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\Dtitle{2 次元非静力学モデルの離散化}
\Dauthor{山下達也, 杉山耕一朗, 石渡正樹}
\Ddate{2010 年 3 月 17 日}




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$\displaystyle - \langle c_p \rangle
  [\overline{\theta_{v}}]_{i,k(w)}\left[\DP{\Pi}{z}\right]_{i,k(w)} 
  + \left[ D_{w} \right]_{i,k(w)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6367}%
$\displaystyle + g \frac{\theta_{i,k(w)}}{\overline{\theta}_{i,k(w)}} g$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6368}%
$\displaystyle + \frac{ [q_d]_{i,k(w)} \langle M \rangle /M_d + \sum [q_v]_{i,k(w)}
    \langle M \rangle / M_v }
     { [\overline{q_d}]_{i,k(w)} \langle M \rangle  /M_d +
    \sum [\overline{q_v}]_{i,k(w)} \langle M \rangle / M_v} g
  \Deqlab{空間離散化された z 方向運動方程式}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6371}%
$\displaystyle \DP{ \Pi_{i,k}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6373}%
$\displaystyle - \frac{\overline{  \langle {c_{s}} \rangle^{2} }_{i,k} }
  { \langle c_p \rangle \bar{\rho}_{i,k}
 [\bar{\theta_v}^{2}]_{i,k} }
 [ \Ddiv \left(
        \bar{\rho} \bar{\theta_v} \Dvect{u}
       \right) ]_{i,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6374}%
$\displaystyle + \frac{ \overline{\langle c_s \rangle^2}_{i,k} }{\langle c_p \rangle
 [ \bar{\theta_v} ]_{I,k} }
\Bigg[ \Dinv{\bar{\rho}_{i,k}} \sum [ M_{fall} (\rho_r) ]_{i,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6375}%
$\displaystyle + \Dinv{ \bar{\theta}_{i,k} }
    \left\{ \Dinv{\bar{\Pi}_{i,k}} 
     ( [Q_{cond}]_{i,k} + [Q_{rad}]_{i,k} + [Q_{dis}]_{i,k} )
  + [D_{\theta}]_{i,k} \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6376}%
$\displaystyle + \Dinv{ [\bar{q_d}]_{i,k}  \langle M \rangle / M_d
    + \sum [\bar{q_v}]_{i,k} \langle M \rangle / M_v}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6377}%
$\displaystyle \Bigg\{ \frac{\langle M \rangle}{M_d}
 \left( - \frac{ [\bar{q_d}]_{i,k}}{\bar{\rho}_{i,k}} 
  \sum [ M_{fall} (\rho_r) ]_{i,k} 
  + [ D_{q_d} ]_{i,k} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6378}%
$\displaystyle + \sum \frac{\langle M \rangle}{M_v}
 \left( - \frac{[\bar{q_v}]_{i,k}}{\bar{\rho}_{i,k}} 
  \sum [M_{fall} (\rho_r)]_{i,k} 
  + [M_{src} (q_v)]_{i,k} +  [ D_{q_v} ]_{i,k} \right)
\Bigg\}
\Bigg].$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6379}%
$\displaystyle \Deqlab{空間離散化された圧力方程式}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline758}%
$\overline{ \langle c_s \rangle}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6382}%
$\displaystyle \overline{ \langle c_s \rangle}_{i,k}^{2} 
    = \frac{\langle c_p \rangle \langle R \rangle}
       { \langle c_{v} \rangle} 
         \overline{\Pi}_{i,k} [\overline{\theta_{v}}]_{i,k}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6385}%
$\displaystyle \DP{\theta_{i,k}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6387}%
$\displaystyle - u_{i,k}\left[\DP{\theta}{x}\right]_{i,k}
                         - w_{i,k}\left[\DP{\theta}{z}\right]_{i,k}
                         - w_{i,k}\left[\DP{\overline{\theta}}{z}\right]_{i,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6388}%
$\displaystyle + \Dinv{\overline{\Pi}_{i,k}}
	\left([Q_{cond}]_{i,k} + [Q_{rad}]_{i,k} +
	 [Q_{dis}]_{i,k}\right)
         + \left[ D_{\theta} \right]_{i,k}
         + \left[ D_{\overline{\theta}}\right]_{i,k}
  \Deqlab{空間離散化された熱力学の式}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6391}%
$\displaystyle \DP{ [q_d]_{i,k}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6393}%
$\displaystyle - u_{i,k} \left[ \DP{q_d}{x} \right]_{i,k}
     - w_{i,k} \left[ \DP{q_d}{z} \right]_{i,k}
     - w_{i,k} \left[ \DP{\overline{q_d}}{z} \right]_{i,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6394}%
$\displaystyle - \frac{ [\overline{q_d}]_{i,k}}{\overline{\rho}_{i,k}} 
      \sum [ M_{fall} (\rho_r) ]_{i,k}
      + [ D_{q_d} ]_{i,k}, \Deqlab{quasi-equations:u-w-pi-theta:qd}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6395}%
$\displaystyle \DP{ [q_v]_{i,k}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6397}%
$\displaystyle - u_{i,k} \left[ \DP{q_v}{x} \right]_{i,k}
     - w_{i,k} \left[ \DP{q_v}{z} \right]_{i,k}
     - \overline{u}_{i,k} \left[ \DP{q_v}{x} \right]_{i,k}
     - w_{i,k} \left[ \DP{\overline{q_v}}{z} \right]_{i,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6398}%
$\displaystyle - \frac{ [\overline{q_v}]_{i,k}}{\overline{\rho}_{i,k}} 
     \sum [ M_{fall} (\rho_r) ]_{i,k}
     + \Dinv{\overline{\rho}_{i,k}} [ M_{src} (\rho_v) ]_{i,k}
     + [ D_{\overline{q_v}} ]_{i,k} + [D_{q_v}]_{i,k},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6399}%
$\displaystyle \Deqlab{quasi-equations:u-w-pi-theta:qv}
\DP{ [q_c]_{i,k}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6401}%
$\displaystyle - u_{i,k} \left[ \DP{q_c}{x} \right]_{i,k}
     - w_{i,k} \left[ \DP{q_c}{z} \right]_{i,k}
     - \frac{ [\overline{q_c}]_{i,k}}{\overline{\rho}_{i,k}} 
     \sum [ M_{fall} (\rho_r)]_{i,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6402}%
$\displaystyle + \Dinv{ \overline{\rho}_{i,k}} [M_{src} (\rho_c)]_{i,k}
     + [D_{q_c}]_{i,k},   \Deqlab{quasi-equations:u-w-pi-theta:qc}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6403}%
$\displaystyle \DP{ [q_r]_{i,k}}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6405}%
$\displaystyle - u_{i,k} \left[ \DP{q_r}{x} \right]_{i,k}
     - w_{i,k} \left[ \DP{q_r}{z} \right]_{i,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6406}%
$\displaystyle + \Dinv{\overline{\rho}_{i,k}} [ M_{fall} (\rho_r) ]_{i,k}
     + \Dinv{\overline{\rho}_{i,k}} [ M_{src} (\rho_r) ]_{i,k}
     + [ D_{q_r}]_{i,k}. \Deqlab{quasi-equations:u-w-pi-theta:qr}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline836}%
$1(u)\sim im(u)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline838}%
$2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6415}%
$\displaystyle u_{0(u), k} = u_{im(u), k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6416}%
$\displaystyle u_{-1(u), k} = u_{im-1(u), k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6417}%
$\displaystyle u_{im+1(u), k} = u_{1(u), k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6418}%
$\displaystyle u_{im+2(u), k} = u_{2(u), k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline840}%
$k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline842}%
$-1 \leq k \leq km + 2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6426}%
$\displaystyle u_{0(u),k} = u_{im(u),k} = 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6427}%
$\displaystyle u_{-1(u),k} = - u_{1(u),k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6428}%
$\displaystyle u_{im+1(u),k} = - u_{im-1(u),k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6429}%
$\displaystyle u_{im+2(u),k} = - u_{im-2(u),k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6431}%
$\displaystyle \Pi_{0,k} = - \Pi_{1,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6432}%
$\displaystyle \Pi_{-1,k} = - \Pi_{1,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6433}%
$\displaystyle \Pi_{im+1,k} = - \Pi_{im,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6434}%
$\displaystyle \Pi_{im+2,k} = - \Pi_{im-1,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6444}%
$\displaystyle \Pi_{0,k} =  \Pi_{1,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6445}%
$\displaystyle \Pi_{-1,k} =  \Pi_{1,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6446}%
$\displaystyle \Pi_{im+1,k} =  \Pi_{im,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6447}%
$\displaystyle \Pi_{im+2,k} =  \Pi_{im-1,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2280}%
$w, \Pi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2284}%
$\tau +\Delta \tau$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2288}%
$\Pi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2290}%
$u, \Pi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2292}%
$w$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2294}%
$F_u, F_w$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6462}%
$\displaystyle \DP{u_{i(u),k}}{t} = - \left[\langle c_p \rangle \bar{\theta}_{v} 
                       \DP{(\Pi - \alpha Div )}{x}\right]_{i(u),k} 
  + [F_{u}]_{i(u),k}^{t},
  \Deqlab{uwpi:u}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6463}%
$\displaystyle \DP{w_{i,k(w)}}{t} = - \left[\langle c_p \rangle \bar{\theta}_{v} 
                       \DP{(\Pi - \alpha Div )}{z}\right]_{i,k(w)} 
  + [F_{w}]_{i,k(w)}^{t},
  \Deqlab{uwpi:w}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6464}%
$\displaystyle \DP{\Pi_{i,k}}{t}  
  + \left[\frac{\overline{ \langle c_s \rangle}^{2}}
   {\langle c_p \rangle \bar{\rho} \bar{\theta}_{v}^{2}}
  \DP{(\bar{\rho} \bar{\theta}_{v} w)}{z}\right]_{i,k}
  = 
  -  \left[ \frac{\overline{ \langle c_s \rangle}^{2}}
   { \langle c_p \rangle \bar{\theta}_{v}}
      \DP{u}{x} \right]_{i,k}.
  \Deqlab{uwpi:pi}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2298}%
$\alpha Div$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2300}%
$F_{u}, F_{w}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6469}%
$\displaystyle [F_{u}]_{i(u),k}^{t} =
   - \left[{\rm Adv}.{u}\right]_{i(u),k}^{t}
   + \left[{\rm Turb}.{u}\right]_{i(u),k}^{t - \Delta t}
   + \left[{\rm Diff}.u\right]_{i(u),k}^{t - \Delta t}
  \Deqlab{uwpi:Fu}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6470}%
$\displaystyle \left[F_{w}\right]_{i,k(w)}^{t} =
   - \left[{\rm Adv}.{w}\right]_{i,k(w)}^{t}
   + [{\rm Buoy}]_{i,k(w)}^{t}
   + \left[{\rm Turb}.{w}\right]_{i,k(w)}^{t - \Delta t}.
   + \left[{\rm Diff}.w \right]_{i,k(w)}^{t - \Delta t}.
