{\bar{1}}{a} \DP{V}{\mu} \right]
+ T' D$">|; 

$key = q/displaystyle-frac{1}{a}DP{}{mu}(zetaV)-frac{1}{a(1-mu^2)}DP{}{lambda}(zetaU);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img345.png"
 ALT="$\displaystyle -\frac{1}{a}\DP{}{\mu} ( \zeta V )
-\frac{1}{a (1-\mu^2)} \DP{}{\lambda} ( \zeta U )$">|; 

$key = q/a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img233.png"
 ALT="$a$">|; 

$key = q/{displaymath}DrotDvect{A}=left(frac{1}{h_2h_3}left[DP{(h_3A_3)}{xi_2}-DP{(h_2A_2left[DP{(h_2A_2)}{xi_1}-DP{(h_1A_1)}{xi_2}right]right),{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="706" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img177.png"
 ALT="\begin{displaymath}
\Drot \Dvect{A}
= \left( \frac{1}{h_2 h_3}
\left[ \DP{(h_...
...DP{(h_2 A_2)}{\xi_1} - \DP{(h_1 A_1)}{\xi_2} \right]
\right),
\end{displaymath}">|; 

$key = q/displaystylefrac{u}{acosphi}DP{bullet}{lambda}+frac{v}{a}DP{bullet}{phi};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img337.png"
 ALT="$\displaystyle \frac{u}{a \cos\phi}\DP{\bullet}{\lambda}
+ \frac{v}{a} \DP{\bullet}{\phi}$">|; 

$key = q/displaystyleDD{w}{t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img213.png"
 ALT="$\displaystyle \DD{w}{t}$">|; 

$key = q/{displaymath}DD{bullet}{t}=DP{bullet}{t}+frac{v_1}{h_1}DP{bullet}{xi_1}+frac{v_2}{h_2}DP{bullet}{xi_2}+frac{v_3}{h_3}DP{bullet}{xi_3},{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img178.png"
 ALT="\begin{displaymath}
\DD{\bullet}{t}
= \DP{\bullet}{t}
+ \frac{v_1}{h_1} \DP{...
...2} \DP{\bullet}{\xi_2}
+ \frac{v_3}{h_3} \DP{\bullet}{\xi_3},
\end{displaymath}">|; 

$key = q/S;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img107.png"
 ALT="$S$">|; 

$key = q/displaystyleqquad+kappaTleft(DP{pi}{t}+Dvect{v}_{H}cdotnabla_{sigma}pi+frac{dot{sigma}}{sigma}right)+frac{Q^*}{C_p^d}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="283" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img381.png"
 ALT="$\displaystyle \qquad
+ \kappa T \left( \DP{\pi}{t}
+ \Dvect{v}_{H} \cdot \nabla_{\sigma} \pi
+ \frac{ \dot{\sigma} }{ \sigma }
\right)
+ \frac{Q^*}{C_p^d}.$">|; 

$key = q/displaystylefrac{1}{acosvarphi}left[DP[][sigma]{u}{lambda}+frac{gsigma}{R^dT_v}DP{u}{sigma}DP[][sigma]{z}{lambda}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img275.png"
 ALT="$\displaystyle \frac{1}{a \cos \varphi}
\left[ \DP[][\sigma]{u}{\lambda}
+ \frac{g \sigma}{R^d T_v} \DP{u}{\sigma}
\DP[][\sigma]{z}{\lambda} \right]$">|; 

$key = q/nabla^{N_D};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$\nabla^{N_D}$">|; 

$key = q/{displaymath}Phi=Phi_s(lambda,varphi){{rm{at}sigma=1.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img294.png"
 ALT="\begin{displaymath}
\Phi = \Phi_s (\lambda, \varphi)     {\rm at}   \sigma=1.
\end{displaymath}">|; 

$key = q/e^*;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img400.png"
 ALT="$e^*$">|; 

$key = q/varepsilon;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img119.png"
 ALT="$\varepsilon$">|; 

$key = q/displaystyle-frac{1}{a(1-mu^2)}DP{}{lambda}left[+frac{R^dT_v}{a}(1-mu^2)DP{pi}{mu}right]-frac{1}{a}DP{}{mu}left[-frac{R^dT_v}{a}DP{pi}{lambda}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="412" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img359.png"
 ALT="$\displaystyle - \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ + \frac{R^d T_v}{a}...
...]
- \frac{1}{a} \DP{}{\mu}
\left[ - \frac{R^d T_v}{a} \DP{\pi}{\lambda} \right]$">|; 

$key = q/{displaymath}DP{q}{t}=-frac{1}{a(1-mu^{2})}DP{Uq}{lambda}-frac{1}{a}DP{Vq}{mu}+qD-dot{sigma}frac{partialq}{partialsigma}+S_{q}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="354" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img382.png"
 ALT="\begin{displaymath}
\DP{q}{t}
= - \frac{1}{a(1-\mu^{2})}
\DP{Uq}{\lambda}
-...
...
- \dot{\sigma} \frac{\partial q }{\partial \sigma}
+ S_{q}.
\end{displaymath}">|; 

$key = q/displaystylefrac{1}{a(1-mu^{2})}frac{partialV}{partiallambda}-frac{1}{a}frac{partialU}{partialmu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$\displaystyle \frac{1}{a ( 1-\mu^{2} ) }
\frac{\partial V}{\partial \lambda}
- \frac{1}{a} \frac{\partial U}{\partial \mu}$">|; 

$key = q/{displaymath}h_lambda=rcosvarphi,h_varphi=r,h_r=1.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="213" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img192.png"
 ALT="\begin{displaymath}
h_\lambda = r \cos \varphi,   h_\varphi = r,   h_r = 1.
\end{displaymath}">|; 

$key = q/{calD}'(Dvect{v});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="${\cal D}' (\Dvect{v})$">|; 

$key = q/displaystylefrac{U}{a(1-mu^{2})}left(frac{partial}{partiallambda}right)_{sigma}+frac{V}{a}left(frac{partial}{partialmu}right)_{sigma};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$\displaystyle \frac{U}{a ( 1 -\mu^{2} )}
\left( \frac{\partial }{\partial \lamb...
...)_{\sigma}
+ \frac{V}{a}
\left( \frac{\partial }{\partial \mu} \right)_{\sigma}$">|; 

$key = q/displaystyle+frac{ucosphi}{acos^2phi}DP{bullet}{lambda}+frac{vcosphi}{acosphi}DP{bullet}{phi};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img341.png"
 ALT="$\displaystyle + \frac{u \cos \phi }{a \cos^2 \phi}\DP{\bullet}{\lambda}
+ \frac{v \cos \phi }{a \cos \phi } \DP{\bullet}{\phi}$">|; 

$key = q/displaystyleDP{T}{t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img351.png"
 ALT="$\displaystyle \DP{T}{t}$">|; 

$key = q/displaystyleD;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$\displaystyle D$">|; 

$key = q/displaystyle-frac{1}{acosvarphi}DP{}{varphi}(zetavcosvarphi)-frac{1}{acosvarphi}DP{}{lambda}(zetau);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="276" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img314.png"
 ALT="$\displaystyle - \frac{1}{a \cos \varphi} \DP{}{\varphi}
( \zeta v \cos \varphi )
- \frac{1}{a \cos \varphi} \DP{}{\lambda}
( \zeta u )$">|; 

$key = q/displaystylembox{{sl{VA};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$\displaystyle \mbox{\sl VA}$">|; 

$key = q/displaystylep^v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="$\displaystyle p^v$">|; 

$key = q/displaystyleubiggl{-frac{1}{rhorcosvarphi}DP{p}{lambda}+underbrace{2vOmegasinvar{uv}{r}tanvarphi}_{(3)}-underbrace{frac{uw}{r}}_{(4)}+F_lambdabiggl};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="455" HEIGHT="84" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img225.png"
 ALT="$\displaystyle u \biggl\{
- \frac{1}{\rho r \cos \varphi } \DP{p}{\lambda}
+ \un...
... \tan \varphi }_{(3)}
- \underbrace{ \frac{u w}{r} }_{(4)}
+ F_\lambda \biggl\}$">|; 

$key = q/{displaymath}DP{}{t}(rhov_i)+DP{}{x_j}(rhov_iv_j)+DP{p}{x_i}-DP{sigma_{ij}}{x_j}+rhoDP{Phi^*}{x_i}=F'_i.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="351" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img111.png"
 ALT="\begin{displaymath}
\DP{}{t}(\rho v_i)
+ \DP{}{x_j}( \rho v_i v_j )
+ \DP{p}{x_i}
- \DP{\sigma_{ij}}{x_j}
+ \rho \DP{\Phi^*}{x_i}
= F'_i.
\end{displaymath}">|; 

$key = q/Q^*;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img135.png"
 ALT="$Q^*$">|; 

$key = q/Phi^*;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img113.png"
 ALT="$\Phi^*$">|; 

$key = q/displaystyleDvect{i}A_x+Dvect{j}A_y+Dvect{k}A_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img149.png"
 ALT="$\displaystyle \Dvect{i} A_x
+ \Dvect{j} A_y
+ \Dvect{k} A_z$">|; 

$key = q/{displaymath}Dequivfrac{1}{acosvarphi}DP{u}{lambda}+frac{1}{acosvarphi}DP{}{varphi}(vcosvarphi).{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img308.png"
 ALT="\begin{displaymath}
D \equiv \frac{1}{a \cos \varphi} \DP{u}{\lambda}
+ \frac{1}{a \cos \varphi} \DP{}{\varphi} ( v \cos \varphi).
\end{displaymath}">|; 

$key = q/displaystyleT_v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$\displaystyle T_v$">|; 

$key = q/muequivsinvarphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img326.png"
 ALT="$\mu \equiv \sin \varphi$">|; 

$key = q/displaystyleleft(DP{bullet}{t}right)_{sigma}+frac{gsigma}{R^dT_v}DP{bullet}{sigma}left(DP{z}{t}right)_{sigma}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img257.png"
 ALT="$\displaystyle \left( \DP{\bullet}{t} \right)_{\sigma}
+ \frac{g \sigma}{R^d T_v} \DP{\bullet}{\sigma}
\left( \DP{z}{t} \right)_{\sigma}.$">|; 

$key = q/{displaymath}frac{partialzeta}{partialt}=frac{1}{a(1-mu^{2})}frac{partialmbox{{s{1}{a}frac{partialmbox{{sl{UA}}{partialmu}+{calD}(zeta){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="\begin{displaymath}
\frac{\partial \zeta}{\partial t}
= \frac{1}{a(1-\mu^{2})...
...frac{\partial \mbox{\sl UA}}{\partial \mu}
+ {\cal D}(\zeta)
\end{displaymath}">|; 

