# LaTeX2HTML 2K.1beta (1.48)
# Associate images original text with physical files.


$key = q/partialoverline{A}slashpartiallambda=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$ \partial \overline{A}/\partial\lambda = 0$">|; 

$key = q/displaystyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$\displaystyle =$">|; 

$key = q/T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$ T$">|; 

$key = q/displaystyleoverline{A}(phi,p,t)=Dinv{2pi}int_0^{2pi}A(lambda,phi,p,t)Ddlambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="284" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$\displaystyle \overline{A}(\phi, p, t) = \Dinv{2\pi}\int_0^{2\pi} A(\lambda, \phi, p, t) \Dd \lambda$">|; 

$key = q/displaystyletheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="$\displaystyle \theta$">|; 

$key = q/{subequations}align{DP{overline{u}}{t}<col_mark>+Dinv{a}overline{v}DP{overline{uhi}}-overline{omega'DP{theta'}{p}}align{{subequations};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="555" HEIGHT="450" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="\begin{subequations}\begin{align}
 \DP{\overline{u}}{t}&amp;
 + \Dinv{a}\overline{v}...
...eta'}{\phi}}
 - \overline{\omega'\DP{\theta'}{p}}
 \end{align}\end{subequations}">|; 

$key = q/Q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$ Q$">|; 

$key = q/{subequations}align{overline{v}^*<col_mark>equivoverline{v}-DP{}{p}left(frac{ovea'}}{DP{overline{theta}}{p}}right)align{{subequations};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="555" HEIGHT="198" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="\begin{subequations}\begin{align}
 \overline{v}^* &amp;\equiv \overline{v} 
 - \DP{}...
...e{v'\theta'}}
 {\DP{\overline{\theta}}{p}}\right)
 \end{align}\end{subequations}">|; 

$key = q/displaystyle(u,v,w);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$\displaystyle (u, v, w)$">|; 

$key = q/displaystyle=-Dinv{acosphi}overline{DP{(u')^2}{lambda}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$\displaystyle = - \Dinv{a\cos\phi}\overline{\DP{(u')^2}{\lambda}}$">|; 

$key = q/T_{rot};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$ T_{rot}$">|; 

$key = q/displaystyleQ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$\displaystyle Q$">|; 

$key = q/F_phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$ F_\phi$">|; 

$key = q/%latex2htmlidmarker1773displaystyleitemize{<comment_mark>item»Äº¹½Û´Ä<comment_manv{acosphi}DP{cosphi}{phi}+DP{}{p}tag{ref{div}}align{itemize{;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="4" HEIGHT="5" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="% latex2html id marker 1773
$\displaystyle \begin{itemize}
 &lt;tex2html_comment_ma...
...phi} \DP{\cos \phi}{\phi} + \DP{}{p}\tag{\ref{div}}
 \end{align}
 \end{itemize}$">|; 

$key = q/{subequations}align{{F_phi}=<col_mark>acosphileft(DP{overline{u}}{overline{p}}frta}}{p}}-overline{u'omega'}right).align{{subequations};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="555" HEIGHT="133" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="\begin{subequations}\begin{align}
 {F_\phi} =&amp; a
 \cos \phi \left(\DP{\overline{...
...rline{\theta}}{p}} - \overline{u'\omega'}\right).
 \end{align}\end{subequations}">|; 

$key = q/displaystylehspace{5em}-Dinv{acos^2phi}DP{}{phi}(overline{v'u'}cos^2phi)-DP{}{p}(overline{omega'u'});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="392" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="$\displaystyle \hspace{5em}
 -\Dinv{a\cos^2\phi}\DP{}{\phi}(\overline{v'u'}\cos^2\phi)
 -\DP{}{p}(\overline{\omega'u'})$">|; 

$key = q/Psi^*;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$ \Psi^*$">|; 

$key = q/phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$ \phi$">|; 

$key = q/p=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$ p=0$">|; 

$key = q/displaystyleDdiv{}=Dinv{acosphi}DP{cosphi}{phi}+DP{}{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="213" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$\displaystyle \Ddiv{} = \Dinv{a \cos \phi} \DP{\cos \phi}{\phi} + \DP{}{p}$">|; 

$key = q/displaystyleDP{overline{u}}{t}+Dinv{a}overline{v}DP{overline{u}}{phi}+overline{one{v}-frac{tanphi}{a}overline{u}overline{v}-overline{X}=notag;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="359" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$\displaystyle \DP{\overline{u}}{t}
 + \Dinv{a}\overline{v}\DP{\overline{u}}{\ph...
...ine{v} 
 - \frac{\tan\phi}{a}\overline{u}\overline{v}
 - \overline{X} =
 \notag$">|; 

$key = q/theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$ \theta$">|; 

$key = q/displaystylef=2Omegasinphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$\displaystyle f = 2\Omega\sin\phi$">|; 