   \Deqlab{uwpi:Fw}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2302}%
$t$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6475}%
$\displaystyle u^{\tau + \Delta \tau}_{i(u),k}
  =  u^{\tau}_{i(u), k}
  -   \left[
  \langle c_p \rangle \bar{\theta}_{v} \Delta \tau
  \left\{
   \DP{\Pi^{\tau}}{x} 
   - \DP{(\alpha Div)^{\tau}}{x} 
  \right\}
 \right]_{i(u),k}
  + 
     F_{u,i(u),k}^{t} \Delta \tau
  \Deqlab{uwpi:u_sabun}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2312}%
$u^{\tau +\Delta \tau}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6483}%
$\displaystyle w^{\tau + \Delta \tau}_{i,k(w)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6485}%
$\displaystyle w^{\tau}_{i,k(w)}
  - \langle c_p \rangle \bar{\theta}_{v} \Delta \tau
  \left\{
   \beta \DP{\Pi^{\tau + \Delta \tau}}{z} 
   + (1 - \beta) \DP{\Pi^{\tau}}{z} 
   - \DP{(\alpha Div)^{\tau}}{z} 
  \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6486}%
$\displaystyle + F_{w,i,k(w)}^{t} \Delta \tau. 
 \Deqlab{uwpi:w_sabun}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6488}%
$\displaystyle \Pi^{\tau + \Delta \tau} 
 + \beta \frac{\bar{c_s}^{2}\Delta \tau}{\langle c_p \rangle \bar{\rho}
 \bar{\theta}_{v}^{2}} 
   \DP{(\bar{\rho} \bar{\theta}_{v} w^{\tau + \Delta \tau})}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6490}%
$\displaystyle \Pi^{\tau}
  - (1 - \beta) \frac{\bar{c_s}^{2}\Delta \tau}{\langle c_p \rangle
  \bar{\rho} \bar{\theta}_{v}^{2}} 
    \DP{(\bar{\rho} \bar{\theta}_{v} w^{\tau})}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6491}%
$\displaystyle -  \frac{\bar{c_s}^{2} \Delta \tau}{\langle c_p \rangle
  \bar{\theta}_{v}} \DP{u^{\tau + \Delta \tau}}{x}
 - \overline{u} \Delta \tau \DP{\Pi^{\tau}}{x}
 + H_{i,k}^{\tau} \Delta \tau.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6492}%
$\displaystyle \Deqlab{uwpi:pi_sabun}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6494}%
$\displaystyle H_{i,k}^{\tau}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6496}%
$\displaystyle \frac{\bar{c_s}^{2}}{\langle c_p \rangle \bar{\theta}_v}
   \Bigg[
    \Dinv{\bar{\rho}} \sum M_{fall}^{\tau}
    + \Dinv{\bar{\theta}} 
      \Bigg\{ \Dinv{\bar{\Pi}} 
       (Q_{cond}^{\tau} + Q_{rad}^{\tau} + Q_{dis}^{\tau}) 
       + D_{\theta}^{t - \Delta t}
      \Bigg\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6497}%
$\displaystyle \Dinv{\bar{q}_d 
     \langle M \rangle / M_d + \sum \bar{q}_v \langle M \rangle / M_v}
   \Bigg\{
    \frac{\langle M \rangle}{M_d}
     \Bigg( - \frac{\bar{q}_d}{\bar{\rho}} \sum M_{fall}^{\tau} 
       + D_{q_d}^{t - \Delta t } \Bigg)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6498}%
$\displaystyle + \sum \frac{\langle M \rangle}{M_v}
     \Bigg( - \frac{\bar{q}_v}{\bar{\rho}} \sum M_{fall}^{\tau} 
       + M_{src}^{\tau}(q_v) D_{q_v}^{t - \Delta t }
     \Bigg)    
   \Bigg\}
   \Bigg]_{i,k}
 \Deqlab{Hdef}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2314}%
$w^{\tau +
\Delta \tau}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6501}%
$\displaystyle \Pi^{\tau + \Delta \tau} 
  - 
  \beta^{2} 
  \frac{\bar{c_s}^{2}{\Delta \tau}^{2}}{\langle c_p \rangle \bar{\rho} 
  \bar{\theta}_{v}^{2}}
  \DP{}{z}
  \left\{
   \left(\langle c_p \rangle \bar{\rho} \bar{\theta}_{v}^{2}\right)
   \left(
     \DP{\Pi^{\tau + \Delta \tau}}{z} 
   \right)
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6503}%
$\displaystyle \Pi^{\tau}
  -(1 - \beta) 
 \frac{\bar{c_s}^{2}\Delta \tau}{\langle c_p \rangle \bar{\rho}
 \bar{\theta}_{v}^{2}} 
   \DP{(\bar{\rho} \bar{\theta}_{v} w^{\tau})}{z}
  -  \frac{\bar{c_s}^{2} \Delta \tau}{\langle c_p \rangle \bar{\theta}_{v}} 
  \DP{u^{\tau + \Delta \tau}}{x}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6504}%
$\displaystyle - \beta  \frac{\bar{c_s}^{2}\Delta \tau}{\langle c_p \rangle
  \bar{\rho} \bar{\theta}_{v}^{2}} 
   \left[
    \DP{}{z}
    \bar{\rho} \bar{\theta}_{v}
   \left\{
   w^{\tau}
  - \langle c_p \rangle \bar{\theta}_{v} \Delta \tau
  \left\{
    (1 - \beta) \DP{\Pi^{\tau}}{z} 
   - \DP{(\alpha Div)^{\tau}}{z} 
  \right\}
 + F_{w}^{t} \Delta \tau   
\right\}
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6505}%
$\displaystyle - \overline{u} \Delta \tau \DP{\Pi^{\tau}}{x}
 + H_{i,k}^{\tau} \Delta \tau.
\Deqlab{uwpi:sabun}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6507}%
$\displaystyle \left\{
   - \beta^{2}
  \left(
  \frac{\bar{c_s}^{2}{\Delta \tau}^{2}}{\langle c_p \rangle \bar{\rho}
  \bar{\theta}_{v}^{2}} 
  \right)_{k}
  \Dinv{\Delta z^{2}} 
  \left(
    \langle c_p \rangle \bar{\rho} \bar{\theta}_{v}^{2}
  \right)_{k(w)}
  \right\}
   \Pi^{\tau + \Delta \tau}_{i,k+1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6508}%
$\displaystyle \hspace{10mm}+ \left[
  1 + \beta^{2}
  \left(
   \frac{\bar{c_s}^{2}{\Delta \tau}^{2}}{\langle c_p \rangle \bar{\rho}
   \bar{\theta}_{v}^{2}} 
  \right)_{k}
  \Dinv{\Delta z^{2}} 
   \left\{
   \left(
   \langle c_p \rangle \bar{\rho} \bar{\theta}_{v}^{2} 
   \right)_{k(w)}
   + 
   \left(
   \langle c_p \rangle \bar{\rho} \bar{\theta}_{v}^{2} 
   \right)_{k-1(w)}
   \right\} 
    \right]
 \Pi^{\tau + \Delta \tau}_{i,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6509}%
$\displaystyle \hspace{10mm}+ \left\{
   - \beta^{2}
  \left(
   \frac{\bar{c_s}^{2}{\Delta \tau}^{2}}{\langle c_p \rangle \bar{\rho}
   \bar{\theta}_{v}^{2}} 
  \right)_{k}
  \Dinv{\Delta z^{2}} 
   \left(
    \langle c_p \rangle \bar{\rho} \bar{\theta}_{v}^{2} 
       \right)_{k-1(w)}
   \right\}
   \Pi^{\tau + \Delta \tau}_{i,k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6510}%
$\displaystyle = 
  \Pi^{\tau}_{i,k}
  - (1 - \beta)  
  \left(
   \frac{\bar{c_s}^{2}\Delta \tau}{\langle c_p \rangle \bar{\rho}
   \bar{\theta}_{v}^{2}} 
  \right)_{k}
  \left\{
    \DP{(\bar{\rho} \bar{\theta}_{v} w^{\tau})}{z}
  \right\}_{i,k}
   -\left(
     \frac{\bar{c_s}^{2} \Delta \tau}{\langle c_p \rangle \bar{\theta}_{v}} 
    \right)_{k}
  \left(
  \DP{u^{\tau + \Delta \tau}}{x} 
  \right)_{i,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6511}%
$\displaystyle \hspace{2mm} - \beta  
  \left(
   \frac{\bar{c_s}^{2}\Delta \tau}{\langle c_p \rangle \bar{\rho}
   \bar{\theta}_{v}^{2}} 
  \right)_{k}
   \left[
    \DP{}{z}
    \left( \bar{\rho} \bar{\theta}_{v} \right)_{i,k(w)} 
   \left\{
   w^{\tau}_{i,k(w)}
\right. \right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6512}%
$\displaystyle \left. \left.
  - \left( \langle c_p \rangle \bar{\theta}_{v} \right)_{i,k(w)} \Delta \tau
  \left\{
    (1 - \beta)  \DP{\Pi^{\tau}}{z}
   -  \DP{(\alpha Div)^{\tau}}{z} 
  \right\}_{i,k(w)}
 + \left( F_{w}^{t} \right)_{i,k(w)} \Delta \tau   
\right\}
\right]_{i,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6513}%
$\displaystyle - \left( \overline{u} \Delta \tau \DP{\Pi^{\tau}}{x} \right)_{i,k}
 + H_{i,k}^{\tau} \Delta \tau.