$key = q/pi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img299.png"
 ALT="$\pi$">|; 

$key = q/Vequivcosphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img329.png"
 ALT="$V \equiv \cos \phi$">|; 

$key = q/{displaymath}p=rhoRT.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img100.png"
 ALT="\begin{displaymath}
p = \rho R T.
\end{displaymath}">|; 

$key = q/bullet^d;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="$\bullet^d$">|; 

$key = q/displaystyle-frac{1}{a(1-mu^{2})}DP{UT'}{lambda}-frac{1}{a}DP{VT'}{mu}+T'D.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="256" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img373.png"
 ALT="$\displaystyle - \frac{1}{a(1-\mu^{2})} \DP{UT'}{\lambda}
- \frac{1}{a} \DP{VT'}{\mu}
+ T' D.$">|; 

$key = q/displaystylefrac{1}{a(1-mu^{2})}frac{partialU}{partiallambda}+frac{1}{a}frac{partialV}{partialmu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$\displaystyle \frac{1}{a ( 1-\mu^{2} ) }
\frac{\partial U}{\partial \lambda}
+ \frac{1}{a} \frac{\partial V}{\partial \mu}$">|; 

$key = q/displaystyleleft(DD{bullet}{t}right)_{sigma}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img262.png"
 ALT="$\displaystyle \left( \DD{\bullet}{t} \right)_{\sigma}.$">|; 

$key = q/displaystyle+Dvect{e}_{varphi}frac{1}{rcosvarphi}left[DP{}{r}(rcosvarphiA_{lambda})-DP{A_r}{lambda}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img199.png"
 ALT="$\displaystyle + \Dvect{e}_{\varphi} \frac{1}{r \cos \varphi}
\left[ \DP{}{r} (r \cos \varphi A_{\lambda}) -
\DP{A_r}{\lambda} \right]$">|; 

$key = q/Dvect{A}=Dvect{v}_{{rm{a};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img162.png"
 ALT="$\Dvect{A}=\Dvect{v}_{\rm a}$">|; 

$key = q/displaystyle+frac{1}{2}v_i^2DP{rho}{t}+frac{1}{2}v_i^2DP{}{x_j}(rhov_j);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img126.png"
 ALT="$\displaystyle + \frac{1}{2} v_i^2 \DP{\rho}{t}
+ \frac{1}{2} v_i^2 \DP{}{x_j} ( \rho v_j )$">|; 

$key = q/displaystyle-frac{1}{rhorcosvarphi}DP{p}{lambda}+2Omegavsinvarphi-2Omegawcosvarphi+frac{uv}{r}tanvarphi-frac{uw}{r}+F_lambda,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="431" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img210.png"
 ALT="$\displaystyle - \frac{1}{\rho r \cos \varphi } \DP{p}{\lambda}
+ 2 \Omega v \si...
...\Omega w \cos \varphi
+ \frac{u v}{r} \tan \varphi
- \frac{u w}{r}
+ F_\lambda,$">|; 

$key = q/{displaymath}frac{partialPhi}{partialsigma}=-frac{RT_v}{sigma}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="\begin{displaymath}
\frac{\partial \Phi}{\partial \sigma} = - \frac{RT_v}{\sigma}
\end{displaymath}">|; 

$key = q/displaystyle-frac{1}{a(1-mu^2)}DP{}{lambda}left[frac{R^dT_v}{a}DP{pi}{lambda}right]-frac{1}{a}DP{}{mu}left[frac{R^dT_v}{a}(1-mu^2)DP{pi}{mu}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="387" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img365.png"
 ALT="$\displaystyle - \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ \frac{R^d T_v}{a} \...
...rac{1}{a} \DP{}{\mu}
\left[ \frac{R^d T_v}{a} ( 1-\mu^2 ) \DP{\pi}{\mu} \right]$">|; 

$key = q/c_p=c_v+R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img137.png"
 ALT="$c_p = c_v + R$">|; 

$key = q/%latex2htmlidmarker4819setcounter{footnote}{2}fnsymbol{footnote};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="6" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="% latex2html id marker 4819
\setcounter{footnote}{2}\fnsymbol{footnote}">|; 

$key = q/Dvect{r};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img157.png"
 ALT="$\Dvect{r}$">|; 

$key = q/sigma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$\sigma $">|; 

$key = q/displaystyle-frac{1}{a(1-mu^{2})}DP{Uq}{lambda}-frac{1}{a}DP{Vq}{mu}+qD;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img355.png"
 ALT="$\displaystyle - \frac{1}{a(1-\mu^{2})}
\DP{Uq}{\lambda}
- \frac{1}{a}
\DP{Vq}{\mu}
+ q D$">|; 

$key = q/displaystyleDP{}{t}left(frac{1}{2}rhov_i^2right)+DP{}{x_j}(frac{1}{2}rhov_jv_i^2)+frac{1}{2}v_i^2left{DP{rho}{t}+DP{}{x_j}(rhov_j)right};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="376" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img127.png"
 ALT="$\displaystyle \DP{}{t} \left( \frac{1}{2} \rho v_i^2 \right)
+ \DP{}{x_j} ( \fr...
...2 )
+ \frac{1}{2} v_i^2
\left\{ \DP{\rho}{t} + \DP{}{x_j} ( \rho v_j ) \right\}$">|; 

$key = q/{displaymath}dot{sigma}=0atsigma=0,1.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="\begin{displaymath}
\dot{\sigma} = 0    at   \sigma = 0 ,  1 .
\end{displaymath}">|; 

$key = q/{displaymath}DP{sigma}{z}=-frac{gsigma}{R^dT_v}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img245.png"
 ALT="\begin{displaymath}
\DP{\sigma}{z} = - \frac{g \sigma}{R^d T_v}.
\end{displaymath}">|; 

$key = q/{displaymath}DD{}{t}=DP{}{t}+frac{u}{acosvarphi}DP{}{lambda}+frac{v}{a}DP{}{varphi}+wDP{}{z},{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="263" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img240.png"
 ALT="\begin{displaymath}
\DD{}{t}
= \DP{}{t}
+ \frac{u}{a \cos \varphi} \DP{}{\lambda}
+ \frac{v}{a} \DP{}{\varphi}
+ w \DP{}{z},
\end{displaymath}">|; 

$key = q/displaystyleleft(DP{bullet}{t}right)_z+frac{u}{acosvarphi}left(DP{bullet}{lambdarac{v}{a}left(DP{bullet}{varphi}right)_z+wleft(DP{bullet}{z}right)_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="358" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img259.png"
 ALT="$\displaystyle \left( \DP{\bullet}{t} \right)_z
+ \frac{u}{a \cos \varphi} \left...
...{a} \left( \DP{\bullet}{\varphi} \right)_z
+ w \left( \DP{\bullet}{z} \right)_z$">|; 

$key = q/F_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img116.png"
 ALT="$F_i$">|; 

$key = q/L;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img395.png"
 ALT="$L$">|; 

$key = q/{displaymath}DD{rho}{t}+frac{1}{rcosvarphi}DP{}{lambda}(u)+frac{1}{rcosvarphi}DP{}{varphi}(cosvarphiv)+frac{1}{r^2}DP{}{r}(r^2w)=0.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="410" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img215.png"
 ALT="\begin{displaymath}
\DD{\rho}{t}
+ \frac{1}{r \cos \varphi} \DP{}{\lambda} ( ...
...i} ( \cos \varphi v)
+ \frac{1}{r^2} \DP{}{r} ( r^2 w )
= 0.
\end{displaymath}">|; 

$key = q/{displaymath}DP{zeta}{t}=-frac{1}{a(1-mu^2)}DP{VA}{lambda}-frac{1}{a}DP{UA}{mu},{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img374.png"
 ALT="\begin{displaymath}
\DP{\zeta}{t}
= -\frac{1}{a (1-\mu^2)} \DP{VA}{\lambda}
-\frac{1}{a} \DP{UA}{\mu},
\end{displaymath}">|; 

$key = q/{displaymath}DD{T}{t}=frac{1}{c_p^drho}DD{p}{t}+frac{Q^*}{c_p^d}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img140.png"
 ALT="\begin{displaymath}
\DD{T}{t} = \frac{1}{c_p^d \rho} \DD{p}{t} + \frac{Q^*}{c_p^d}.
\end{displaymath}">|; 

$key = q/%latex2htmlidmarker4922setcounter{footnote}{3}fnsymbol{footnote};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="6" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="% latex2html id marker 4922
\setcounter{footnote}{3}\fnsymbol{footnote}">|; 

$key = q/displaystylePhi^*left{DP{rho}{t}+DP{}{x_i}(rhov_i)right}+rhoDP{Phi^*}{t}+v_irhoDP{Phi^*}{x_i};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="286" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img130.png"
 ALT="$\displaystyle \Phi^* \left\{ \DP{\rho}{t} + \DP{}{x_i}(\rho v_i) \right\}
+ \rho \DP{\Phi^*}{t}
+ v_i \rho \DP{\Phi^*}{x_i}$">|; 

$key = q/sigma=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img297.png"
 ALT="$\sigma=0$">|; 

$key = q/{displaymath}DP{}{t}(rhovarepsilon)+DP{}{x_j}(rhovarepsilonv_j)=-pDP{v_j}{x_j}+sigma_{ij}DP{v_i}{x_j}+rhoQ.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="321" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img133.png"
 ALT="\begin{displaymath}
\DP{}{t} ( \rho \varepsilon )
+ \DP{}{x_j} ( \rho \varepsi...
... )
= - p \DP{v_j}{x_j} + \sigma_{ij} \DP{v_i}{x_j}
+ \rho Q.
\end{displaymath}">|; 

$key = q/u,v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img327.png"
 ALT="$u, v$">|; 

$key = q/displaystyle+vbiggl{-frac{1}{rhor}DP{p}{varphi}-underbrace{2Omegausinvarphi}_{(1u^2}{r}tanvarphi}_{(3)}-underbrace{frac{vw}{r}}_{(5)}+F_varphibiggl};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="344" HEIGHT="84" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img226.png"
 ALT="$\displaystyle + v \biggl\{ - \frac{1}{\rho r} \DP{p}{\varphi}
- \underbrace{ 2 ...
... \tan \varphi }_{(3)}
- \underbrace{ \frac{v w}{r} }_{(5)}
+ F_\varphi \biggl\}$">|; 

$key = q/%latex2htmlidmarker4816setcounter{footnote}{1}fnsymbol{footnote};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="6" HEIGHT="8" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="% latex2html id marker 4816
\setcounter{footnote}{1}\fnsymbol{footnote}">|; 