$key = q/displaystyleitemize{<comment_mark>item±¿Æ°ÊýÄø¼°<comment_mark>align{<col_mark>DPtheta}}{p}}+overline{omega'theta'}right)right].align{itemize{;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="4" HEIGHT="5" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="$\displaystyle \begin{itemize}
 &lt;tex2html_comment_mark&gt; \item ±¿Æ°ÊýÄø¼°
 &lt;tex2h...
...{p}} + \overline{\omega'\theta'}
 \right)
 \right].
 \end{align}
 \end{itemize}$">|; 

$key = q/kappa=RslashC_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$ \kappa=R/C_p$">|; 

$key = q/phi,p,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$ \phi, p, t$">|; 

$key = q/displaystyle-Dinv{acosphi}overline{u'DP{u'}{lambda}}-Dinv{a}overline{v'DP{u'}{phi}}-overline{omega'DP{u'}{p}}notag;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="274" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$\displaystyle - \Dinv{a\cos\phi}\overline{u'\DP{u'}{\lambda}}
 - \Dinv{a}\overline{v'\DP{u'}{\phi}}
 - \overline{\omega'\DP{u'}{p}}\notag$">|; 

$key = q/C_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$ C_p$">|; 

$key = q/displaystyleequiv;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$\displaystyle \equiv$">|; 

$key = q/displaystyleA'=A-overline{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$\displaystyle A' = A - \overline{A}$">|; 

$key = q/overline{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$ \overline{A}$">|; 

$key = q/displaystyleitemize{<comment_mark>item±¿Æ°ÊýÄø¼°<comment_mark>align{DD{u}{t}<col¼°<comment_mark>align{DD{theta}{t}<col_mark>=Q,align{itemize{;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="4" HEIGHT="5" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$\displaystyle \begin{itemize}
 &lt;tex2html_comment_mark&gt; \item ±¿Æ°ÊýÄø¼°
 &lt;tex2h...
..._comment_mark&gt; \begin{align}
 \DD{\theta}{t} &amp;= Q, 
 \end{align}
 \end{itemize}$">|; 

$key = q/displaystyle-Dinv{a}overline{v'DP{u'}{phi}}-Dinv{a}overline{u'DP{v'}{phi}}+frac{2tanphi}{a}overline{u'v'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$\displaystyle - \Dinv{a}\overline{v'\DP{u'}{\phi}}
 - \Dinv{a}\overline{u'\DP{v'}{\phi}}
 + \frac{2\tan\phi}{a}\overline{u'v'}$">|; 

$key = q/displaystylesigmaoverline{v}^*;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$\displaystyle \sigma\overline{v}^*$">|; 

$key = q/p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$ p$">|; 

$key = q/displaystyleDP{overline{u}}{t}+overline{v}^*left[Dinv{acosphi}DP{}{phi}(overlineerline{u}}{p}-overline{X}=Dinv{sigmacosphi}DdivDvect{hat{F}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="514" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$\displaystyle \DP{\overline{u}}{t}
 + \overline{v}^*\left[\Dinv{a\cos\phi}\DP{}...
...\overline{u}}{p}
 - \overline{X} =
 \Dinv{\sigma \cos\phi}\Ddiv\Dvect{\hat{F}}.$">|; 

$key = q/alpha=Dinv{rho};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$ \alpha=\Dinv{\rho}$">|; 

$key = q/J;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$ J$">|; 

$key = q/displaystyleitemize{<comment_mark>item±¿Æ°ÊýÄø¼°<comment_mark>align{DP{overline{theta'}cosphi)-DP{}{p}(overline{omega'theta'}).align{itemize{;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="4" HEIGHT="5" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$\displaystyle \begin{itemize}
 &lt;tex2html_comment_mark&gt; \item ±¿Æ°ÊýÄø¼°
 &lt;tex2h...
...'}\cos\phi)
 - \DP{}{p}(\overline{\omega'\theta'}).
 \end{align}
 \end{itemize}$">|; 

$key = q/displaystyle+Dinv{a}overline{v}DP{overline{u}}{phi}+overline{omega}DP{overline{une{v}-frac{tanphi}{a}overline{u}overline{v}-overline{X}=notag;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="324" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$\displaystyle + \Dinv{a}\overline{v}\DP{\overline{u}}{\phi}
 + \overline{\omega...
...rline{v} 
 - \frac{\tan\phi}{a}\overline{u}\overline{v}
 - \overline{X} =\notag$">|; 

$key = q/displaystyle=gDinv{2pia^2cosphi}DP{}{phi}Psi^*;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$\displaystyle = g\Dinv{2\pi a^2\cos\phi}\DP{}{\phi}\Psi^*$">|; 

$key = q/Psi^*=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$ \Psi^* = 0$">|; 

$key = q/lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$ \lambda$">|; 

$key = q/A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$ A$">|; 

$key = q/a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$ a$">|; 

$key = q/u'times;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$ u' \times $">|; 

$key = q/displaystyle=-Dinv{acos^2phi}DP{}{phi}(overline{v'u'}cos^2phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$\displaystyle = -\Dinv{a\cos^2\phi}\DP{}{\phi}(\overline{v'u'}\cos^2\phi)$">|; 