\Deqlab{uwpi:sabun_ik}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6517}%
$\displaystyle w(i,0(w)) = 0,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6518}%
$\displaystyle w(i,km(w)) = 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2318}%
$k(w) = 0(w)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6521}%
$\displaystyle \beta \left(
	\DP{\Pi^{\tau + \Delta \tau}}{z}  
       \right)_{i,0(w)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6523}%
$\displaystyle \left( \DP{(\alpha Div)^{\tau}}{z} \right)_{i,0(w)} 
  - (1 - \beta) \left( \DP{\Pi^{\tau}}{z} \right)_{i,0(w)} 
  + \left(\Dinv{\langle c_p \rangle \bar{\theta}_{v}}
     F_{w}^{t}\right)_{i,0(w)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6524}%
$\textstyle \equiv$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6525}%
$\displaystyle E_{i,0(w)}
  \Deqlab{uwpi:w_sabun_kabu}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6527}%
$\displaystyle \left\{
 - \beta^{2} 
  \left(
  \frac{\bar{c_s}^{2}{\Delta \tau}^{2}}{\langle c_p \rangle \bar{\rho}
  \bar{\theta}_{v}^{2}}
  \right)_{1}
  \Dinv{\Delta z^{2}}
   \left(
   \langle c_p \rangle \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{1(w)}
  \right\}
  \Pi^{\tau + \Delta \tau}_{i,2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6528}%
$\displaystyle + 
  \left\{
  1 + \beta^{2} 
  \left(
  \frac{\bar{c_s}^{2}{\Delta \tau}^{2}}{\langle c_p \rangle \bar{\rho}
  \bar{\theta}_{v}^{2}}
  \right)_{1}
  \Dinv{\Delta z^{2}}
   \left(
   \langle c_p \rangle \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{1(w)}
  \right\} \Pi^{\tau + \Delta \tau}_{i,1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6530}%
$\displaystyle \Pi^{\tau}_{i,1}
 -(1 - \beta)  
  \left(
   \frac{\bar{c_s}^{2}\Delta \tau}{\langle c_p \rangle \bar{\rho}
   \bar{\theta}_{v}^{2}} 
  \right)_{1}
  \left\{
  \DP{(\bar{\rho} \bar{\theta}_{v} w^{\tau})}{z}
  \right\}_{i,1}
  -  
  \left(
   \frac{\bar{c_s}^{2} \Delta \tau}{\langle c_p \rangle \bar{\theta}_{v}}
  \right)_{1}
  \left(
  \DP{u^{\tau + \Delta \tau}}{x}
  \right)_{i,1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6531}%
$\displaystyle - \beta  
  \left(
   \frac{\bar{c_s}^{2}\Delta \tau}{\langle c_p \rangle \bar{\rho}
   \bar{\theta}_{v}^{2}} 
  \right)_{1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6532}%
$\displaystyle \left[
    \DP{}{z}
    \bar{\rho} \bar{\theta}_{v}
   \left\{
   w^{\tau}
  - \langle c_p \rangle \bar{\theta}_{v} \Delta \tau
  \left\{
    (1 - \beta) \DP{\Pi^{\tau}}{z} 
   - \DP{(\alpha Div)^{\tau}}{z} 
  \right\}
 + F_{w}^{t} \Delta \tau   
\right\}
\right]_{i,1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6533}%
$\displaystyle - \beta
  \left(
  \frac{\bar{c_s}^{2}{\Delta \tau}^{2}}{\langle c_p \rangle \bar{\rho}
  \bar{\theta}_{v}^{2}} 
  \right)_{1}
  \Dinv{\Delta z} 
\left(
   \langle c_p \rangle \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{i,0(w)}
   E_{i,0(w)}
   - \left( \overline{u} \DP{\Pi^{\tau}}{x} \right)_{i,1} \Delta \tau
   + H_{i,1}^{\tau} \Delta \tau.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6534}%
$\displaystyle \Deqlab{uwpi:sabun_kabu}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2320}%
$k(w) = km(w)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6537}%
$\displaystyle \beta \left(
	\DP{\Pi^{\tau + \Delta \tau}}{z}  
      \right)_{i,km(w)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6539}%
$\displaystyle \left( \DP{(\alpha Div)^{\tau}}{z} \right)_{i,km(w)}
  - (1 - \beta) \left( \DP{\Pi^{\tau}}{z} \right)_{i,km(w)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6540}%
$\displaystyle + \left(\Dinv{\langle c_p \rangle \bar{\theta}_{v}}
     F_{w}^{t}\right)_{i,km(w)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6542}%
$\displaystyle E_{i,km(w)}
  \Deqlab{uwpi:w_sabun_joubu}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6544}%
$\displaystyle \left\{
   1 + 
  \beta^{2} 
  \left(
   \frac{\bar{c_s}^{2}{\Delta \tau}^{2}}{\langle c_p \rangle \bar{\rho}
   \bar{\theta}_{v}^{2}} 
  \right)_{km}
  \Dinv{\Delta z^{2}}
   \left(
   \langle c_p \rangle \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{km-1(w)}
  \right\}
    \Pi^{\tau + \Delta \tau}_{i,km}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6545}%
$\displaystyle + \left\{
  - \beta^{2} 
  \left(
   \frac{\bar{c_s}^{2}{\Delta \tau}^{2}}{\langle c_p \rangle \bar{\rho}
   \bar{\theta}_{v}^{2}} 
  \right)_{km}
  \Dinv{\Delta z^{2}}
   \left(
   \langle c_p \rangle \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{km-1(w)}
  \right\}
     \Pi^{\tau + \Delta \tau}_{i,km-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6547}%
$\displaystyle \Pi^{\tau}_{i,km}
-(1 - \beta)  
  \left(
   \frac{\bar{c_s}^{2}\Delta \tau}{\langle c_p \rangle \bar{\rho}
   \bar{\theta}_{v}^{2}} 
  \right)_{km}
  \left\{
    \DP{(\bar{\rho} \bar{\theta}_{v} w^{\tau})}{z}
  \right\}_{i,km}
-  
  \left(
   \frac{\bar{c_s}^{2} \Delta \tau}{\langle c_p \rangle \bar{\theta}_{v}} 
  \right)_{km}
  \left(
    \DP{u^{\tau + \Delta \tau}}{x}
  \right)_{i,km}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6548}%
$\displaystyle - \beta  
  \left(
   \frac{\bar{c_s}^{2}\Delta \tau}{\langle c_p \rangle \bar{\rho}
   \bar{\theta}_{v}^{2}} 
  \right)_{km}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6549}%
$\displaystyle \left[
    \DP{}{z}
    \bar{\rho} \bar{\theta}_{v}
   \left\{
   w^{\tau}
  - \langle c_p \rangle \bar{\theta}_{v} \Delta \tau
  \left\{
    (1 - \beta) \DP{\Pi^{\tau}}{z} 
   - \DP{(\alpha Div)^{\tau}}{z} 
  \right\}
 + F_{w}^{t} \Delta \tau   
\right\}
\right]_{i,km}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6550}%
$\displaystyle + \frac{\beta}{\Delta z}
  \left(
  \frac{\bar{c_s}^{2}{\Delta \tau}^{2}}{\langle c_p \rangle \bar{\rho}
  \bar{\theta}_{v}^{2}}   
  \right)_{km}
   \left(
   \langle c_p \rangle \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{km(w)}
   E_{i,km(w)} 
   - \left( \overline{u} \DP{\Pi^{\tau}}{x} \right)_{i,km} \Delta \tau
   + H_{i,km}^{\tau} \Delta \tau.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6551}%
$\displaystyle \Deqlab{uwpi:sabun_joubu}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6554}%
$\displaystyle \left(\begin{array}{cccc}
          A_{1} &amp; B_{2}  &amp;        &amp;   0      \\  
          C_{1} &amp; \ddots &amp; \ddots &amp;          \\ 
	 &amp; \ddots &amp; \ddots &amp; B_{km}   \\ 
            0   &amp;        &amp; C_{km-1} &amp; A_{km} \\ 
        \end{array}
  \right)
  \left(\begin{array}{cccc}
          \Pi_{1,1} &amp; \Pi_{2,1}  &amp; \cdots &amp; \Pi_{im,1} \\ 
          \Pi_{1,2} &amp; \ddots    &amp; \ddots &amp; \vdots        \\ 
          \vdots   &amp;           &amp; \ddots &amp; \vdots        \\ 
          \Pi_{1, km} &amp; \cdots &amp; \cdots &amp; \Pi_{im, km} \\ 
        \end{array}
  \right)^{\tau + \Delta \tau}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6555}%
$\displaystyle = 
  \left(\begin{array}{cccc}
   D_{1,1} &amp; D_{2,1}  &amp; \cdots &amp; D_{im,1} \\ 
   D_{1,2} &amp; \ddots    &amp; \ddots &amp; \vdots        \\ 
        \vdots   &amp;           &amp; \ddots &amp; \vdots        \\ 
   D_{1,km} &amp; \cdots &amp; \cdots &amp; D_{im,km} \\ 
        \end{array}
  \right)^{\tau}
  .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6558}%
$\displaystyle A_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6560}%
$\displaystyle 1 + \beta^{2}
  \left(
  \frac{\bar{c_s}^{2}{\Delta \tau}^{2}}{\langle c_p \rangle \bar{\rho}
  \bar{\theta}_{v}^{2}} 
  \right)_{k}
  \Dinv{\Delta z^{2}} 
   \left\{
   \left(
   \langle c_p \rangle \bar{\rho} \bar{\theta}_{v}^{2} 
   \right)_{k(w)}
   + 
   \left(
   \langle c_p \rangle \bar{\rho} \bar{\theta}_{v}^{2} 
   \right)_{k-1(w)}
   \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6561}%
$\displaystyle (k = 2, 3, \cdots km-1),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6562}%
$\displaystyle A_{1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6564}%
$\displaystyle 1 + \beta^{2}
  \left(
  \frac{\bar{c_s}^{2}{\Delta \tau}^{2}}{\langle c_p \rangle \bar{\rho}
  \bar{\theta}_{v}^{2}} 
  \right)_{1}
  \Dinv{\Delta z^{2}} 
   \left(
   \langle c_p \rangle \bar{\rho} \bar{\theta}_{v}^{2} 
   \right)_{1(w)},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6565}%
$\displaystyle A_{km}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6567}%
$\displaystyle 1 + \beta^{2}
  \left(
  \frac{\bar{c_s}^{2}{\Delta \tau}^{2}}{\langle c_p \rangle \bar{\rho}
  \bar{\theta}_{v}^{2}} 
  \right)_{km}
  \Dinv{\Delta z^{2}} 
   \left(
   \langle c_p \rangle \bar{\rho} \bar{\theta}_{v}^{2} 
   \right)_{km-1(w)},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6568}%
$\displaystyle B_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6570}%
$\displaystyle - \beta^{2}
  \left(
   \frac{\bar{c_s}^{2}{\Delta \tau}^{2}}{\langle c_p \rangle \bar{\rho}
   \bar{\theta}_{v}^{2}} 
  \right)_{k-1}
  \Dinv{\Delta z^{2}} 
  \left(
   \langle c_p \rangle \bar{\rho} \bar{\theta}_{v}^{2}
  \right)_{k-1(w)},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6571}%
$\displaystyle (k = 2, 3, \cdots km),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6572}%
$\displaystyle C_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6574}%
$\displaystyle - \beta^{2}
  \left(
   \frac{\bar{c_s}^{2}{\Delta \tau}^{2}}{\langle c_p \rangle \bar{\rho}
   \bar{\theta}_{v}^{2}} 
  \right)_{k+1}
  \Dinv{\Delta z^{2}} 
   \left(
    \langle c_p \rangle \bar{\rho} \bar{\theta}_{v}^{2} 
       \right)_{k(w)},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6575}%
$\displaystyle (k = 1, 2, \cdots km-1),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6576}%
$\displaystyle D_{i,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6578}%
$\displaystyle \Pi^{\tau}_{i,k}
   -(1 - \beta)  
  \left(
   \frac{\bar{c_s}^{2}\Delta \tau}{\langle c_p \rangle \bar{\rho}
   \bar{\theta}_{v}^{2}} 
  \right)_{k}
  \left\{
    \DP{(\bar{\rho} \bar{\theta}_{v} w^{\tau})}{z}
  \right\}_{i,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6579}%
$\displaystyle -\left(
     \frac{\bar{c_s}^{2} \Delta \tau}{\langle c_p \rangle \bar{\theta}_{v}} 
    \right)_{k}
  \left(
  \DP{u^{\tau + \Delta \tau}}{x} 
  \right)_{i,k}
+ F_{i,k}
  \hspace{20mm} (k = 2, 3,  \cdots km-1),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6580}%