$key = q/D;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img302.png"
 ALT="$D$">|; 

$key = q/displaystyle-frac{1}{a(1-mu^2)}DP{}{lambda}left[frac{R^dbar{T}_v}{a}DP{pi}{lambdc{1}{a(1-mu^2)}DP{}{lambda}left[frac{R^dT'_v}{a}DP{pi}{lambda}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="385" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img366.png"
 ALT="$\displaystyle - \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ \frac{R^d \bar{T}_v...
...a (1-\mu^2)} \DP{}{\lambda}
\left[ \frac{R^d T'_v}{a} \DP{\pi}{\lambda} \right]$">|; 

$key = q/{displaymath}rhoDD{Dvect{v}}{t}+Dgradp+rhoDgradPhi^*=Dvect{F}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img117.png"
 ALT="\begin{displaymath}
\rho \DD{\Dvect{v}}{t}
+ \Dgrad p
+ \rho \Dgrad \Phi^*
= \Dvect{F}.
\end{displaymath}">|; 

$key = q/displaystyle+frac{U}{a(1-mu^2)}DP{bullet}{lambda}+frac{V}{a}DP{bullet}{mu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img342.png"
 ALT="$\displaystyle + \frac{U}{a (1-\mu^2)} \DP{\bullet}{\lambda}
+ \frac{V}{a} \DP{\bullet}{\mu}$">|; 

$key = q/Q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$Q$">|; 

$key = q/R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="$R$">|; 

$key = q/N_D;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="$N_D$">|; 

$key = q/displaystylemu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$\displaystyle \mu$">|; 

$key = q/displaystyleDvect{i}left(DD{A_x}{t}right)_{{rm{a}+Dvect{j}left(DD{A_y}{t}right)_{{rm{a}+Dvect{k}left(DD{A_z}{t}right)_{{rm{a};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="264" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img152.png"
 ALT="$\displaystyle \Dvect{i} \left( \DD{A_x}{t} \right)_{\rm a}
+ \Dvect{j} \left( \DD{A_y}{t} \right)_{\rm a}
+ \Dvect{k} \left( \DD{A_z}{t} \right)_{\rm a}$">|; 

$key = q/displaystyle-frac{1}{a}DP{}{mu}left[dot{sigma}DP{V}{sigma}+frac{R^dT_v}{a}(1-mu^2)DP{pi}{mu}-F_{varphi}cosvarphi+fUright];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="364" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img350.png"
 ALT="$\displaystyle - \frac{1}{a} \DP{}{\mu}
\left[ \dot{\sigma} \DP{V}{\sigma}
+ \frac{R^d T_v}{a} ( 1-\mu^2 ) \DP{\pi}{\mu}
- F_{\varphi} \cos \varphi + f U \right]$">|; 

$key = q/{calF}_lambda,{calF}_varphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="${\cal F}_\lambda, {\cal F}_\varphi$">|; 

$key = q/^{-2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img392.png"
 ALT="$^{-2}$">|; 

$key = q/(u,v,w);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img191.png"
 ALT="$(u, v, w)$">|; 

$key = q/frac{1}{acosvarphi}DP{}{lambda};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img312.png"
 ALT="$\frac{1}{a \cos \varphi} \DP{}{\lambda}$">|; 

$key = q/{displaymath}DD{T}{t}=frac{R^dT_v}{c_p^d}left{DP{pi}{t}+Dvect{v}_Hcdotnabla_{sigma}pi+frac{dot{sigma}}{sigma}right}+frac{Q^*}{c_p^d}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="297" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img293.png"
 ALT="\begin{displaymath}
\DD{T}{t}
= \frac{R^d T_v}{c_p^d}
\left\{ \DP{\pi}{t}
...
... + \frac{\dot{\sigma}}{\sigma} \right\}
+ \frac{Q^*}{c_p^d}.
\end{displaymath}">|; 

$key = q/displaystyle-frac{1}{acosvarphi}DP{}{lambda}left[dot{sigma}DP{u}{sigma}+frac{R^dT_v}{acosvarphip_s}DP{p_s}{lambda}-F_{lambda}-fvright];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="329" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img319.png"
 ALT="$\displaystyle - \frac{1}{a \cos \varphi} \DP{}{\lambda}
\left[ \dot{\sigma} \DP...
...frac{R^d T_v}{a \cos \varphi p_s} \DP{p_s}{\lambda}
- F_{\lambda} - f v \right]$">|; 

$key = q/displaystyle-frac{1}{a(1-mu^2)}DP{}{lambda}left[+frac{R^dbar{T}_v}{a}(1-mu^2)DP{a(1-mu^2)}DP{}{lambda}left[+frac{R^dT'_v}{a}(1-mu^2)DP{pi}{mu}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="523" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img360.png"
 ALT="$\displaystyle - \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ + \frac{R^d \bar{T}...
...^2)} \DP{}{\lambda}
\left[ + \frac{R^d T'_v}{a} (1-\mu^2) \DP{\pi}{\mu} \right]$">|; 

$key = q/sigma_{ij};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img112.png"
 ALT="$\sigma_{ij}$">|; 

$key = q/{displaymath}DD{q}{t}=S_q.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img110.png"
 ALT="\begin{displaymath}
\DD{q}{t} = S_q.
\end{displaymath}">|; 

$key = q/displaystyleTleft(pslashp_{0}right)^{-kappa};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$\displaystyle T \left( p/p_{0} \right)^{- \kappa}$">|; 

$key = q/displaystyleDP{}{t}left(frac{1}{2}rhov_i^2right)+DP{}{x_j}(frac{1}{2}rhov_jv_i^2).;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img128.png"
 ALT="$\displaystyle \DP{}{t} \left( \frac{1}{2} \rho v_i^2 \right)
+ \DP{}{x_j} ( \frac{1}{2} \rho v_j v_i^2 ).$">|; 

$key = q/displaystylefrac{1}{a(1-mu^2)}DP{}{lambda}(Ubullet)-frac{bullet}{a(1-mu^2)}DP{U}{lambda}+frac{1}{amu}DP{}{phi}(Vbullet)-frac{bullet}{a}DP{V}{mu};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="400" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img339.png"
 ALT="$\displaystyle \frac{1}{a (1-\mu^2)} \DP{}{\lambda} (U\bullet)
-\frac{\bullet}{a...
...\lambda}
+\frac{1}{a \mu} \DP{}{\phi} (V\bullet)
-\frac{\bullet}{a} \DP{V}{\mu}$">|; 

$key = q/{displaymath}nabla^2bullet=frac{1}{r^2cosvarphi}left[DP{}{lambda}left(frac{1}{coght)+DP{}{r}left(r^2cosvarphiDP{bullet}{r}right)right],{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="511" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img196.png"
 ALT="\begin{displaymath}
\nabla^2 \bullet
= \frac{1}{r^2 \cos \varphi}
\left[ \D...
...}{r} \left( r^2 \cos \varphi \DP{\bullet}{r} \right)
\right],
\end{displaymath}">|; 

$key = q/{displaymath}Ddiv{Dvect{v}}equivfrac{1}{acosvarphi}DP{u}{lambda}+frac{1}{acosvarphi}DP{v}{varphi}(vcosvarphi)+DP{w}{z}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="319" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img241.png"
 ALT="\begin{displaymath}
\Ddiv{\Dvect{v}}
\equiv \frac{1}{a \cos \varphi} \DP{u}{\l...
...cos \varphi} \DP{v}{\varphi}
( v \cos \varphi )
+ \DP{w}{z}.
\end{displaymath}">|; 

$key = q/displaystyle-(zeta+f)U-dot{sigma}frac{partialV}{partialsigma}-frac{RT^{prime}}{a}(1-mu^{2})frac{partialpi}{partialmu}+{calF}_{varphi}cosvarphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="340" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$\displaystyle - ( \zeta + f ) U
- \dot{\sigma} \frac{\partial V}{\partial \sigm...
...- \mu^{2} )
\frac{\partial \pi}{\partial \mu}
+ {\cal F}_{\varphi} \cos \varphi$">|; 

$key = q/displaystyleDD{Dvect{A}}{t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img202.png"
 ALT="$\displaystyle \DD{\Dvect{A}}{t}$">|; 

$key = q/p;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$p$">|; 

$key = q/{displaymath}DP{pi}{t}+Dvect{v}_HcdotDgrad_{sigma}pi=-Dgrad_{sigma}cdotDvect{v}_H-DP{dot{sigma}}{sigma}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="240" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img344.png"
 ALT="\begin{displaymath}
\DP{\pi}{t} + \Dvect{v}_H \cdot \Dgrad_{\sigma} \pi
= -\Dgrad_{\sigma} \cdot \Dvect{v}_H - \DP{\dot{\sigma}}{\sigma}.
\end{displaymath}">|; 

$key = q/displaystyleDvect{v}_HcdotDgrad_{sigma}bullet.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img343.png"
 ALT="$\displaystyle \Dvect{v}_H \cdot \Dgrad_{\sigma} \bullet.$">|; 

$key = q/displaystylelnp_{S};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$\displaystyle \ln p_{S}$">|; 

$key = q/mathcal{D}(T);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img387.png"
 ALT="$\mathcal{D}(T)$">|; 

$key = q/(xi_1,xi_2,xi_3)=(lambda,varphi,r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img181.png"
 ALT="$(\xi_1, \xi_2, \xi_3) = (\lambda, \varphi, r)$">|; 

$key = q/displaystylepi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$\displaystyle \pi$">|; 

$key = q/textstyle=;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$\textstyle =$">|; 

$key = q/displaystylerho^{v}R^vT,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="$\displaystyle \rho^{v} R^v T,$">|; 

$key = q/%latex2htmlidmarker5025setcounter{footnote}{8}fnsymbol{footnote};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img141.png"
 ALT="% latex2html id marker 5025
\setcounter{footnote}{8}\fnsymbol{footnote}">|; 

$key = q/{displaymath}frac{partialpi}{partialt}+Dvect{v}_{H}cdotnabla_{sigma}pi=-nabla_{s}cdotDvect{v}_{H}-frac{partialdot{sigma}}{partialsigma}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="\begin{displaymath}
\frac{\partial \pi}{\partial t}
+ \Dvect{v}_{H} \cdot \na...
...Dvect{v}_{H}
- \frac{\partial \dot{\sigma}}{\partial \sigma}
\end{displaymath}">|; 