$key = q/displaystyle-Dinv{acosphi}overline{u'DP{u'}{lambda}}-Dinv{acosphi}overline{u'DP{u'}{lambda}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$\displaystyle - \Dinv{a\cos\phi}\overline{u'\DP{u'}{\lambda}}
 - \Dinv{a\cos\phi}\overline{u'\DP{u'}{\lambda}}$">|; 

$key = q/displaystyleleft(acosphiDD{lambda}{t},aDD{phi}{t},DD{p}{t}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$\displaystyle \left(a\cos\phi\DD{\lambda}{t}, a\DD{\phi}{t}, \DD{p}{t}\right)$">|; 

$key = q/displaystyle=Tleft(frac{p_{00}}{p}right)^kappa,kappa=RslashC_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="$\displaystyle = T \left(\frac{p_{00}}{p}\right)^\kappa, \kappa = R/C_p$">|; 

$key = q/overline{bullet};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$ \overline{\bullet}$">|; 

$key = q/displaystyleDinv{acosphi}left[DP{u'}{lambda}+DP{}{phi}(v'cosphi)right]+DP{omega'}{p}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="325" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$\displaystyle \Dinv{a\cos\phi}\left[\DP{u'}{\lambda}
+ \DP{}{\phi}(v'\cos\phi)\right]
+ \DP{\omega'}{p}
= 0$">|; 

$key = q/A';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$ A'$">|; 

$key = q/Phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$ \Phi$">|; 

$key = q/X,Y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$ X,Y$">|; 

$key = q/{subequations}align{DP{}{t}(overline{u}+u')<col_mark>+frac{overline{u}+u'}{acosprow_mark><col_mark>=overline{Q}+Q'align{{subequations};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="612" HEIGHT="512" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="\begin{subequations}\begin{align}
 \DP{}{t}(\overline{u} + u') &amp;
 + \frac{\overl...
...theta} + \theta')\notag\  
 &amp;= \overline{Q} + Q'
 \end{align}\end{subequations}">|; 

$key = q/bullet';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$ \bullet'$">|; 

$key = q/displaystyle=-DP{}{p}(overline{omega'u'});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$\displaystyle = -\DP{}{p}(\overline{\omega'u'})$">|; 

$key = q/R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="$ R$">|; 

$key = q/displaystyleOmega=frac{2pi}{T_{rot}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$\displaystyle \Omega = \frac{2\pi}{T_{rot}}$">|; 

$key = q/displaystyle-Dinv{acosphi}overline{u'DP{u'}{lambda}}-Dinv{a}overline{u'DP{v'}{phi}}-overline{u'DP{omega'}{p}}+frac{2tanphi}{a}overline{u'v'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="389" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$\displaystyle - \Dinv{a\cos\phi}\overline{u'\DP{u'}{\lambda}}
 - \Dinv{a}\overl...
...}{\phi}}
 - \overline{u'\DP{\omega'}{p}}
 + \frac{2\tan\phi}{a}\overline{u'v'}.$">|; 

$key = q/F_{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$ F_{p}$">|; 

$key = q/displaystyle=-gDinv{2piacosphi}DP{}{p}Psi^*;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$\displaystyle = -g\Dinv{2\pi a \cos\phi }\DP{}{p}\Psi^*$">|; 

$key = q/Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$ \Omega$">|; 

$key = q/displaystyleDP{overline{u}}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$\displaystyle \DP{\overline{u}}{t}$">|; 

$key = q/{subequations}align{DP{overline{u}}{t}<col_mark>+frac{overline{u}}{acosphi}DP{ov{theta}}{p}-omega'DP{theta'}{p}+Q'align{{subequations};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="597" HEIGHT="1103" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="\begin{subequations}\begin{align}
 \DP{\overline{u}}{t} &amp;
 + \frac{\overline{u}}...
...rline{\theta}}{p}
 - \omega'\DP{\theta'}{p}
 + Q'
 \end{align}\end{subequations}">|; 

$key = q/displaystylesigmaoverline{w}^*;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$\displaystyle \sigma\overline{w}^*$">|; 

$key = q/displaystyle=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$\displaystyle = 0,$">|; 

$key = q/f;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$ f$">|; 

$key = q/overline{A'}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$ \overline{A'}=0$">|; 

$key = q/displaystyle-overline{omega'DP{u'}{p}}-overline{u'DP{omega'}{p}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$\displaystyle - \overline{\omega'\DP{u'}{p}}
 - \overline{u'\DP{\omega'}{p}}$">|; 

$key = q/u,v,w;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$ u, v, w$">|; 

$key = q/displaystylefrac{J}{C_p}left(frac{p_s}{p}right)^{kappa},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$\displaystyle \frac{J}{C_p}\left(\frac{p_s}{p}\right)^{\kappa},$">|; 

$key = q/(0,overline{v}^*,overline{w}^*);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$ (0, \overline{v}^*, \overline{w}^*)$">|; 

$key = q/displaystylePsi^*(theta,p)=frac{2piacosphi}{g}int_{0}^{p}overline{v}^*Ddp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="243" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$\displaystyle \Psi^*(\theta, p) = \frac{2\pi a \cos\phi}{g} \int_{0}^{p}\overline{v}^*\Dd p$">|; 

1;