$\displaystyle D_{i,1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6582}%
$\displaystyle \Pi^{\tau}_{i,1}
 -(1 - \beta)  
  \left(
   \frac{\bar{c_s}^{2}\Delta \tau}{\langle c_p \rangle \bar{\rho}
   \bar{\theta}_{v}^{2}} 
  \right)_{1}
  \left\{
    \DP{(\bar{\rho} \bar{\theta}_{v} w^{\tau})}{z}
  \right\}_{i,1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6583}%
$\displaystyle -  
  \left(
   \frac{\bar{c_s}^{2} \Delta \tau}{\langle c_p \rangle \bar{\theta}_{v}}
  \right)_{1}
  \left(
  \DP{u^{\tau + \Delta \tau}}{x}
  \right)_{i,1} 
+ F_{i,1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6584}%
$\displaystyle - \beta
  \left(
  \frac{\bar{c_s}^{2}{\Delta \tau}^{2}}{\langle c_p \rangle \bar{\rho}
  \bar{\theta}_{v}^{2}}
  \right)_{1}
  \Dinv{\Delta z} 
   \left(
   \langle c_p \rangle \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{i,0(w)}
   E_{i,0(w)},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6585}%
$\displaystyle D_{i,km}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6587}%
$\displaystyle \Pi^{\tau}_{i,km}
  -(1 - \beta)  
  \left(
   \frac{\bar{c_s}^{2}\Delta \tau}{\langle c_p \rangle \bar{\rho}
   \bar{\theta}_{v}^{2}} 
  \right)_{km}
  \left\{
   \DP{(\bar{\rho} \bar{\theta}_{v} w^{\tau})}{z}
  \right\}_{i,km}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6588}%
$\displaystyle -  
  \left(
   \frac{\bar{c_s}^{2} \Delta \tau}{\langle c_p \rangle \bar{\theta}_{v}} 
  \right)_{km}
  \left(
  \DP{u^{\tau + \Delta \tau}}{x}
  \right)_{i,km} 
+ F_{i,km}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6589}%
$\displaystyle + \beta
  \left(
  \frac{\bar{c_s}^{2}{\Delta \tau}^{2}}{\langle c_p \rangle \bar{\rho}
  \bar{\theta}_{v}^{2}} 
  \right)_{km}
  \Dinv{\Delta z}
   \left(
   \langle c_p \rangle \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{km(w)}
   E_{i,km(w)}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6591}%
$\displaystyle E_{i,k(w)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6593}%
$\displaystyle \left( \DP{(\alpha Div)^{\tau}}{z} \right)_{i,k(w)}
  - (1 - \beta) \left( \DP{\Pi^{\tau}}{z} \right)_{i,k(w)}
  + \left(\Dinv{\langle c_p \rangle \bar{\theta}_{v}}
     F_{w}^{t}\right)_{i,k(w)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6594}%
$\displaystyle F_{i,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6596}%
$\displaystyle - \beta  
  \left(
   \frac{\bar{c_s}^{2}\Delta \tau}{\langle c_p \rangle \bar{\rho}
   \bar{\theta}_{v}^{2}} 
  \right)_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6597}%
$\displaystyle \Bigg[
    \DP{}{z}
    \left( \bar{\rho} \bar{\theta}_{v} \right)_{i,k(w)} 
   \Bigg\{
   w^{\tau}_{i,k(w)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6598}%
$\displaystyle - \left( \langle c_p \rangle \bar{\theta}_{v} \right)_{i,k(w)} \Delta
  \tau 
  \left\{
    (1 - \beta)  \DP{\Pi^{\tau}}{z}
   -  \DP{(\alpha Div)^{\tau}}{z} 
  \right\}_{i,k(w)} 
 + \left( F_{w}^{t} \right)_{i,k(w)} \Delta \tau   
\Bigg\}
\Bigg]_{i,k}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6599}%
$\displaystyle - \left( \overline{u} \DP{\Pi^{\tau}}{x} \right)_{i,k} \Delta \tau
 + H_{i,k}^{\tau}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6604}%
$\displaystyle + \sum \frac{\langle M \rangle}{M_v}
     \Bigg( - \frac{\bar{q}_v}{\bar{\rho}} \sum M_{fall}^{\tau} 
       + M_{src}^{\tau}(q_v) D_{q_v}^{t - \Delta t }
     \Bigg)    
   \Bigg\}
   \Bigg]_{i,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6607}%
$\displaystyle F_{u,i(u),k}^{t} =
   - \left[ {\rm Adv}.u \right]_{i(u),k}^{t} 
   + \left[{\rm Turb}.{u} \right]_{i(u),k}^{t-\Delta t}
   + \left[{\rm Diff}.u \right]_{i(u),k}^{t-\Delta t}, 
  \Deqlab{uwpi:Fu2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6608}%
$\displaystyle F_{w,i,k(w)}^{t} =
   - \left[ {\rm Adv}.w \right]_{i(u),k}^{t}
   + \left[ {\rm Buoy} \right]_{i, k(w)}^{t} 
   + \left[ {\rm Turb}.{w} \right]_{i,k(w)}^{t - \Delta t}
   + \left[ {\rm Diff}.w \right]_{i,k(w)}^{t - \Delta t}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6609}%
$\displaystyle \Deqlab{uwpi:Fw2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6611}%
$\displaystyle \left[ {\rm Adv}.{u} \right]_{i(u),k}^{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6613}%
$\displaystyle u_{i(u),k}^{t} \left[\DP{u}{x}\right]_{i(u),k}^{t}
   + w_{i(u),k}^{t} \left[\DP{u}{z}\right]_{i(u),k}^{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6614}%
$\displaystyle + \overline{u}_{i(u),k} \left[\DP{u}{x}\right]_{i(u),k}^{t} 
   + w_{i(u),k}^{t} \left[\DP{\overline{u}}{z}\right]_{i(u),k},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6615}%
$\displaystyle \left[ {\rm Adv}.{w} \right]_{i,k(w)}^{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6617}%
$\displaystyle u_{i,k(w)}^{t} \left[\DP{w}{x}\right]_{i,k(w)}^{t}
   + w_{i,k(w)}^{t} \left[\DP{w}{z}\right]_{i,k(w)}^{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6618}%
$\displaystyle + \overline{u}_{i,k(w)} \left[\DP{w}{x}\right]_{i,k(w)}^{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6620}%
$\displaystyle [{\rm Buoy}]^{t}_{i,k(w)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6622}%
$\displaystyle g \frac{\theta_{i,k(w)}^{t}}{\overline{\theta}_{i,k(w)}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6623}%
$\displaystyle + g 
  \frac{[q_d]_{i,k(w)}^{t} \langle M \rangle / M_d 
        + \sum [q_v]_{i,k(w)}^{t} \langle M \rangle / M_v }
       {[\overline{q_d}]_{i,k(w)} \langle M \rangle / M_d 
        + \sum [\overline{q_v}]_{i,k(w)}^{t} \langle M \rangle / M_v }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6625}%
$\displaystyle \left[ {\rm Turb}.{u} \right]_{i(u),k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6627}%
$\displaystyle 2 \left[ 
      \DP{}{x}\left\{ 
          \left( K_{m} \right)_{i,k} \left( \DP{u}{x} \right)_{i,k}
       \right\} 
    \right]_{i(u),k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6628}%
$\displaystyle +\left[ \DP{}{z}\left\{
       \left( K_{m} \right)_{i(u),k(w)}
       \left( \DP{w}{x} \right)_{i(u),k(w)}
     + \left( K_{m} \right)_{i(u),k(w)}
       \left( \DP{u}{z} \right)_{i(u),k(w)}
     \right\} \right]_{i(u),k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6629}%
$\displaystyle - \frac{2}{3 C_{m}^{2} l^{2}} 
     \left( \DP{ K_{m}^{2} }{x} \right)_{i(u),k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6630}%
$\displaystyle \left[ {\rm Turb}.{w} \right]_{i,k(w)}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6632}%
$\displaystyle 2 \left[ 
      \DP{}{z}\left\{ 
          \left( K_{m} \right)_{i,k} \left( \DP{w}{z} \right)_{i,k}
       \right\} 
    \right]_{i,k(w)}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6633}%
$\displaystyle +\left[ \DP{}{x}\left\{
       \left( K_{m} \right)_{i(u),k(w)}
       \left( \DP{w}{x} \right)_{i(u),k(w)}
     + \left( K_{m} \right)_{i(u),k(w)}
       \left( \DP{u}{z} \right)_{i(u),k(w)}
     \right\} \right]_{i,k(w)}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6634}%
$\displaystyle - \frac{2}{3 C_{m}^{2} l^{2}} 
     \left( \DP{ K_{m}^{2} }{z} \right)_{i,k(w)}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6636}%
$\displaystyle \left[ {\rm Diff}.u \right]_{i(u),k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6638}%
$\displaystyle \nu_{h} \left\{ \DP{}{x} \left(\DP{u}{x}\right)_{i,k} \right\}_{i(u),k}^{t - \Delta t}
   + \nu_{v} \left\{ \DP{}{z} \left(\DP{u}{z}\right)_{i(u),k(w)} \right\}_{i(u),k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6639}%
$\displaystyle \left[ {\rm Diff}.w \right]_{i,k(w)}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6641}%
$\displaystyle \nu_{h} \left\{ \DP{}{x} \left(\DP{w}{x}\right)_{i(u),k(w)} \right\}_{i,k(w)}^{t - \Delta t}
   + \nu_{v} \left\{ \DP{}{z} \left(\DP{w}{z}\right)_{i,k} \right\}_{i,k(w)}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2324}%
$K_{m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2326}%
$\nu_{h}, \nu_{v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6645}%
$\displaystyle \nu_{h} = \frac{\alpha_{h} \Delta x^{2}}{\Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6646}%
$\displaystyle \nu_{v} = \frac{\alpha_{v} \Delta z^{2}}{\Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2328}%
$\Delta x, \Delta z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2330}%
$\alpha_{h}, \alpha_{v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6650}%
$\displaystyle \alpha_{h}  \le \Dinv{8}, \hspace{3em}
  \alpha_{v}  \le \Dinv{8} 
\Deqlab{nu}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3058}%
$F$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6655}%
$\displaystyle \theta_{i,k}^{t + \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6657}%
$\displaystyle \theta_{i,k}^{t - \Delta t} + 2 \Delta t  [F_{\theta}]_{i,k}^{t}
\Deqlab{risan:time-div_theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6658}%
$\displaystyle \left[ q_{v} \right]_{i,k}^{t+\Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6660}%
$\displaystyle \left[ q_{v} \right]_{i,k}^{t-\Delta t}
 + 2 \Delta t [F_{q_{v}}]_{i,k}^{t}
\Deqlab{risan:time-div_qv}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6661}%
$\displaystyle \left[ q_{c} \right]_{i,k}^{t+\Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6663}%
$\displaystyle \left[ q_{c} \right]_{i,k}^{t-\Delta t}
 + 2 \Delta t [F_{q_{c}}]_{i,k}^{t}
\Deqlab{risan:time-div_qc}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6664}%
$\displaystyle \left[ q_{r} \right]_{i,k}^{t+\Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6666}%
$\displaystyle \left[ q_{r} \right]_{i,k}^{t-\Delta t}
 + 2 \Delta t [F_{q_{r}}]_{i,k}^{t}
\Deqlab{risan:time-div_qr}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6668}%
$\displaystyle [F_{\theta}]_{i,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6670}%
$\displaystyle - \left[{\rm Adv}.{\theta}\right]_{i,k}^{t}
  - \left[{\rm Adv}.{\bar{\theta}}\right]_{i,k}^{t}
  + \left[{\rm Turb}.{\theta} \right]_{i,k}^{t - \Delta t} 
  + \left[{\rm Turb}.{\bar{\theta}} \right]_{i,k}^{t - \Delta t} 
  + \left[{\rm Diff}.{\theta} \right]_{i,k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6671}%
$\displaystyle + [Q_{cnd}]_{i,k}^{t} 
   + [Q_{rad}]_{i,k}^{t-\Delta t} 
   + [Q_{dis}]_{i,k}^{t-\Delta t} 
  \Deqlab{Ftheta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6672}%