$key = q/displaystylefrac{1}{acos^2phi}left{DP{}{lambda}(ucosphibullet)-bulletDP{}{lambdaacosphi}left{DP{}{phi}(vcosphibullet)-bulletDP{}{phi}(vcosphi)right};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="555" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img338.png"
 ALT="$\displaystyle \frac{1}{a \cos^2 \phi}
\left\{ \DP{}{\lambda} (u \cos \phi \bull...
...DP{}{\phi} (v \cos \phi \bullet)
- \bullet \DP{}{\phi} ( v \cos \phi ) \right\}$">|; 

$key = q/{displaymath}DD{pi}{t}+Ddiv{Dvect{v}_H}+DP{dot{sigma}}{sigma}=0.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img287.png"
 ALT="\begin{displaymath}
\DD{\pi}{t}
+ \Ddiv{\Dvect{v}_H}
+ \DP{\dot{\sigma}}{\sigma}
= 0.
\end{displaymath}">|; 

$key = q/displaystyle-frac{gsigma}{R^dT_v}DP{}{sigma}left[DP[][sigma]{z}{t}+frac{u}{acosvambda}+frac{v}{a}DP[][sigma]{z}{varphi}+dot{sigma}DP{z}{sigma}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="420" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img278.png"
 ALT="$\displaystyle - \frac{g \sigma}{R^d T_v} \DP{}{\sigma} \left[
\DP[][\sigma]{z}{...
...}
+ \frac{v}{a} \DP[][\sigma]{z}{\varphi}
+ \dot{\sigma} \DP{z}{\sigma}
\right]$">|; 

$key = q/displaystyleleft(DdivDvect{v}right)_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img274.png"
 ALT="$\displaystyle \left( \Ddiv \Dvect{v} \right)_z$">|; 

$key = q/d_{H_2O};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img398.png"
 ALT="$d_{H_2O}$">|; 

$key = q/displaystyleVA;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img378.png"
 ALT="$\displaystyle VA$">|; 

$key = q/{displaymath}frac{partialpi}{partialt}=-int_{0}^{1}Dvect{v}_{H}cdotnabla_{sigma}pidsigma-int_{0}^{1}Ddsigma.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="244" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img300.png"
 ALT="\begin{displaymath}
\frac{\partial \pi}{\partial t}
= - \int_{0}^{1} \Dvect{v}...
...\cdot \nabla_{\sigma} \pi d \sigma
- \int_{0}^{1} D d \sigma.
\end{displaymath}">|; 

$key = q/displaystyle-frac{1}{a(1-mu^{2})}DP{Ubar{T}}{lambda}-frac{1}{a(1-mu^{2})}DP{UT'}{lambda}-frac{1}{a}DP{Vbar{T}}{mu}-frac{1}{a}DP{VT'}{mu}+bar{T}D+T'D;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="492" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img371.png"
 ALT="$\displaystyle - \frac{1}{a(1-\mu^{2})} \DP{U \bar{T}}{\lambda}
- \frac{1}{a(1-\...
... \frac{1}{a} \DP{V \bar{T}}{\mu}
- \frac{1}{a} \DP{VT'}{\mu}
+ \bar{T} D
+ T' D$">|; 

$key = q/displaystyle-dot{sigma}DP{T}{sigma}+kappaTleft(DP{pi}{t}+Dvect{v}_{H}cdotnabla_{sigma}pi+frac{dot{sigma}}{sigma}right)+frac{Q^*}{C_{p}}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="306" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img353.png"
 ALT="$\displaystyle - \dot{\sigma}
\DP{T}{\sigma}
+ \kappa T \left( \DP{\pi}{t}
+ \Dv...
...bla_{\sigma} \pi
+ \frac{ \dot{\sigma} }{ \sigma }
\right)
+ \frac{Q^*}{C_{p}}.$">|; 

$key = q/{displaymath}DD{Dvect{v}_a}{t}=DD{Dvect{v}}{t}+2Dvect{Omega}timesDvect{v}+Dvect{Omega}times(Dvect{Omega}timesDvect{r}),{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="252" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img163.png"
 ALT="\begin{displaymath}
\DD{\Dvect{v}_a}{t}
= \DD{\Dvect{v}}{t} + 2 \Dvect{\Omega}...
...
+ \Dvect{\Omega} \times ( \Dvect{\Omega} \times \Dvect{r} ),
\end{displaymath}">|; 

$key = q/{displaymath}DD{}{t}=DP{}{t}+frac{u}{rcosphi}DP{}{lambda}+frac{v}{r}DP{}{phi}+wDP{}{r},{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img217.png"
 ALT="\begin{displaymath}
\DD{}{t}
= \DP{}{t}
+ \frac{u}{r \cos \phi} \DP{}{\lambda}
+ \frac{v}{r} \DP{}{\phi}
+ w \DP{}{r},
\end{displaymath}">|; 

$key = q/displaystyle-Dgrad^2_{sigma}(R^dbar{T}_vpi)-frac{1}{a(1-mu^2)}DP{}{lambda}left[fht]-frac{1}{a}DP{}{mu}left[frac{R^dT'_v}{a}(1-mu^2)DP{pi}{mu}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="493" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img370.png"
 ALT="$\displaystyle - \Dgrad^2_{\sigma} ( R^d \bar{T}_v \pi )
- \frac{1}{a (1-\mu^2)}...
...c{1}{a} \DP{}{\mu}
\left[ \frac{R^d T'_v}{a} ( 1-\mu^2 ) \DP{\pi}{\mu} \right].$">|; 

$key = q/displaystyle(zeta+f)V-dot{sigma}DP{U}{sigma}-frac{RT'}{a}DP{pi}{lambda}+F_{lambda}cosvarphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="272" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img377.png"
 ALT="$\displaystyle ( \zeta + f ) V
- \dot{\sigma} \DP{U}{\sigma}
- \frac{RT'}{a}
\DP{\pi}{\lambda}
+ F_{\lambda} \cos \varphi$">|; 

$key = q/displaystyleuDD{u}{t}+vDD{v}{t}+wDD{w}{t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img224.png"
 ALT="$\displaystyle u \DD{u}{t} + v \DD{v}{t} + w \DD{w}{t}$">|; 

$key = q/{displaymath}{calD}(D)=-K_{HD}left[(-1)^{N_Dslash2}nabla^{N_D}-left(frac{2}{a^2}right)^{N_Dslash2}right]D,{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="347" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="\begin{displaymath}
{\cal D}(D) = - K_{HD}
\left[ (-1)^{N_D/2} \nabla^{N_D}
- \left( \frac{2}{a^2} \right)^{N_D/2}
\right]
D ,
\end{displaymath}">|; 

$key = q/{displaymath}DD{Dvect{v}}{t}=-frac{1}{rho}Dgradp-2Dvect{Omega}timesDvect{v}-Dveca}times(Dvect{Omega}timesDvect{r})+DgradPhi^*+Dvect{F}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="350" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img164.png"
 ALT="\begin{displaymath}
\DD{\Dvect{v}}{t}
= - \frac{1}{\rho} \Dgrad p
- 2 \Dvect...
...vect{\Omega} \times \Dvect{r} )
+ \Dgrad \Phi^* + \Dvect{F}.
\end{displaymath}">|; 

$key = q/h_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img172.png"
 ALT="$h_i$">|; 

$key = q/displaystylefrac{1}{a^{2}(1-mu^{2})}frac{partial^{2}}{partiallambda^{2}}+frac{1}ac{partial}{partialmu}left[(1-mu^{2})frac{partial}{partialmu}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="277" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$\displaystyle \frac{1}{a^{2}(1-\mu^{2})}
\frac{\partial^{2} }{\partial \lambda^...
...ial }{\partial \mu}
\left[ (1-\mu^{2})
\frac{\partial }{\partial \mu} \right] .$">|; 

$key = q/p=p^d+p^v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="$p=p^d+p^v$">|; 

$key = q/displaystyle+Dvect{e}_rfrac{1}{rcosvarphi}left[DP{A_{varphi}}{lambda}-DP{}{varphi}(cosvarphiA_{lambda})right],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="252" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img200.png"
 ALT="$\displaystyle + \Dvect{e}_r \frac{1}{r \cos \varphi}
\left[ \DP{A_{\varphi}}{\lambda} - \DP{}{\varphi} (\cos
\varphi A_{\lambda}) \right],$">|; 

$key = q/{displaymath}DD{}{t}T=frac{1}{c_p^drho}DD{p}{t}+frac{Q^*}{c_p^d}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img216.png"
 ALT="\begin{displaymath}
\DD{}{t} T = \frac{1}{c_p^d \rho} \DD{p}{t} + \frac{Q^*}{c_p^d}.
\end{displaymath}">|; 

$key = q/sigma=sigma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img303.png"
 ALT="$\sigma=\sigma$">|; 

$key = q/C_v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img396.png"
 ALT="$C_v$">|; 

$key = q/displaystylerhoR^d(1+epsilon_vq)T,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="$\displaystyle \rho R^d ( 1 + \epsilon_v q ) T,$">|; 

$key = q/displaystyle(zeta+f)V-dot{sigma}frac{partialU}{partialsigma}-frac{RT^{prime}}{a}frac{partialpi}{partiallambda}+{calF}_{lambda}cosvarphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="271" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$\displaystyle ( \zeta + f ) V
- \dot{\sigma} \frac{\partial U}{\partial \sigma}...
...me}}{a}
\frac{\partial \pi}{\partial \lambda}
+ {\cal F}_{\lambda} \cos \varphi$">|; 

$key = q/displaystylefrac{R^dT_v}{c_p^d}left{DP{pi}{t}+Dvect{v}_Hcdotnabla_{sigma}pi+frac{dot{sigma}}{sigma}right}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img291.png"
 ALT="$\displaystyle \frac{R^d T_v}{c_p^d} \left\{ \DP{\pi}{t}
+ \Dvect{v}_H \cdot \nabla_{\sigma} \pi
+ \frac{\dot{\sigma}}{\sigma} \right\}.$">|; 

$key = q/{displaymath}dot{sigma}=-sigmafrac{partialpi}{partialt}-int_{0}^{sigma}Ddsigma-int_{0}^{sigma}Dvect{v}_{H}cdotnabla_{sigma}pidsigma,{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="285" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="\begin{displaymath}
\dot{\sigma}
= - \sigma
\frac{\partial \pi}{\partial t}...
...^{\sigma}
\Dvect{v}_{H} \cdot \nabla_{\sigma} \pi d \sigma ,
\end{displaymath}">|; 