$\displaystyle \left[F_{q_{v}}\right]_{i,k}^{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6674}%
$\displaystyle - \left[ {\rm Adv}.q_{v} \right]_{i,k}^{t}
  - \left[ {\rm Adv}.\bar{q_{v}} \right]_{i,k}^{t}
  + \left[ {\rm Turb}.q_{v} \right]_{i,k}^{t - \Delta t}
  + \left[ {\rm Turb}.\bar{q_{v}} \right]_{i,k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6675}%
$\displaystyle + \left[ {\rm Diff}.q_{v} \right]_{i,k}^{t - \Delta t}
  + \left[ EV_{rv} \right]_{i,k}^{t}
\Deqlab{risan:time-div_qv2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6676}%
$\displaystyle \left[F_{q_{c}}\right]_{i,k}^{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6678}%
$\displaystyle - \left[ {\rm Adv}.q_{c} \right]_{i,k}^{t}
  + \left[ {\rm Turb}.q_{c} \right]^{t-\Delta t}
  + \left[ {\rm Diff}.q_{c} \right]^{t-\Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6679}%
$\displaystyle - \left[ CN_{cr} + CL_{cr} \right]_{i,k}^{t}
\Deqlab{risan:time-div_qc2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6680}%
$\displaystyle \left[F_{q_{r}}\right]_{i,k}^{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6682}%
$\displaystyle - \left[ {\rm Adv}.q_{r} \right]_{i,k}^{t}
  + \left[ {\rm Turb}.q_{r} \right]_{i,k}^{t-\Delta t}
  + \left[ {\rm Diff}.q_{c} \right]^{t-\Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6683}%
$\displaystyle + \left[CN_{cr} + CL_{cr} - EV_{rv} \right]_{i,k}^{t}
  + \left[ PR_{r} \right]_{i,k}^{t}
\Deqlab{risan:time-div_qr2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3060}%
$CN_{vc}, EV_{cv}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3062}%
$\theta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3064}%
$q_{v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3066}%
$q_{c}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3068}%
$q_{r}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6691}%
$\displaystyle \left[{\rm Adv}.{\phi}\right]_{i,k}^{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6693}%
$\displaystyle \left[
         u_{i(u),k}  \left[ \DP{\phi}{x} \right]_{i(u),k} 
      \right]_{i,k}^{t}
      + 
      \left[
         w_{i,k(w)} \left[ \DP{\phi}{z} \right]_{i,k(w)} 
      \right]_{i,k}^{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6695}%
$\displaystyle \left[{\rm Adv}.{\bar{\phi}}\right]_{i,k}^{t} =
      \left[
         w_{i,k(w)} \left[ \DP{\overline{\phi}}{z} \right]_{i,k(w)} 
      \right]_{i,k}^{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6697}%
$\displaystyle \left[{\rm Turb}.{\phi} \right]_{i,k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6699}%
$\displaystyle \left[ \DP{}{x} 
      \left\{
         \left( K_{h} \right)_{i(u),k}
         \left( \DP{\phi}{x} \right)_{i(u),k}
       \right\}
   \right]_{i,k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6700}%
$\displaystyle + \left[ \DP{}{z}\left\{
       \left( K_{h} \right)_{i,k(w)}
       \left( \DP{\phi }{z} \right)_{i,k(w)}
     \right\} \right]_{i,k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6702}%
$\displaystyle \left[{\rm Turb}.{\bar{\phi}} \right]_{i,k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6704}%
$\displaystyle \left[ \DP{}{z}\left\{
       \left( K_{h} \right)_{i,k(w)}
       \left( \DP{\overline{\phi}}{z} \right)_{i,k(w)}
     \right\} \right]_{i,k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6706}%
$\displaystyle \left[ {\rm Diff}_{\phi} \right]_{i,k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6708}%
$\displaystyle \nu_{h} \left\{ \DP{}{x} \left(\DP{\phi}{x}\right)_{i(u),k} \right\}_{i,k}^{t - \Delta t}
   + \nu_{v} \left\{ \DP{}{z} \left(\DP{\phi}{z}\right)_{i,k(w)} \right\}_{i,k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3072}%
$K_{h}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3076}%
$Q_{cnd}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2662}%
\begin{displaymath}
 [Q_{cnd}]_{i,k}^{t} 
  = - \left[ \frac{L}{{c_{p} \bar{\Pi}}_{d} \bar{\Pi}} EV_{rv} \right]_{i,k}^{t} 
  = - \frac{L}{{c_{p}}_{d} \bar{\Pi}} 
  \left\{
   4.85 \times 10^{-2} ([q_{vsw}]_{i,k}^{t} - [q_{v}]_{i,k}^{t}) 
    (\bar{\rho}_{i,k} [q_{r}]_{i,k})^{0.65}
  \right\}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3078}%
$Q_{dis}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2692}%
\begin{displaymath}
  [Q_{dis}]_{i,k}^{t-\Delta t} 
   = \frac{1}{{c_{p}}_{d} \bar{\Pi}}
   \frac{C_{\varepsilon}}{l}
            \frac{(K_{m,i,k}^{t-\Delta t})^{3}}{(C_{m}l)^{3}}
   = \frac{1}{{c_{p}}_{d} \bar{\Pi}}
   \frac{(K_{m,i,k}^{t-\Delta t})^{3}}{{C_{m}}^{2} l^{4}}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3080}%
$l=(\Delta x\Delta z)^{1/2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3082}%
$[Q_{rad}]_{i,k}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3084}%
$CN_{cr}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3086}%
$CL_{cr}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6720}%
$\displaystyle [CN_{cr}]_{i,k}^{t} = (q_{c,i,k}^{t} - q_{c0})/\tau _{ac}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6721}%
$\displaystyle \left[ CL_{cr} \right]_{i,k}^{t}
   = 2.2   [q_{c}]_{i,k}^{t} 
   \left(
    [\bar{\rho}]_{i,k}
     \left[ q_{r} \right]_{i,k}^{t}
   \right)^{0.875}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3088}%
$EV_{rv}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6724}%
$\displaystyle \left[ EV_{rv} \right]_{i,k}^{t} = 
 4.85 \times 10^{-2} ([q_{vsw}]_{i,k}^{t} - [q_{v}]_{i,k}^{t})
 ([\bar{\rho}]_{i,k} [q_{r}]_{i,k}^{t})^{0.65}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3090}%
$PR_{r}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6727}%
$\displaystyle \left[
      PR_{r}
     \right]_{i,k}^{t} 
  = \Dinv{[\bar{\rho}]_{i,k}} \DP{}{z}([\bar{\rho}]_{i,k}
  [U_{r}]_{i,k}^{t} 
  [q_{r}]_{i,k}^{t}).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6728}%
$\displaystyle [U_{r}]_{i,k}^{t} = 12.2 ([q_{r}]_{i,k}^{t})^{0.125}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3092}%
$-CN_{vc} + EV_{cv}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3094}%
$dS=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3096}%
$\mu_{vapar} = \mu_{condensed phase}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3098}%
$\mu$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3100}%
$*$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3102}%
$[\theta]^{*}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3104}%
$[q_{v}]^{*}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3106}%
$[q_{c}]^{*}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3108}%
$[q_{r}]^{*}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6741}%
$\displaystyle \Delta q_{c} = MAX\{0, [q_{v}]^{*} - q_{vsw}([\theta]^{*})\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3110}%
$\Delta q_{c} &gt; 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3112}%
$q_{c}^{*} &gt; 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6748}%
$\displaystyle \left[ \theta \right]^{t + \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6750}%
$\displaystyle \theta^{*} + 
  \frac
  { \gamma ( [q_{v}]^{*} -  q_{vsw}([\theta]^{*})) }
  { 1 + \gamma \DP{q_{vsw}([\theta]^{*})}{\theta} }
\Deqlab{moistajst_theta1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6751}%
$\displaystyle \left[ q_{v} \right]^{t + \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6753}%
$\displaystyle [q_{v}]^{*} + \frac{[\theta]^{*} - [\theta]^{t + \Delta t}}{\gamma},
\Deqlab{moistajst_qv1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6754}%
$\displaystyle \left[ q_{c} \right]^{t + \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6756}%
$\displaystyle [q_{v}]^{*} + [q_{c}]^{*} - [q_{v}]^{t + \Delta t} .
\Deqlab{moistajst_qc1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3120}%
$\gamma = L_{v}/(c_{p} \Pi)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3122}%
$[q_c]^{t + \Delta t} &gt; 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3126}%
$q_{c}^{t + \Delta t} &lt; 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6762}%
$\displaystyle \left[ \theta \right]^{t + \Delta t} = 
  [\theta]^{*}  - \gamma [q_{c}]^{*},
  \Deqlab{moistajst_theta2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6763}%
$\displaystyle \left[ q_{v} \right]^{t + \Delta t},
  = [q_{v}]^{*} + [q_{c}]^{*}
  \Deqlab{moistajst_qv2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6764}%
$\displaystyle \left[ q_{c} \right]^{t + \Delta t} 
  = 0
 \Deqlab{moistajst_qc2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6767}%
$\displaystyle {\rm NH_{3}} + {\rm H_{2}S} \rightarrow {\rm NH_{4}SH}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6769}%
$\displaystyle K_{p} 
  \equiv  \ln(p_{\rm NH_{3}} \cdot p_{\rm H_{2}S}) 
  = 61.781 - \frac{10834}{T}  - \ln{10^{2}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3128}%
$T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3130}%
$_{4}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3132}%
$X$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6774}%
$\displaystyle (p_{\rm NH_{3}} - X) ( p_{\rm H_{2}S} - X )
  = e^{k_{p}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6775}%
$\displaystyle X^{2} - (p_{\rm NH_{3}} + p_{\rm H_{2}S}) X  
  +  p_{\rm NH_{3}} \cdot p_{\rm H_{2}S}
  - e^{k_{p}} = 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6777}%
$\displaystyle X = \Dinv{2} 
  \left\{ 
   (p_{\rm NH_{3}} + p_{\rm H_{2}S}) 
   \pm \sqrt{   (p_{\rm NH_{3}} + p_{\rm H_{2}S})^{2} 
   - 4 (p_{\rm NH_{3}} \cdot p_{\rm H_{2}S} - e^{K_{p}}) }
  \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6778}%
$\displaystyle X = \Dinv{2} 
  \left\{ 
   (p_{\rm NH_{3}} + p_{\rm H_{2}S}) 
   \pm \sqrt{   (p_{\rm NH_{3}} - p_{\rm H_{2}S})^{2} 
   + 4 e^{K_{p}} }
  \right\} 
  \Deqlab{def_X_NH4SH}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3134}%
$\exp{(K_{p})} \approx 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6783}%
$\displaystyle X = {\rm min}(P_{\rm NH_3}, P_{\rm H_{2}S} )$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3140}%
$P_{\rm NH_3} &gt; P_{\rm H_{2}S}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3142}%
$X =  P_{\rm H_{2}S}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6789}%
$\displaystyle X = \Dinv{2} 
  \left\{ 
   (p_{\rm NH_{3}} + p_{\rm H_{2}S}) 
   - \sqrt{   (p_{\rm NH_{3}} - p_{\rm H_{2}S})^{2} 
   + 4 e^{K_{p}} }.
  \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6792}%
$\displaystyle 0 \leq X \leq {\rm min}(P_{\rm NH_{3}}, P_{\rm H_{2}S}) 
\Deqlab{NH4SH-condition}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3150}%
$X = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6799}%
$\displaystyle \left[ q_{\rm NH_3} \right]^{t + \Delta t}
 = [q_{\rm NH_3}]^{*} + \Delta q_{\rm NH_3},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6800}%
$\displaystyle \left[ q_{\rm H_2S} \right]^{t + \Delta t}
  = [q_{\rm H_2S}]^{*} + \Delta q_{\rm H_2S},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6801}%
$\displaystyle \left[ q_{\rm NH_4SH} \right]^{t + \Delta t}
  = [q_{\rm NH_3}]^{*} + [q_{\rm H_2S}]^{*}
  - [q_{\rm NH_3}]^{t + \Delta t} - [q_{\rm H_2S}]^{t + \Delta t} ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6802}%
$\displaystyle \left[ \theta \right]^{t + \Delta t} 
  = 
  \theta^{*} + \gamma \left([q_{\rm NH_3}]^{*} + [q_{\rm H_2S}]^{*}
  - [q_{\rm NH_3}]^{t + \Delta t} - [q_{\rm H_2S}]^{t + \Delta t} 
\right).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3160}%
$\gamma = L_{\rm NH_4SH}/({c_{p}}_{d} \Pi)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3162}%
$\Delta q_{\rm NH_3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3164}%
$\Delta q_{\rm H_2S}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3168}%
$_3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3170}%
$_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6811}%
$\displaystyle [E_{turb}]_{i,k}^{t + \Delta t} = [E_{turb}]_{i,k}^{t - \Delta t}  
  + 2 \Delta t [F_{E_{turb}}]_{i,k}^{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6813}%
$\displaystyle [F_{E_{turb}}]_{i,k}^{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6815}%
$\displaystyle - [{\rm Adv}.E_{turb}]_{i,k}^{t} 
  + [{\rm Buoy}.E_{turb}]_{i,k}^{t - \Delta t}  
  + [{\rm Shear}.E_{turb}]_{i,k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6816}%
$\displaystyle + [{\rm Turb}.E_{turb}]_{i,k}^{t - \Delta t}  
  + [{\rm Disp}.E_{turb}]_{i,k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3563}%
$t - \Delta t$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3565}%
$F_{E_{turb}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6821}%
$\displaystyle [{\rm Adv}.E_{turb}]_{i,k}^{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6823}%
$\displaystyle \left\{
        u_{i(u),k} \left( \DP{E_{turb}}{x} \right)_{i(u), k} 
     \right\}_{i,k}^{t} 
    + 
    \left\{
        w_{i,k(w)} \left( \DP{E_{turb}}{z} \right)_{i, k(w)} 
     \right\}_{i,k}^{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6824}%
$\displaystyle \left[{\rm Buoy}.E_{turb}\right]_{i,k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6826}%
$\displaystyle - \left\{
      \frac{3 g C_{m} l}{ 2 \overline{\theta_{v}}} 
       E_{turb_{i,k}}
      \left(\DP{\theta_{el}}{z} \right)_{i,k(w)}
     \right\}_{i,k}^{t-\Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6827}%
$\displaystyle \left[{\rm Shear}.K_m\right]_{i,k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6829}%
$\displaystyle 2 C_m l [E_{turb}^{1/2}]_{i,k}^{t - \Delta t} 
    \left\{ 
      \left[
       \left( \DP{u}{x} \right)^{2} 
      \right]_{i,k}^{t - \Delta t}
      +
      \left[
       \left( \DP{w}{z} \right)^{2}
      \right]_{i,k}^{t - \Delta t}
    \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6830}%
$\displaystyle + C_m l [E_{turb}^{1/2}]_{i,k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6831}%
$\displaystyle \left[
     \left\{ 
       \left( \DP{u}{z} \right)_{i(u),k(w)}
     \right\}_{i,k}^{t-\Delta t}     
    +
     \left\{ 
       \left( \DP{w}{x} \right)_{i(u),k(w)} 
     \right\}_{i,k}^{t - \Delta t}
    \right]^{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6832}%
$\displaystyle - \frac{2}{3} [E_{turb}]_{i,k}^{t - \Delta t}
    \left\{
     \left( \DP{u}{x} \right)_{i,k}^{t-\Delta t}
  + 
     \left( \DP{w}{z} \right)_{i,k}^{t-\Delta t}
    \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6833}%
$\displaystyle \left[{\rm Turb}.E_{turb}\right]_{i,k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6835}%
$\displaystyle C_{m} l 
    \left\{ \DP{}{x} \left[ [E_{turb}^{1/2}]_{i,k} \left( \DP{E_{turb}}{x}
     \right)_{i(u),k} \right] \right\}_{i,k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6836}%
$\displaystyle + C_{m} l 
    \left\{ \DP{}{z} \left[ [E_{turb}^{1/2}]_{i,k} \left( \DP{E_{turb}}{z}
     \right)_{i,k(w)} \right] \right\}_{i,k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6837}%
$\displaystyle \left[{\rm Disp}.E_{turb}\right]_{i,k}^{t - \Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6839}%
$\displaystyle - \frac{C_{\varepsilon}}{l} 
 \left( E_{turb}^{3/2} \right)_{i,k}^{t - \Delta t}
\Deqlab{TurbE_risan}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3567}%
$C_{\varepsilon} = C_{m} = 0.2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3569}%
$l = \left(\Delta x \Delta z \right)^{1/2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3571}%
$\theta_{el}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6844}%
$\displaystyle \theta_{el}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6846}%
$\displaystyle \overline{ \theta_{v}} + \theta_{v}^{'} \;\;\; (for \;\; q_{c} = 0)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6849}%
$\displaystyle \overline{\theta_{v}} + \theta_{v}^{'} + \frac{ \sum L
  q_{v}}{{c_p}_{d} \bar{\pi}}  
   \;\;\; (for \;\; q_{c} &gt; 0)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6851}%
$\displaystyle \overline{\theta_{v}} + \theta_{v}^{'}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6853}%
$\displaystyle \left( 
   \frac{\langle M \rangle}{M_d} \overline{q_d} 
   + \sum \frac{\langle M \rangle}{M_v} \overline{q_v} 
  \right) ( \overline{\theta} + \theta )
   + 
   \left( 
   \frac{\langle M \rangle}{M_d} q_d 
   + \sum \frac{\langle M \rangle}{M_v} q_v
  \right) \overline{\theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3637}%
$N_{\tau}\equiv 2\Delta t/\Delta
\tau$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3639}%
$ u^{t + \Delta t}_{i(u),k}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6858}%
$\displaystyle u^{*}_{i(u),k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6860}%
$\displaystyle u^{\tau + (N_{\tau}-1)\Delta \tau}_{i(u), k} 
    -   \left[
  \bar{c_{p}} \bar{\theta}_{v} \Delta \tau
  \left\{
   \DP{\pi^{\tau + (N_{\tau}-1)\Delta \tau}}{x} 
   - \DP{(\alpha Div)^{\tau + (N_{\tau}-1)\Delta \tau}}{x} 
  \right\}
 \right]_{i(u),k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6861}%
$\displaystyle + 
     F_{u,i(u),k}^{t} \Delta \tau,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6862}%
$\displaystyle u^{t+\Delta t}_{i(u),k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6864}%
$\displaystyle (1-2 \gamma)u^{t}_{i(u),k} + 
    \gamma (u^{*}_{i(u),k} + u^{t -\Delta t}_{i(u),k})
  \Deqlab{uwpi:timefilter}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3641}%
$\gamma$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6868}%
$\displaystyle \DP{\phi}{t} = -{\rm Adv}.\phi + \cdots + \gamma_{h}(x) (\phi - \phi_{e})
  + \gamma_{v}(z) (\phi - \phi_{e})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3743}%
$\phi_{e}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3747}%
$2 \Delta t$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6874}%
$\displaystyle [\pi]^{t + \Delta t} = 2 \Delta t 
  \left\{
    [{\rm Adv}.\pi]^{t} 
  + \cdots 
  + \left\{
     \gamma_{h}(x)  + \gamma_{v}(z)
    \right\} (\pi - \bar{\pi})^{t - \Delta t}
  \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6875}%
$\displaystyle [u]^{t + \Delta t} = 2 \Delta t 
  \left\{
    [{\rm Adv}.u]^{t} 
  + \cdots 
  + \left\{
     \gamma_{h}(x)  + \gamma_{v}(z)
    \right\} [u]^{t - \Delta t}
  \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6876}%
$\displaystyle [w]^{t + \Delta t} = 2 \Delta t 
  \left\{
    [{\rm Adv}.w]^{t} 
  + \cdots 
  + \left\{
     \gamma_{h}(x)  + \gamma_{v}(z)
    \right\} [w]^{t - \Delta t}
  \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6877}%
$\displaystyle [\theta]^{t + \Delta t} = 2 \Delta t 
  \left\{
   [{\rm Adv}.\theta]^{t} 
   + \cdots 
   + \left\{
      \gamma_{h}(x)  + \gamma_{v}(z)
     \right\} [\theta]^{t - \Delta t}
  \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3749}%
$\bar{\pi}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3751}%
$\gamma_{h}, \gamma_{v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3753}%
$d_{h}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3757}%
$0 \leq x \leq
x_{max}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6884}%
$\displaystyle \gamma_{h} = \alpha_{h} \left( 1 - \frac{x}{d_{h}}\right)^{3}
  \hspace{5em} (x &lt;  d_{h}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6885}%
$\displaystyle \gamma_{h} = 0  \hspace{10em} ( d_{h} \leq x \leq  x_{max} - d_{h}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6886}%
$\displaystyle \gamma_{h} = \alpha_{h} \left( 1 - \frac{(x_{max} - x)}{d_{h}}\right)^{3}
 \;\; (x &gt; x_{max} - d_{h}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3759}%
$d_{v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3763}%
$0 \leq z \leq z_{max}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6891}%
$\displaystyle \gamma_{v} = 0  \hspace{12em} ( z \leq  z_{max} - d_{v}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6892}%
$\displaystyle \gamma_{v} = \alpha_{v} \left
			     ( 1 - \cos{\frac{\pi (z - z_{max} - d_{v})}{d_{v}}}
			    \right)^{3}
 \;\; (z &gt; z_{max} - d_{v}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3765}%
$\alpha_h, \alpha_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3769}%
$1/\alpha_{h}, 1/\alpha_{v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3771}%
$d_{h}, d_{v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
\appendix
\stepcounter{chapter}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6901}%
$\displaystyle \Deqref{uwpi:sabun}\mbox{left side}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6903}%
$\displaystyle \Pi^{\tau + \Delta \tau}_{i,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6904}%
$\displaystyle - \beta^{2} 
  \left(
   \frac{\bar{c}^{2}{\Delta \tau}^{2}}{\bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}}
  \right)_{k}
  \Dinv{\Delta z}
  \left\{
   \left(
   \bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{k(w)}
   \left(
     \DP{\Pi^{\tau + \Delta \tau}}{z} 
   \right)_{i,k(w)}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6905}%
$\displaystyle + \beta^{2} 
  \left(
   \frac{\bar{c}^{2}{\Delta \tau}^{2}}{\bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}}
  \right)_{k}
  \Dinv{\Delta z}
  \left\{
   \left(
   \bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{k-1(w)}
   \left(
     \DP{\Pi^{\tau + \Delta \tau}}{z} 
   \right)_{i,k-1(w)}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6908}%
$\displaystyle - \beta^{2} 
  \left(
   \frac{\bar{c}^{2}{\Delta \tau}^{2}}{\bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}}
  \right)_{k}
  \Dinv{\Delta z}
  \left\{
   \left(
   \bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{k(w)}
   \left(
    \frac{\Pi^{\tau + \Delta \tau}_{i,k+1} 
    - \Pi^{\tau + \Delta \tau}_{i,k}}{\Delta z} 
   \right)
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6909}%
$\displaystyle + \beta^{2} 
  \left(
   \frac{\bar{c}^{2}{\Delta \tau}^{2}}{\bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}}
  \right)_{k}
  \Dinv{\Delta z}
  \left\{
   \left(
   \bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{k-1(w)}
   \left(
    \frac{\Pi^{\tau + \Delta \tau}_{i,k} 
    - \Pi^{\tau + \Delta \tau}_{i,k-1}}{\Delta z} 
   \right)
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6911}%
$\displaystyle \left\{
   - \beta^{2}
  \left(
  \frac{\bar{c}^{2}{\Delta \tau}^{2}}{\bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}}
  \right)_{k}
  \Dinv{\Delta z^{2}} 
  \left(
    \bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}
  \right)_{k(w)}
  \right\}
   \Pi^{\tau + \Delta \tau}_{i,k+1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6912}%
$\displaystyle + \left[
  1 + \beta^{2}
  \left(
   \frac{\bar{c}^{2}{\Delta \tau}^{2}}{\bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}}
  \right)_{k}
  \Dinv{\Delta z^{2}} 
   \left\{
   \left(
   \bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2} 
   \right)_{k(w)}
   + 
   \left(
   \bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2} 
   \right)_{k-1(w)}
   \right\} 
    \right]
 \Pi^{\tau + \Delta \tau}_{i,k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6913}%
$\displaystyle + \left\{
   - \beta^{2}
  \left(
   \frac{\bar{c}^{2}{\Delta \tau}^{2}}{\bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}}
  \right)_{k}
  \Dinv{\Delta z^{2}} 
   \left(
    \bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2} 
       \right)_{k-1(w)}
   \right\}
   \Pi^{\tau + \Delta \tau}_{i,k-1}.