$key = q/displaystyle-frac{1}{a^2}DP{}{mu}left[(1-mu^2)DP{}{mu}(R^dbar{T}_vpi)right]-frac{1}{a}DP{}{mu}left[frac{R^dT'_v}{a}(1-mu^2)DP{pi}{mu}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="412" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img369.png"
 ALT="$\displaystyle - \frac{1}{a^2} \DP{}{\mu}
\left[ (1-\mu^2) \DP{}{\mu} ( R^d \bar...
...ac{1}{a} \DP{}{\mu}
\left[ \frac{R^d T'_v}{a} ( 1-\mu^2 ) \DP{\pi}{\mu} \right]$">|; 

$key = q/displaystyle-frac{1}{acosvarphi}DP{}{lambda}left[dot{sigma}DP{v}{sigma}+frac{R^dT_v}{ap_s}DP{p_s}{varphi}-F_{varphi}+furight];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="307" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img315.png"
 ALT="$\displaystyle - \frac{1}{a \cos \varphi} \DP{}{\lambda}
\left[ \dot{\sigma} \DP{v}{\sigma}
+ \frac{R^d T_v}{a p_s} \DP{p_s}{\varphi}
- F_{\varphi} + f u \right]$">|; 

$key = q/{displaymath}DD{q}{t}=S_q,{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img235.png"
 ALT="\begin{displaymath}
\DD{q}{t} = S_q,
\end{displaymath}">|; 

$key = q/displaystylenabla^2_{sigma};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img322.png"
 ALT="$\displaystyle \nabla^2_{\sigma}$">|; 

$key = q/displaystyleDvect{v}_{H}cdotnabla;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$\displaystyle \Dvect{v}_{H} \cdot \nabla$">|; 

$key = q/displaystyleV;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$\displaystyle V$">|; 

$key = q/displaystyle2Dvect{Omega}timesDvect{v};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img206.png"
 ALT="$\displaystyle 2 \Dvect{\Omega} \times \Dvect{v}$">|; 

$key = q/{displaymath}{calD}(T)=-(-1)^{N_Dslash2}K_{HD}nabla^{N_D}T,{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="222" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="\begin{displaymath}
{\cal D}(T) = - (-1)^{N_D/2} K_{HD} \nabla^{N_D} T ,
\end{displaymath}">|; 

$key = q/displaystyle-frac{1}{a(1-mu^2)}DP{}{lambda}left[+frac{R^dT'_v}{a}(1-mu^2)DP{pi}{right]-frac{1}{a}DP{}{mu}left[-frac{R^dT'_v}{a}DP{pi}{lambda}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="418" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img364.png"
 ALT="$\displaystyle - \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ + \frac{R^d T'_v}{a...
...- \frac{1}{a} \DP{}{\mu}
\left[ - \frac{R^d T'_v}{a} \DP{\pi}{\lambda} \right].$">|; 

$key = q/{displaymath}sigmaequivfrac{p}{p_s},{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img244.png"
 ALT="\begin{displaymath}
\sigma \equiv \frac{p}{p_s},
\end{displaymath}">|; 

$key = q/displaystyle-frac{1}{a(1-mu^2)}DP{}{lambda}left[dot{sigma}DP{U}{sigma}+frac{R^dT_v}{a}DP{pi}{lambda}-F_{lambda}cosvarphi-fVright];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="364" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img349.png"
 ALT="$\displaystyle - \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ \dot{\sigma} \DP{U}...
...
+ \frac{R^d T_v}{a} \DP{\pi}{\lambda}
- F_{\lambda} \cos \varphi - f V \right]$">|; 

$key = q/displaystyle+frac{1}{acosvarphi}left[left(DP{}{varphi}(vcosvarphi)right)_{sigma}c{gsigma}{R^dT_v}DP{}{sigma}(vcosvarphi)DP[][sigma]{z}{lambda}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="398" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img277.png"
 ALT="$\displaystyle + \frac{1}{a \cos \varphi}
\left[ \left( \DP{}{\varphi} (v \cos \...
...igma}{R^d T_v}\DP{}{\sigma} ( v \cos \varphi)
\DP[][\sigma]{z}{\lambda} \right]$">|; 

$key = q/Dvect{A}=(A_1,A_2,A_3);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img171.png"
 ALT="$\Dvect{A}=(A_1, A_2, A_3)$">|; 

$key = q/displaystylefrac{1}{rho}left{DP[][sigma]{p}{lambda}+frac{gsigma}{R^dT_v}DP{p}{sigma}DP[][sigma]{z}{lambda}right};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="239" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img267.png"
 ALT="$\displaystyle \frac{1}{\rho} \left\{ \DP[][\sigma]{p}{\lambda}
+ \frac{g \sigma}{R^d T_v} \DP{p}{\sigma} \DP[][\sigma]{z}{\lambda}
\right\}$">|; 

$key = q/{displaymath}DP{D}{t}=frac{1}{a(1-mu^2)}DP{UA}{lambda}-frac{1}{a}DP{VA}{mu}-Dgrad^2_{sigma}(Phi+Rbar{T}_vpi+KE).{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="397" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img375.png"
 ALT="\begin{displaymath}
\DP{D}{t}
= \frac{1}{a (1-\mu^2)} \DP{UA}{\lambda}
- \fra...
...A}{\mu}
- \Dgrad^2_{\sigma} ( \Phi + R \bar{T}_v \pi + KE ).
\end{displaymath}">|; 

$key = q/f;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img231.png"
 ALT="$f$">|; 

$key = q/{displaymath}nabla^2bullet=frac{1}{h_1h_2h_3}left[DP{}{xi_1}left(frac{h_2h_3}{h_i_3}left(frac{h_1h_2}{h_3}DP{bullet}{xi_3}right)right],{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="523" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img176.png"
 ALT="\begin{displaymath}
\nabla^2 \bullet
= \frac{1}{h_1 h_2 h_3}
\left[ \DP{}{\...
...eft( \frac{h_1 h_2}{h_3} \DP{\bullet}{\xi_3} \right)
\right],
\end{displaymath}">|; 

$key = q/displaystyle(rho^dR^d+rho^vR^v)T;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="$\displaystyle (\rho^d R^d + \rho^v R^v) T$">|; 

$key = q/bar{T}_v(sigma);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img357.png"
 ALT="$\bar{T}_v(\sigma)$">|; 

$key = q/displaystyle-frac{1}{rho}DP{p}{r}-g+2Omegaucosvarphi+frac{u^2}{r}+frac{v^2}{r}+F_r.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="281" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img214.png"
 ALT="$\displaystyle - \frac{1}{\rho} \DP{p}{r} -g
+ 2 \Omega u \cos \varphi
+ \frac{u^2}{r}
+ \frac{v^2}{r}
+ F_r.$">|; 

$key = q/fequiv2Omegasinvarphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img232.png"
 ALT="$f \equiv 2\Omega \sin \varphi$">|; 

$key = q/kappa=RslashC_p;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img407.png"
 ALT="$\kappa = R/C_p$">|; 

$key = q/displaystyle-frac{1}{a}DP{}{mu}left[-frac{R^dbar{T}_v}{a}DP{pi}{lambda}right]-frac{1}{a}DP{}{mu}left[-frac{R^dT'_v}{a}DP{pi}{lambda}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="299" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img361.png"
 ALT="$\displaystyle - \frac{1}{a} \DP{}{\mu}
\left[ - \frac{R^d \bar{T}_v}{a} \DP{\pi...
...
- \frac{1}{a} \DP{}{\mu}
\left[ - \frac{R^d T'_v}{a} \DP{\pi}{\lambda} \right]$">|; 

$key = q/{displaymath}Dvect{v}_a=Dvect{v}+Dvect{Omega}timesDvect{r}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img161.png"
 ALT="\begin{displaymath}
\Dvect{v}_a = \Dvect{v} + \Dvect{\Omega} \times \Dvect{r}.
\end{displaymath}">|; 

$key = q/displaystylegz;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$\displaystyle gz$">|; 

$key = q/displaystyleDvect{i}'A'_x+Dvect{j}'A'_y+Dvect{k}'A'_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img150.png"
 ALT="$\displaystyle \Dvect{i}' A'_x
+ \Dvect{j}' A'_y
+ \Dvect{k}' A'_z$">|; 

$key = q/%latex2htmlidmarker5026setcounter{footnote}{8}fnsymbol{footnote};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img142.png"
 ALT="% latex2html id marker 5026
\setcounter{footnote}{8}\fnsymbol{footnote}">|; 

$key = q/displaystylep^d;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="$\displaystyle p^d$">|; 

$key = q/displaystyle-dot{sigma}frac{partialq}{partialsigma}+S_{q}+{calD}(q);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$\displaystyle - \dot{\sigma} \frac{\partial q }{\partial \sigma}
+ S_{q}
+ {\cal D}(q)$">|; 

$key = q/F'_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img114.png"
 ALT="$F'_i$">|; 

$key = q/{displaymath}zetaequivfrac{1}{acosvarphi}DP{v}{lambda}-frac{1}{acosvarphi}DP{}{varphi}(ucosvarphi).{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="257" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img307.png"
 ALT="\begin{displaymath}
\zeta \equiv \frac{1}{a \cos \varphi} \DP{v}{\lambda}
- \frac{1}{a \cos \varphi} \DP{}{\varphi} ( u \cos \varphi).
\end{displaymath}">|; 

$key = q/displaystyleKE;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img324.png"
 ALT="$\displaystyle KE$">|; 

$key = q/{displaymath}DD{rho}{t}+rhoDdivDvect{v}=0.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img105.png"
 ALT="\begin{displaymath}
\DD{\rho}{t}
+ \rho \Ddiv \Dvect{v}
= 0.
\end{displaymath}">|; 

$key = q/displaystyle2Omega(Dvect{e}_{varphi}cosvarphi+Dvect{e}_rsinvarphi)times(uDvect{e}_{lambda}+vDvect{e}_{varphi}+wDvect{e}_r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="312" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img207.png"
 ALT="$\displaystyle 2 \Omega ( \Dvect{e}_{\varphi} \cos \varphi
+ \Dvect{e}_r \sin \varphi)
\times ( u \Dvect{e}_{\lambda} + v \Dvect{e}_{\varphi}
+ w \Dvect{e}_r)$">|; 

$key = q/psi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img144.png"
 ALT="$\psi$">|; 

$key = q/sigma_{SB};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img401.png"
 ALT="$\sigma_{SB}$">|; 

$key = q/displaystyleT(1+epsilon_vq);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$\displaystyle T ( 1+\epsilon_v q )$">|; 

$key = q/displaystyleucosvarphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$\displaystyle u \cos \varphi$">|; 