   \Deqlab{uwpi:LH_sabun}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6919}%
$\displaystyle \left[
\left( \DP{(\alpha Div)^{\tau}}{z} \right)
  - (1 - \beta) \left( \DP{\Pi^{\tau}}{z} \right)
  + \left(\Dinv{\bar{c_{p}} \bar{\theta}_{v}} F_{w}^{t}\right)
\right]_{i,0(w)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6921}%
$\displaystyle E_{i,0(w)}
  \Deqlab{uwpi:w_sabun_kabu2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4449}%
$k = 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6926}%
$\displaystyle \Pi^{\tau + \Delta \tau}_{i,1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6927}%
$\displaystyle - \beta^{2} 
  \left(
   \frac{\bar{c}^{2}{\Delta \tau}^{2}}{\bar{c_{p}} \bar{\rho}
   \bar{\theta}_{v}^{2}}
  \right)_{1}
  \Dinv{\Delta z}
  \left\{
   \left(
    \bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{1(w)}
   \left(
    \DP{\Pi^{\tau + \Delta \tau}}{z} 
   \right)_{i,1(w)}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6928}%
$\displaystyle + \beta^{2} 
  \left(
   \frac{\bar{c}^{2}{\Delta \tau}^{2}}{\bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}}
  \right)_{1}
  \Dinv{\Delta z}
  \left\{
   \left(
   \bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{0(w)}
   \left(
     \DP{\Pi^{\tau + \Delta \tau}}{z} 
   \right)_{i,0(w)}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6931}%
$\displaystyle - \beta^{2} 
  \left(
   \frac{\bar{c}^{2}{\Delta \tau}^{2}}{\bar{c_{p}} \bar{\rho}
   \bar{\theta}_{v}^{2}}
  \right)_{1}
  \Dinv{\Delta z}
  \left\{
   \left(
    \bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{1(w)}
   \left(
    \frac{\Pi^{\tau + \Delta \tau}_{i,2} 
    - \Pi^{\tau + \Delta \tau}_{i,1}}{\Delta z} 
   \right)
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6934}%
$\displaystyle \left\{
 - \beta^{2} 
  \left(
  \frac{\bar{c}^{2}{\Delta \tau}^{2}}{\bar{c_{p}} \bar{\rho}
  \bar{\theta}_{v}^{2}}
  \right)_{1}
  \Dinv{\Delta z^{2}}
   \left(
   \bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{1(w)}
  \right\}
  \Pi^{\tau + \Delta \tau}_{i,2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6935}%
$\displaystyle + 
  \left\{
  1 + \beta^{2} 
  \left(
  \frac{\bar{c}^{2}{\Delta \tau}^{2}}{\bar{c_{p}} \bar{\rho}
  \bar{\theta}_{v}^{2}}
  \right)_{1}
  \Dinv{\Delta z^{2}}
   \left(
   \bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{1(w)}
  \right\} \Pi^{\tau + \Delta \tau}_{i,1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6936}%
$\displaystyle + \beta 
  \left(
   \frac{\bar{c}^{2}{\Delta \tau}^{2}}{\bar{c_{p}} \bar{\rho}
   \bar{\theta}_{v}^{2}}
  \right)_{1}
  \Dinv{\Delta z}
\left(
   \bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{0(w)}
   E_{i,0(w)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6942}%
$\displaystyle \left[
 \left( \DP{(\alpha Div)^{\tau}}{z} \right)
  - (1 - \beta) \left( \DP{\Pi^{\tau}}{z} \right)
  + \left(\Dinv{\bar{c_{p}} \bar{\theta}_{v}} F_{w}^{t}\right)
\right]_{i,km(w)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6944}%
$\displaystyle E_{i,km(w)}
  \Deqlab{uwpi:w_sabun_joubu2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6949}%
$\displaystyle \Pi^{\tau + \Delta \tau}_{i,km}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6950}%
$\displaystyle - \beta^{2} 
  \left(
   \frac{\bar{c}^{2}{\Delta \tau}^{2}}{\bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}}
  \right)_{km}
  \Dinv{\Delta z}
  \left\{
   \left(
   \bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{km(w)}
   \left(
     \DP{\Pi^{\tau + \Delta \tau}}{z} 
   \right)_{i,km(w)}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6951}%
$\displaystyle + \beta^{2} 
  \left(
   \frac{\bar{c}^{2}{\Delta \tau}^{2}}{\bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}}
  \right)_{km}
  \Dinv{\Delta z}
  \left\{
   \left(
   \bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{km-1(w)}
   \left(
     \DP{\Pi^{\tau + \Delta \tau}}{z} 
   \right)_{i,km-1(w)}
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6954}%
$\displaystyle - \beta 
  \left(
   \frac{\bar{c}^{2}{\Delta \tau}^{2}}{\bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}}
  \right)_{km}
  \Dinv{\Delta z}
   \left(
   \bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{km(w)}
   E_{i,km(w)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6955}%
$\displaystyle + \beta^{2} 
  \left(
   \frac{\bar{c}^{2}{\Delta \tau}^{2}}
        {\bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}}
  \right)_{km}
  \Dinv{\Delta z}
  \left\{
   \left(
   \bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{km-1(w)}
   \left(
    \frac{\Pi^{\tau + \Delta \tau}_{i,km}
          - \Pi^{\tau + \Delta \tau}_{i,km-1}}{\Delta z}
   \right)
\right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6957}%
$\displaystyle \left\{
   1 + 
  \beta^{2} 
  \left(
   \frac{\bar{c}^{2}{\Delta \tau}^{2}}{\bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}}
  \right)_{km}
  \Dinv{\Delta z^{2}}
   \left(
   \bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{km-1(w)}
  \right\}
    \Pi^{\tau + \Delta \tau}_{i,km}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6958}%
$\displaystyle + \left\{
  - \beta^{2} 
  \left(
   \frac{\bar{c}^{2}{\Delta \tau}^{2}}{\bar{c_{p}} \bar{\rho}
   \bar{\theta}_{v}^{2}} 
  \right)_{km}
  \Dinv{\Delta z^{2}}
   \left(
   \bar{c_{p}} \bar{\rho} \bar{\theta}_{v}^{2}
   \right)_{km-1(w)}
  \right\}
     \Pi^{\tau + \Delta \tau}_{i,km-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4636}%
$2\Delta t/\Delta \tau$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6963}%
$\displaystyle \DP{u}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6965}%
$\displaystyle - \overline{c}_{p}\overline{\theta}_{v}
                 \DP{\Pi}{x} + \alpha\DP{D}{x} ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6966}%
$\displaystyle \DP{w}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6968}%
$\displaystyle - \overline{c}_{p}\overline{\theta}_{v}
                 \DP{\Pi}{z} + \alpha\DP{D}{z} 
               + g\frac{\theta}{\overline{\theta}_{v}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6969}%
$\displaystyle \DP{\Pi}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6971}%
$\displaystyle - \frac{\overline{c}^{2}}{\overline{c}_{p}
                 \overline{\rho}\overline{\theta}_{v}^{2}}
                 \left[\DP{\overline{\rho}\overline{\theta}_{v}u}{x} +
                       \DP{\overline{\rho}\overline{\theta}_{v}w}{z}
                 \right],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6972}%
$\displaystyle \DP{\theta}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6974}%
$\displaystyle -w\DP{\overline{\theta}_{v}}{z},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6975}%
$\displaystyle D$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6977}%
$\displaystyle \DP{u}{x}+\DP{w}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6979}%
$\displaystyle \DP{D}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6981}%
$\displaystyle - \overline{c}_{p}\overline{\theta}_{v}\Dlapla \Pi   
               + g\DP{}{z}\left(\frac{\theta}{\overline{\theta}_{v}}\right)
             + \alpha \Dlapla D, \Deqlab{音波減衰項を含む線形発散方程式}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6982}%
$\displaystyle \Dlapla$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6984}%
$\displaystyle \DP[2]{}{x} + \DP[2]{}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4638}%
$u=\hat{u}e^{i(kx+lz -\omega t)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4541}%
\begin{displaymath}
  \omega ^{4} + i\alpha (k^{2}+l^{2})\omega ^{3}  - 
  [\overline{c}^{2}(k^{2}+l^{2}) + N^{2}] \omega ^{2}
  - i\alpha k^{2}N^{2}\omega + \overline{c}^{2}k^{2}N^{2}=0, 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4640}%
$N^{2} = \frac{g}{\overline{\theta}_{v}}\DP{
\overline{\theta}_{v}}{z}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4634}%
\begin{displaymath}
 \omega ^{2} = \frac{N^{2}k^{2}}{k^{2}+l^{2}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4642}%
$\alpha$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4646}%
$\epsilon \equiv \alpha \sqrt{k^{2}+l^{2}}/\overline{c}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4648}%
$\omega$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4650}%
$\epsilon$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4577}%
\begin{displaymath}
 \frac{\alpha \Delta \tau}{\mbox{Min}(\Delta x^{2}, \Delta z^{2})} \leq \frac{1}{2}
 \Deqlab{音波減衰項係数の条件1}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{eqnarraystar4587}%
\begin{eqnarray*}
  \mbox{Max}(\epsilon) 
    &amp;=&amp; \frac{2\alpha}{\mbox{Min}(\Delta x, \Delta z)\overline{c}} \nonumber \\
    &amp;=&amp; \frac{2\alpha \Delta \tau}{\mbox{Min}(\Delta x^{2}, \Delta z^{2})}
        \left/
        \frac{\overline{c}\Delta \tau}{\mbox{Min}(\Delta x, \Delta z)}
        \right.