$key = q/displaystyleDvect{i}'left(DD{A'_x}{t}right)_{{rm{r}+Dvect{j}'left(DD{A'_y}{t}rig}'A'_x+Dvect{Omega}timesDvect{j}'A'_y+Dvect{Omega}timesDvect{k}'A'_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="527" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img154.png"
 ALT="$\displaystyle \Dvect{i}' \left( \DD{A'_x}{t} \right)_{\rm r}
+ \Dvect{j}' \left...
...+ \Dvect{\Omega} \times \Dvect{j}' A'_y
+ \Dvect{\Omega} \times \Dvect{k}' A'_z$">|; 

$key = q/displaystyle-frac{u^2tanvarphi}{a}-fu-frac{1}{rhor}DP{p}{varphi}+F_{varphi}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img230.png"
 ALT="$\displaystyle - \frac{u^2 \tan \varphi}{a}
- fu - \frac{1}{\rho r } \DP{p}{\varphi}
+ F_{\varphi}.$">|; 

$key = q/displaystylefrac{1}{c_p^drho}left{DP{p}{t}+Dvect{v}_Hcdotnabla_{sigma}p+dot{sigma}DP{p}{sigma}right};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img289.png"
 ALT="$\displaystyle \frac{1}{c_p^d \rho} \left\{ \DP{p}{t}
+ \Dvect{v}_H \cdot \nabla_{\sigma} p
+ \dot{\sigma} \DP{p}{\sigma} \right\}$">|; 

$key = q/^{-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img394.png"
 ALT="$^{-1}$">|; 

$key = q/times10^{-8};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img403.png"
 ALT="$\times 10^{-8}$">|; 

$key = q/c_p^d;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="$c_p^d$">|; 

$key = q/displaystylefrac{1}{acosvarphi}DP{}{lambda}(zetav)-frac{1}{acosvarphi}DP{}{varphi}(zetaucosvarphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="264" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img318.png"
 ALT="$\displaystyle \frac{1}{a \cos \varphi} \DP{}{\lambda}
( \zeta v )
- \frac{1}{a \cos \varphi} \DP{}{\varphi}
( \zeta u \cos \varphi)$">|; 

$key = q/%latex2htmlidmarker4925setcounter{footnote}{3}fnsymbol{footnote};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="6" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="% latex2html id marker 4925
\setcounter{footnote}{3}\fnsymbol{footnote}">|; 

$key = q/{displaymath}DD{u}{t}-fv-frac{uv}{a}tanvarphi=-frac{1}{acosvarphi}DP{Phi}{lambda}-frac{R^dT_v}{acosvarphi}DP{pi}{lambda}+F_{lambda},{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="379" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img272.png"
 ALT="\begin{displaymath}
\DD{u}{t} -f v - \frac{uv}{a} \tan \varphi
= - \frac{1}{a ...
...ac{R^d T_v}{a \cos \varphi} \DP{\pi}{\lambda}
+ F_{\lambda},
\end{displaymath}">|; 

$key = q/v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img311.png"
 ALT="$v$">|; 

$key = q/C_p;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img393.png"
 ALT="$C_p$">|; 

$key = q/T'_v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img358.png"
 ALT="$T'_v$">|; 

$key = q/{displaymath}0=-frac{1}{rho}DP{p}{z}-g,{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img238.png"
 ALT="\begin{displaymath}
0 = - \frac{1}{\rho} \DP{p}{z} - g,
\end{displaymath}">|; 

$key = q/{displaymath}DP{}{t}left(frac{1}{2}rhov_i^2+rhoPhi^*right)+DP{}{x_j}left(frac{1}v_iright)=pDP{v_j}{x_j}-sigma_{ij}DP{v_i}{x_j}+F'_iv_i,{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="568" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img132.png"
 ALT="\begin{displaymath}
\DP{}{t} \left( \frac{1}{2} \rho v_i^2 + \rho \Phi^* \right...
...ht)
= p \DP{v_j}{x_j} - \sigma_{ij} \DP{v_i}{x_j} + F'_i v_i,
\end{displaymath}">|; 

$key = q/{displaymath}{calD}(q)=-(-1)^{N_Dslash2}K_{HD}nabla^{N_D}q.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="\begin{displaymath}
{\cal D}(q) = - (-1)^{N_D/2} K_{HD} \nabla^{N_D} q .
\end{displaymath}">|; 

$key = q/{displaymath}0=-frac{1}{rho}DP{p}{z}-g.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img221.png"
 ALT="\begin{displaymath}
0 = - \frac{1}{\rho} \DP{p}{z} - g.
\end{displaymath}">|; 

$key = q/{calD}(zeta),{calD}(D),{calD}(T),{calD}(q);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="${\cal D}(\zeta), {\cal D}(D), {\cal D}(T), {\cal D}(q)$">|; 

$key = q/dot{sigma};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$\dot{\sigma}$">|; 

$key = q/{displaymath}Dvect{v}_Hcdotnabla_{sigma}=frac{u}{acosvarphi}DP{}{lambda}+frac{v}{a}DP{}{varphi}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="208" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img292.png"
 ALT="\begin{displaymath}
\Dvect{v}_H \cdot \nabla_{\sigma}
= \frac{u}{a \cos \varphi} \DP{}{\lambda}
+ \frac{v}{a} \DP{}{\varphi}.
\end{displaymath}">|; 

$key = q/displaystyleleft(DD{Dvect{A}}{t}right)_{{rm{a};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img151.png"
 ALT="$\displaystyle \left( \DD{\Dvect{A}}{t} \right)_{\rm a}$">|; 

$key = q/displaystyleR^dT_vDP[][sigma]{pi}{lambda}+DP{Phi}{lambda},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img269.png"
 ALT="$\displaystyle R^d T_v \DP[][\sigma]{\pi}{\lambda} + \DP{\Phi}{\lambda},$">|; 

$key = q/S_q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$S_q$">|; 

$key = q/Phi_s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img295.png"
 ALT="$\Phi_s$">|; 

$key = q/g;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img391.png"
 ALT="$g$">|; 

$key = q/T_v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img139.png"
 ALT="$T_v$">|; 

$key = q/varepsilon=c_vT;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img136.png"
 ALT="$\varepsilon = c_v T$">|; 

$key = q/displaystyleDP{q}{t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img354.png"
 ALT="$\displaystyle \DP{q}{t}$">|; 

$key = q/displaystyleleft(DP{bullet}{t}right)_{sigma}+frac{u}{acosvarphi}left(DP{bullet}{t(DP{bullet}{varphi}right)_{sigma}+wleft(DP{bullet}{z}right)_{sigma};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="362" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img260.png"
 ALT="$\displaystyle \left( \DP{\bullet}{t} \right)_{\sigma}
+ \frac{u}{a \cos \varphi...
...{\bullet}{\varphi} \right)_{\sigma}
+ w \left( \DP{\bullet}{z} \right)_{\sigma}$">|; 

$key = q/Uequivucosphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img328.png"
 ALT="$U \equiv u
\cos \phi$">|; 

$key = q/displaystyleleft(DP{bullet}{t}right)_{sigma}-DP{sigma}{z}DP{bullet}{sigma}left(DP{z}{t}right)_{sigma};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img256.png"
 ALT="$\displaystyle \left( \DP{\bullet}{t} \right)_{\sigma}
- \DP{\sigma}{z} \DP{\bullet}{\sigma}
\left( \DP{z}{t} \right)_{\sigma}$">|; 

$key = q/lambda;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$\lambda$">|; 

$key = q/displaystylefrac{partialq}{partialt};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$\displaystyle \frac{\partial q}{\partial t}$">|; 

$key = q/displaystyle+Dvect{e}_rleft[DP{A_r}{t}+frac{u}{rcosvarphi}DP{A_r}{lambda}+frac{vvarphi}+wDP{A_r}{r}-frac{v}{r}A_{varphi}-frac{u}{r}A_{lambda}right].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="427" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img205.png"
 ALT="$\displaystyle + \Dvect{e}_r \left[
\DP{A_r}{t} + \frac{u}{r \cos \varphi} \DP{A...
...i} + w \DP{A_r}{r}
- \frac{v}{r} A_{\varphi} - \frac{u}{r} A_{\lambda} \right].$">|; 

$key = q/displaystyleDvect{i}'left(DD{A'_x}{t}right)_{{rm{a}+Dvect{j}'left(DD{A'_y}{t}rigct{j}'}{t}right)_{{rm{a}A'_y+left(DD{Dvect{k}'}{t}right)_{{rm{a}A'_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="569" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img153.png"
 ALT="$\displaystyle \Dvect{i}' \left( \DD{A'_x}{t} \right)_{\rm a}
+ \Dvect{j}' \left...
...t{j}'}{t} \right)_{\rm a} A'_y
+ \left( \DD{\Dvect{k}'}{t} \right)_{\rm a} A'_z$">|; 

$key = q/{displaymath}rhoDD{v_i}{t}+DP{p}{x_i}-DP{tau_{ij}}{x_j}+rhoDP{Phi^*}{x_i}=F'_i,{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="236" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img115.png"
 ALT="\begin{displaymath}
\rho \DD{v_i}{t}
+ \DP{p}{x_i}
- \DP{\tau_{ij}}{x_j}
+ \rho \DP{\Phi^*}{x_i}
= F'_i,
\end{displaymath}">|; 

$key = q/displaystylekappa;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$\displaystyle \kappa$">|; 

$key = q/Q^*=Q+c_pmathcal{D}(Dvect{v});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img384.png"
 ALT="$Q^*=Q+c_p \mathcal{D}(\Dvect{v})$">|; 

$key = q/k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img404.png"
 ALT="$k$">|; 

$key = q/displaystylersinvarphi,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img188.png"
 ALT="$\displaystyle r \sin \varphi,$">|; 

$key = q/displaystyleDP{sigma}{z}DP{bullet}{sigma};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img247.png"
 ALT="$\displaystyle \DP{\sigma}{z} \DP{\bullet}{\sigma}$">|; 

$key = q/displaystyle-frac{1}{a}DP{}{mu}left[-dot{sigma}DP{U}{sigma}-frac{R^dT_v}{a}DP{pi}{lambda}+F_{lambda}cosvarphi+fVright].;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="327" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img347.png"
 ALT="$\displaystyle - \frac{1}{a} \DP{}{\mu}
\left[ - \dot{\sigma} \DP{U}{\sigma}
- \frac{R^d T_v}{a} \DP{\pi}{\lambda}
+ F_{\lambda} \cos \varphi + fV \right].$">|; 

$key = q/displaystyleRslashC_{p};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$\displaystyle R/C_{p}$">|; 

$key = q/rho^v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img106.png"
 ALT="$\rho^v$">|; 

$key = q/{displaymath}left(DD{Dvect{A}}{t}right)_{{rm{a}=left(DD{Dvect{A}}{t}right)_{{rm{r}+Dvect{Omega}timesDvect{A}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img147.png"
 ALT="\begin{displaymath}
\left( \DD{\Dvect{A}}{t} \right)_{\rm a}
= \left( \DD{\Dvect{A}}{t} \right)_{\rm r}
+ \Dvect{\Omega} \times \Dvect{A}.
\end{displaymath}">|; 

$key = q/displaystyle-frac{1}{a(1-mu^2)}DP{}{lambda}left[dot{sigma}DP{V}{sigma}+frac{R^dT_v}{a}(1-mu^2)DP{pi}{mu}-F_{varphi}cosvarphi+fUright];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="421" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img346.png"
 ALT="$\displaystyle - \frac{1}{a (1-\mu^2)} \DP{}{\lambda}
\left[ \dot{\sigma} \DP{V}...
...ac{R^d T_v}{a} (1-\mu^2) \DP{\pi}{\mu}
- F_{\varphi} \cos \varphi + f U \right]$">|; 

$key = q/displaystyleDP{}{t}(rhov_i^2)+DP{}{x_j}(rhov_jv_i^2)-DP{}{t}left(frac{1}{2}rhov_i^2right)-DP{}{x_j}left(frac{1}{2}v_i^2rhov_jright);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="385" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img125.png"
 ALT="$\displaystyle \DP{}{t} ( \rho v_i^2 )
+ \DP{}{x_j} ( \rho v_j v_i^2 )
- \DP{}{t...
...1}{2} \rho v_i^2 \right)
- \DP{}{x_j} \left( \frac{1}{2} v_i^2 \rho v_j \right)$">|; 

$key = q/phi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$\phi$">|; 

$key = q/displaystyle-(zeta+f)U-dot{sigma}DP{V}{sigma}-frac{RT'}{a}(1-mu^{2})DP{pi}{mu}+F_{varphi}cosvarphi.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="346" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img379.png"
 ALT="$\displaystyle - ( \zeta + f ) U
- \dot{\sigma} \DP{V}{\sigma}
- \frac{RT'}{a} ( 1 - \mu^{2} )
\DP{\pi}{\mu}
+ F_{\varphi} \cos \varphi.$">|; 

$key = q/displaystyle+frac{gsigma}{R^dT_v}left{left(DP{z}{t}right)_{sigma}+frac{u}{acosva+frac{v}{a}left(DP{z}{varphi}right)_{sigma}-wright}DP{bullet}{sigma};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="412" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img261.png"
 ALT="$\displaystyle + \frac{g \sigma}{R^d T_v} \left\{
\left( \DP{z}{t} \right)_{\sig...
...{v}{a} \left( \DP{z}{\varphi} \right)_{\sigma}
-w \right\} \DP{\bullet}{\sigma}$">|; 

$key = q/{displaymath}left(DD{psi}{t}right)_{{rm{a}=left(DD{psi}{t}right)_{{rm{r},{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img145.png"
 ALT="\begin{displaymath}
\left( \DD{\psi}{t} \right)_{\rm a}
= \left( \DD{\psi}{t} \right)_{\rm r},
\end{displaymath}">|; 

$key = q/{displaymath}DD{Dvect{v}}{t}=-frac{1}{rho}Dgradp-2Dvect{Omega}timesDvect{v}+Dvect{g}+Dvect{F},{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img166.png"
 ALT="\begin{displaymath}
\DD{\Dvect{v}}{t}
= - \frac{1}{\rho} \Dgrad p
- 2 \Dvect{\Omega} \times \Dvect{v}
+ \Dvect{g} + \Dvect{F},
\end{displaymath}">|; 

$key = q/{displaymath}DD{v}{t}+fu+frac{u^2}{a}tanvarphi=-frac{1}{a}DP{Phi}{varphi}-frac{R^dT_v}{a}DP{pi}{varphi}+F_{varphi}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="333" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img273.png"
 ALT="\begin{displaymath}
\DD{v}{t} + fu + \frac{u^2}{a} \tan \varphi
= - \frac{1}{a...
...arphi}
- \frac{R^d T_v}{a} \DP{\pi}{\varphi}
+ F_{\varphi}.
\end{displaymath}">|; 

$key = q/displaystylefrac{1}{acosvarphi}DP[][sigma]{u}{lambda}+frac{1}{acosvarphi}left(DP{}{varphi}(vcosvarphi)right)_{sigma}+DP{dot{sigma}}{sigma};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="340" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img279.png"
 ALT="$\displaystyle \frac{1}{a \cos \varphi} \DP[][\sigma]{u}{\lambda}
+ \frac{1}{a \...
...t( \DP{}{\varphi} (v \cos
\varphi) \right)_{\sigma}
+ \DP{\dot{\sigma}}{\sigma}$">|; 

$key = q/bullet;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img170.png"
 ALT="$\bullet$">|; 

$key = q/displaystylefrac{1}{a(1-mu^2)}DP{}{lambda}(Ubullet)+frac{1}{amu}DP{}{phi}(Vbullet)+bulletD.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="271" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img340.png"
 ALT="$\displaystyle \frac{1}{a (1-\mu^2)} \DP{}{\lambda} (U\bullet)
+\frac{1}{a \mu} \DP{}{\phi} (V\bullet)
+\bullet D.$">|; 

$key = q/R_v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img397.png"
 ALT="$R_v$">|; 

$key = q/{displaymath}DD{v}{t}=-frac{u^2tanvarphi}{a}-fu-frac{1}{rhoa}DP{p}{varphi}+F_{varphi},{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="256" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img237.png"
 ALT="\begin{displaymath}
\DD{v}{t}
= - \frac{u^2 \tan \varphi}{a}
- fu - \frac{1}{\rho a } \DP{p}{\varphi}
+ F_{\varphi},
\end{displaymath}">|; 

$key = q/displaystyle-frac{1}{rhor}DP{p}{varphi}-2Omegausinvarphi-frac{u^2}{r}tanvarphi-frac{vw}{r}+F_varphi,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="308" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img212.png"
 ALT="$\displaystyle - \frac{1}{\rho r} \DP{p}{\varphi}
- 2 \Omega u \sin \varphi
- \frac{u^2}{r} \tan \varphi
- \frac{v w}{r}
+ F_\varphi,$">|; 

$key = q/displaystylePhi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$\displaystyle \Phi$">|; 

$key = q/(xi_1,xi_2,xi_3);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img169.png"
 ALT="$(\xi_1, \xi_2, \xi_3)$">|; 

$key = q/{displaymath}DD{bullet}{t}=DP{bullet}{t}+frac{u}{rcosvarphi}DP{bullet}{lambda}+frac{v}{r}DP{bullet}{varphi}+wDP{bullet}{r},{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="266" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img201.png"
 ALT="\begin{displaymath}
\DD{\bullet}{t}
= \DP{\bullet}{t} + \frac{u}{r \cos \varp...
...bda}
+ \frac{v}{r} \DP{\bullet}{\varphi} + w \DP{\bullet}{r},
\end{displaymath}">|; 

$key = q/^{circ};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img399.png"
 ALT="$^{\circ}$">|; 

$key = q/Dvect{Omega};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img143.png"
 ALT="$\Dvect{\Omega}$">|; 

$key = q/displaystyleleft(DP{bullet}{t}right)_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img255.png"
 ALT="$\displaystyle \left( \DP{\bullet}{t} \right)_z$">|; 

$key = q/epsilon_v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img405.png"
 ALT="$\epsilon_v$">|; 

$key = q/%latex2htmlidmarker4926setcounter{footnote}{3}fnsymbol{footnote};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="6" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="% latex2html id marker 4926
\setcounter{footnote}{3}\fnsymbol{footnote}">|; 

$key = q/displaystyle-frac{1}{a(1-mu^{2})}frac{partialUq}{partiallambda}-frac{1}{a}frac{partialVq}{partialmu}+qD;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$\displaystyle - \frac{1}{a(1-\mu^{2})}
\frac{\partial Uq}{\partial \lambda}
- \frac{1}{a}
\frac{\partial Vq}{\partial \mu}
+ q D$">|; 

$key = q/displaystyle+frac{1}{a}frac{R^dbar{T}_v}{a}frac{partial^2pi}{partialmupartiallambda}-frac{1}{a}DP{}{mu}left[-frac{R^dT'_v}{a}DP{pi}{lambda}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img363.png"
 ALT="$\displaystyle + \frac{1}{a} \frac{R^d \bar{T}_v}{a}
\frac{\partial^2 \pi}{\part...
...
- \frac{1}{a} \DP{}{\mu}
\left[ - \frac{R^d T'_v}{a} \DP{\pi}{\lambda} \right]$">|; 

$key = q/displaystylep;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="$\displaystyle p$">|; 

$key = q/displaystyleDP{}{t}(rhov_i^2)+DP{}{x_j}(rhov_jv_i^2)-rhoDP{}{t}left(frac{1}{2}v_i^2right)-rhov_jDP{}{x_j}left(frac{1}{2}v_i^2right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="384" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img124.png"
 ALT="$\displaystyle \DP{}{t} ( \rho v_i^2 )
+ \DP{}{x_j} ( \rho v_j v_i^2 )
- \rho \D...
...frac{1}{2} v_i^2 \right)
- \rho v_j \DP{}{x_j} \left( \frac{1}{2} v_i^2 \right)$">|; 

$key = q/displaystylevcosvarphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$\displaystyle v \cos \varphi$">|; 

$key = q/R^d;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="$R^d$">|; 

$key = q/displaystyleleft(DP{bullet}{varphi}right)_{sigma}-DP{sigma}{z}DP{bullet}{sigma}left(DP{z}{varphi}right)_{sigma};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img253.png"
 ALT="$\displaystyle \left( \DP{\bullet}{\varphi} \right)_{\sigma}
- \DP{\sigma}{z} \DP{\bullet}{\sigma}
\left( \DP{z}{\varphi} \right)_{\sigma}$">|; 

$key = q/displaystyle+Dvect{e}_{varphi}left[DP{A_{varphi}}{t}+frac{u}{rcosvarphi}DP{A_{vawDP{A_{varphi}}{r}+frac{v}{r}A_r+frac{utanvarphi}{r}A_{lambda}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="466" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img204.png"
 ALT="$\displaystyle + \Dvect{e}_{\varphi} \left[
\DP{A_{\varphi}}{t} + \frac{u}{r \co...
..._{\varphi}}{r}
+ \frac{v}{r} A_r + \frac{u \tan \varphi}{r} A_{\lambda} \right]$">|; 

$key = q/%latex2htmlidmarker4820setcounter{footnote}{2}fnsymbol{footnote};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="6" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="% latex2html id marker 4820
\setcounter{footnote}{2}\fnsymbol{footnote}">|; 

$key = q/Ddiv{Dvect{v}_H};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img301.png"
 ALT="$\Ddiv{\Dvect{v}_H}$">|; 

$key = q/displaystylembox{{sl{UA};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$\displaystyle \mbox{\sl UA}$">|; 

$key = q/Dvect{A}=(A_{lambda},A_{varphi},A_r);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img193.png"
 ALT="$\Dvect{A}=(A_{\lambda}, A_{\varphi}, A_r)$">|; 

$key = q/sigma=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img298.png"
 ALT="$\sigma=1$">|; 

$key = q/Dvect{e}_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img173.png"
 ALT="$\Dvect{e}_i$">|; 

$key = q/displaystylefrac{1}{acosvarphi}DP{u}{lambda}+frac{1}{acosvarphi}DP{}{varphi}(vcosvarphi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img334.png"
 ALT="$\displaystyle \frac{1}{a \cos \varphi} \DP{u}{\lambda}
+ \frac{1}{a \cos \varphi} \DP{}{\varphi} ( v \cos \varphi)$">|; 

$key = q/epsilonequivR^dslashR^v(=0.622);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img99.png"
 ALT="$\epsilon \equiv R^d/R^v(=0.622)$">|; 

$key = q/displaystylev_irhoDP{Phi^*}{x_i};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img129.png"
 ALT="$\displaystyle v_i \rho \DP{\Phi^*}{x_i}$">|; 

$key = q/displaystyle-frac{1}{a(1-mu^{2})}DP{UT}{lambda}-frac{1}{a}DP{VT}{mu}+TD;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="237" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img352.png"
 ALT="$\displaystyle - \frac{1}{a(1-\mu^{2})} \DP{UT}{\lambda}
- \frac{1}{a}
\DP{VT}{\mu}
+ T D$">|; 

$key = q/textstyleequiv;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$\textstyle \equiv$">|; 

$key = q/displaystyleUA;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img376.png"
 ALT="$\displaystyle UA$">|; 

$key = q/Dvect{A}=Dvect{r};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img156.png"
 ALT="$\Dvect{A}=\Dvect{r}$">|; 

$key = q/displaystylefrac{partialT}{partialt};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$\displaystyle \frac{\partial T}{\partial t}$">|; 

$key = q/displaystyledot{sigma};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$\displaystyle \dot{\sigma}$">|; 

$key = q/displaystyle-frac{1}{a(1-mu^{2})}frac{partialUT^{prime}}{partiallambda}-frac{1}{a}frac{partialVT^{prime}}{partialmu}+T^{prime}D;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="250" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$\displaystyle - \frac{1}{a(1-\mu^{2})}
\frac{\partial UT^{\prime}}{\partial \lambda}
- \frac{1}{a}
\frac{\partial VT^{\prime}}{\partial \mu}
+ T^{\prime} D$">|; 

$key = q/displaystylefrac{1}{rho}left(DP{p}{lambda}right)_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img266.png"
 ALT="$\displaystyle \frac{1}{\rho} \left( \DP{p}{\lambda} \right)_z$">|; 

$key = q/displaystyleDP{bullet}{z};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img246.png"
 ALT="$\displaystyle \DP{\bullet}{z}$">|; 

$key = q/displaystylefrac{1}{a(1-mu^2)}DP{}{lambda}(zetaV)-frac{1}{a}DP{}{mu}(zetaU);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="217" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img348.png"
 ALT="$\displaystyle \frac{1}{a (1-\mu^2)} \DP{}{\lambda} ( \zeta V )
- \frac{1}{a} \DP{}{\mu}
( \zeta U )$">|; 

$key = q/displaystyleleft(DP{bullet}{varphi}right)_z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img252.png"
 ALT="$\displaystyle \left( \DP{\bullet}{\varphi} \right)_z$">|; 

$key = q/times10^6;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img390.png"
 ALT="$\times 10^6$">|; 

$key = q/{displaymath}DP{}{t}left[rholeft(frac{1}{2}Dvect{v}^2+varepsilon+Phi^*right)righn+Phi^*right)v_j+pv_j-sigma_{ij}v_iright]=rhoQ+F'_iv_i,{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="555" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img120.png"
 ALT="\begin{displaymath}
\DP{}{t}
\left[ \rho
\left( \frac{1}{2} \Dvect{v}^2
+...
...v_j
+ p v_j - \sigma_{ij}v_i
\right]
= \rho Q + F'_i v_i,
\end{displaymath}">|; 

$key = q/displaystylex_3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img187.png"
 ALT="$\displaystyle x_3$">|; 

$key = q/displaystyle-frac{1}{acosvarphi}DP{}{varphi}left[cosvarphidot{sigma}DP{v}{sigma}{ap_s}DP{p_s}{varphi}cosvarphi-F_{varphi}cosvarphi+fucosvarphiright];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="453" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img320.png"
 ALT="$\displaystyle - \frac{1}{a \cos \varphi} \DP{}{\varphi}
\left[ \cos \varphi \do...
..._s}{\varphi} \cos \varphi
- F_{\varphi} \cos \varphi + f u \cos \varphi \right]$">|; 

$key = q/displaystyle-frac{1}{a(1-mu^{2})}DP{UT'}{lambda}-frac{1}{a}DP{VT'}{mu}+T'D-dot{sigma}DP{T}{sigma};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="305" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img380.png"
 ALT="$\displaystyle - \frac{1}{a(1-\mu^{2})} \DP{UT'}{\lambda}
- \frac{1}{a} \DP{VT'}{\mu}
+ T' D
- \dot{\sigma}
\DP{T}{\sigma}$">|; 

$key = q/displaystyletheta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$\displaystyle \theta$">|; 

$key = q/displaystyle-frac{gsigma}{R^dT_v}left[DP{}{sigma}DP[][sigma]{z}{t}+frac{u}{acosva}DP[][sigma]{z}{varphi}+dot{sigma}DP{}{sigma}DP[][]{z}{sigma}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="521" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img280.png"
 ALT="$\displaystyle - \frac{g \sigma}{R^d T_v} \left[ \DP{}{\sigma} \DP[][\sigma]{z}{...
...P[][\sigma]{z}{\varphi}
+ \dot{\sigma} \DP{}{\sigma} \DP[][]{z}{\sigma} \right]$">|; 

$key = q/{displaymath}DD{T}{t}=frac{1}{c_p^drho}DD{p}{t}+frac{Q^*}{c_p^d},{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img239.png"
 ALT="\begin{displaymath}
\DD{T}{t} = \frac{1}{c_p^d \rho} \DD{p}{t} + \frac{Q^*}{c_p^d},
\end{displaymath}">|; 

$key = q/displaystyleDvect{e}_{lambda}frac{1}{r}left[DP{A_r}{varphi}-DP{}{r}(rA_{varphi})right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img198.png"
 ALT="$\displaystyle \Dvect{e}_{\lambda} \frac{1}{r}
\left[ \DP{A_r}{\varphi} - \DP{}{r}(r A_{\varphi})
\right]$">|; 

$key = q/Phi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img296.png"
 ALT="$\Phi$">|; 

$key = q/displaystyle-frac{1}{a^2(1-mu^2)}DP[2]{}{lambda}(R^dbar{T}_vpi)-frac{1}{a(1-mu^2)}DP{}{lambda}left[frac{R^dT'_v}{a}DP{pi}{lambda}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="374" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img368.png"
 ALT="$\displaystyle - \frac{1}{a^2 (1-\mu^2)} \DP[2]{}{\lambda}
( R^d \bar{T}_v \pi )...
...a (1-\mu^2)} \DP{}{\lambda}
\left[ \frac{R^d T'_v}{a} \DP{\pi}{\lambda} \right]$">|; 

$key = q/displaystylezeta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$\displaystyle \zeta$">|; 

$key = q/{displaymath}DD{c_pT}{t}=frac{1}{rho}DD{p}{t}+Q^*,{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img138.png"
 ALT="\begin{displaymath}
\DD{c_p T}{t} = \frac{1}{\rho} \DD{p}{t} + Q^*,
\end{displaymath}">|; 

$key = q/displaystyle-dot{sigma}frac{partialT}{partialsigma}+kappaTleft(frac{partialpi}{pgma}}{sigma}right)+frac{Q}{C_{p}}+{calD}(T)+{calD}^{prime}(Dvect{v});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="412" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$\displaystyle - \dot{\sigma}
\frac{\partial T }{\partial \sigma}
+ \kappa T \le...
...\sigma }
\right)
+ \frac{Q}{C_{p}}
+ {\cal D}(T)
+ {\cal D}^{\prime}(\Dvect{v})$">|; 

$key = q/{displaymath}{calD}(zeta)=-K_{HD}left[(-1)^{N_Dslash2}nabla^{N_D}-left(frac{2}{a^2}right)^{N_Dslash2}right]zeta,{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="336" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="\begin{displaymath}
{\cal D}(\zeta) = - K_{HD}
\left[ (-1)^{N_D/2} \nabla^{N_D}
- \left( \frac{2}{a^2} \right)^{N_D/2}
\right]
\zeta ,
\end{displaymath}">|; 

$key = q/{displaymath}p=rhoR^dT_v.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img103.png"
 ALT="\begin{displaymath}
p = \rho R^d T_v.
\end{displaymath}">|; 

$key = q/mathcal{D}(q);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img388.png"
 ALT="$\mathcal{D}(q)$">|; 

$key = q/{displaymath}Ddiv{Dvect{v}_H}equivfrac{1}{acosvarphi}DP[][sigma]{u}{lambda}+fracacosvarphi}left(DP{}{varphi}(vcosvarphi)right)_{sigma}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="359" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img282.png"
 ALT="\begin{displaymath}
\Ddiv{\Dvect{v}_H}
\equiv \frac{1}{a \cos \varphi}
\DP[]...
...hi} \left( \DP{}{\varphi} (v \cos
\varphi ) \right)_{\sigma}.
\end{displaymath}">|; 

$key = q/{displaymath}DP{rho^v}{t}+DP{}{x_j}(rho^vv_j)=S.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img108.png"
 ALT="\begin{displaymath}
\DP{\rho^v}{t}
+ \DP{}{x_j} ( \rho^v v_j )
= S.
\end{displaymath}">|; 

$key = q/frac{1}{acosvarphi}DP{}{varphi}cosvarphi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img310.png"
 ALT="$\frac{1}{a \cos \varphi} \DP{}{\varphi} \cos
\varphi$">|; 

1;