\end{eqnarray*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4658}%
$\mbox{Max}(\epsilon) \leq 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4600}%
\begin{displaymath}
    \frac{\alpha \Delta \tau}{\mbox{Min}(\Delta x^{2}, \Delta z^{2})}
    \leq \frac{1}{2}
        \frac{\overline{c}\Delta \tau}{\mbox{Min}(\Delta x, \Delta z)}
  \Deqlab{音波減衰項係数の条件2}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5041}%
$(i,j)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5037}%
\begin{displaymath}
  \left[\DP{u}{x}\right]_{i,k}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5045}%
$(i(u),j)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5049}%
$(u_{i(u),j})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5053}%
$-\Delta x/2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5059}%
$(u_{i,j})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7018}%
$\displaystyle u _{i(u),j}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7020}%
$\displaystyle u_{i,j} 
  + \left[\DP{u}{x} \right]_{i,k}\frac{\Delta x}{2}
  + \frac{1}{2!}\left[\DP[2]{u}{x} \right]_{i,k}
       \left(\frac{\Delta x}{2}\right)^{2}
  + \frac{1}{3!}\left[\DP[3]{u}{x} \right]_{i,k}
       \left(\frac{\Delta x}{2}\right)^{3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7021}%
$\displaystyle + \frac{1}{4!}\left[\DP[4]{u}{x} \right]_{i,k}
       \left(\frac{\Delta x}{2}\right)^{4}
  + \frac{1}{5!}\left[\DP[5]{u}{x} \right]_{i,k}
       \left(\frac{\Delta x}{2}\right)^{5}
  + \cdots .
\Deqlab{u_{i(u),j} のテーラー展開}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5061}%
$(i-1(u),j)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5065}%
$(u_{i-1(u),j})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5067}%
$u_{i,j}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7027}%
$\displaystyle u_{i-1(u),j}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7029}%
$\displaystyle u_{i,j} 
  - \left[\DP{u}{x} \right]_{i,k}\frac{\Delta x}{2}
  + \frac{1}{2!}\left[\DP[2]{u}{x} \right]_{i,k}
       \left(\frac{\Delta x}{2}\right)^{2}
  - \frac{1}{3!}\left[\DP[3]{u}{x} \right]_{i,k}
       \left(\frac{\Delta x}{2}\right)^{3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7030}%
$\displaystyle + \frac{1}{4!}\left[\DP[4]{u}{x} \right]_{i,k}
       \left(\frac{\Delta x}{2}\right)^{4}
  - \frac{1}{5!}\left[\DP[5]{u}{x} \right]_{i,k}
       \left(\frac{\Delta x}{2}\right)^{5}
  + \cdots .
\Deqlab{u_{i-1(u),j} のテーラー展開}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5069}%
$-$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7033}%
$\displaystyle u _{i(u),j} - u_{i-1(u),j}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7035}%
$\displaystyle \left[\DP{u}{x} \right]_{i,k}\Delta x
  + \frac{1}{3}\left[\DP[3]{u}{x} \right]_{i,k}
       \left(\frac{\Delta x}{2}\right)^{3}
  + \frac{1}{60}\left[\DP[5]{u}{x} \right]_{i,k} 
       \left(\frac{\Delta x}{2}\right)^{5}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7036}%
$\displaystyle + O[(\Delta x)^{7}]
\Deqlab{u_{i,j} の差分式1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7041}%
$\displaystyle \left[\DP{\pi}{x} \right]_{i(u),k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7043}%
$\displaystyle \frac{\pi _{i+1,j}  - \pi _{i,j}}{\Delta x} 
  - \frac{1}{24}\left[\DP[3]{\pi}{x} \right]_{i(u),k}
       \left(\Delta x\right)^{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7044}%
$\displaystyle - \frac{1}{1920}\left[\DP[5]{\pi}{x} \right]_{i(u),k} 
       \left(\Delta x\right)^{4}
  + O[(\Delta x)^{6}]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5077}%
$\left(\Delta x\right)^{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4817}%
\begin{displaymath}
\left[\DP{u}{x} \right]_{i(u),k} = 
  \frac{u_{i+1,j} - u_{i,j}}{\Delta x}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4825}%
\begin{displaymath}
   \left|\frac{1}{24}\left[\DP[3]{u}{x} \right]_{i(u),k}
       \left(\Delta x\right)^{2}\right|
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5083}%
$\pm
\Delta 3x/2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5087}%
$(u _{i+1(u),j}, u
_{i-2(u),j})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7056}%
$\displaystyle u _{i+1(u),j}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7058}%
$\displaystyle u_{i,j} 
  + \left[\DP{u}{x} \right]_{i,k}\frac{3\Delta x}{2}
  + \frac{1}{2!}\left[\DP[2]{u}{x} \right]_{i,k}
       \left(\frac{3\Delta x}{2}\right)^{2}
  + \frac{1}{3!}\left[\DP[3]{u}{x} \right]_{i,k}
       \left(\frac{3\Delta x}{2}\right)^{3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7059}%
$\displaystyle + \frac{1}{4!}\left[\DP[4]{u}{x} \right]_{i,k}
       \left(\frac{3\Delta x}{2}\right)^{4}
  + \frac{1}{5!}\left[\DP[5]{u}{x} \right]_{i,k}
       \left(\frac{3\Delta x}{2}\right)^{5}
  + \cdots . \Deqlab{u_{i+1(u),j} のテーラー展開}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7060}%
$\displaystyle u _{i-2(u),j}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7062}%
$\displaystyle u_{i,j} 
  - \left[\DP{u}{x} \right]_{i,k}\frac{3\Delta x}{2}
  + \frac{1}{2!}\left[\DP[2]{u}{x} \right]_{i,k}
       \left(\frac{3\Delta x}{2}\right)^{2}
  - \frac{1}{3!}\left[\DP[3]{u}{x} \right]_{i,k}
       \left(\frac{3\Delta x}{2}\right)^{3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7063}%
$\displaystyle + \frac{1}{4!}\left[\DP[4]{u}{x} \right]_{i,k}
       \left(\frac{3\Delta x}{2}\right)^{4}
  - \frac{1}{5!}\left[\DP[5]{u}{x} \right]_{i,k}
       \left(\frac{3\Delta x}{2}\right)^{5}
  + \cdots . \Deqlab{u_{i-2(u),j} のテーラー展開}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7066}%
$\displaystyle u _{i+1(u),j} - u_{i-2(u),j}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7068}%
$\displaystyle \left[\DP{u}{x} \right]_{i,k}3\Delta x
  + \frac{1}{3}\left[\DP[3]{u}{x} \right]_{i,k}
       \left(\frac{3\Delta x}{2}\right)^{3}
  + \frac{1}{60}\left[\DP[5]{u}{x} \right]_{i,k} 
       \left(\frac{3\Delta x}{2}\right)^{5}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7069}%
$\displaystyle + O[(\Delta x)^{7}]
\Deqlab{u_{i,j} の差分式2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5093}%
$\times 27 -$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5095}%
$(\Delta x)^{3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7073}%
$\displaystyle 27(u _{i(u),j} - u_{i-1(u),j}) - (u _{i+1(u),j} - u_{i-2(u),j})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7075}%
$\displaystyle \left[\DP{u}{x} \right]_{i,k}24\Delta x
  - \frac{216}{60}\left[\DP[5]{u}{x} \right]_{i,k} 
       \left(\frac{\Delta x}{2}\right)^{5}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7076}%
$\displaystyle + O[(\Delta x)^{7}]
\Deqlab{u_{i,j} の差分式3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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$\displaystyle \left[\DP{u}{x}\right]_{i,k}$%
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\lthtmlinlinemathA{tex2html_wrap_indisplay7083}%
$\displaystyle \frac{9}{8}\left(\frac{u_{i,j}  - u _{i-1,j}}{\Delta x}\right) 
  - \frac{1}{24}\left(\frac{u_{i+1,j}  - u _{i-2,j}}{\Delta x}\right)$%
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$\displaystyle + \frac{3}{640}\left[\DP[5]{u}{x} \right]_{i,k} 
       \left(\Delta x\right)^{4} 
  + O[(\Delta x)^{6}]$%
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{\newpage\clearpage
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$\left(\Delta x\right)^{4}$%
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\begin{displaymath}
\left[\DP{u}{x}\right]_{i,k} = 
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  - \frac{1}{24}\left(\frac{u_{i+1,j}  - u _{i-2,j}}{\Delta x}\right)
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   \left|\frac{3}{640}\left[\DP[5]{u}{x} \right]_{i(u),k}
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$\displaystyle \ln p^{*}= (A - B / (C + T - T_{0})) * \log(10.0) + \ln(133.322)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5300}%
$p^{*}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5304}%
$T_{0} = 273.15$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5306}%
$A, B, C$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5308}%
$^{\circ}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5310}%
$_{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5314}%
$_{3}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7124}%
$\displaystyle K_{p} 
  = \ln(p_{\rm NH_{3}} \cdot p_{\rm H_{2}S}) 
  = 61.781 - \frac{10834}{T}  - \ln{10^{2}}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7128}%
$\displaystyle \DD{p_{v}}{T} =  \frac{p_{v} L_{v}}{R T^{2}}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5316}%
$L_{v}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7131}%
$\displaystyle L_{v} = \DD{\ln p_{v}}{T} {R_{v} T^{2}}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5318}%
$R_{v}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7134}%
$\displaystyle L_{v} = \left\{
	  \frac{B \ln(10.0)}{ (C + T - T_{0})^{2} }
	 \right\} R_{v} T^{2}$%
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\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7137}%
$\displaystyle {\rm NH_{3}} + {\rm H_{2}S} \rightarrow {\rm NH_{4}SH}
  \Deqlab{react_NH4SH}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5320}%
$_4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7143}%
$\displaystyle s_{\rm NH_4SH}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7145}%
$\displaystyle - \DP{\mu_{\rm NH_4SH}}{T}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7147}%
$\displaystyle - \DP{}{T} 
   \left( 
    \mu_{\rm NH_3}^{\circ} + \mu_{\rm H_2S}^{\circ} + RT K_{p}
    - RT \ln {p_{0}}^{2}
   \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7149}%
$\displaystyle s_{\rm NH_3}^{\circ} + s_{\rm H_2S}^{\circ}  
      - RT \DP{K_{p}}{T} - R K_{p} 
      +  R\ln {p_{0}}^{2}
  \Deqlab{react_NH4SH_left}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5328}%
$\mu_{\rm NH_3}^{\circ}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5330}%
$\mu_{\rm H_2S}^{\circ}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5332}%
${}_{3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5334}%
${}_{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5336}%
$s_{\rm NH_3}^{\circ}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5338}%
$s_{\rm H_2S}^{\circ}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5340}%
$K_{p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7160}%
$\displaystyle s_{\rm NH_3}  + s_{\rm H_2S}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7162}%
$\displaystyle s_{\rm NH_3}^{\circ}  + s_{\rm H_2S}^{\circ}
       - R\ln (p_{\rm NH_3}\cdot p_{\rm H_2S}) + R\ln p_{0}^{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7164}%
$\displaystyle s_{\rm NH_3}^{\circ}  + s_{\rm H_2S}^{\circ}
       - R\ln K_{p} + R\ln p_{0}^{2}
\Deqlab{react_NH4SH_right}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7166}%
$\displaystyle \Delta s
  = RT \DP{K_{p}}{T} 
  \Deqlab{react_NH4SH_DeltaS}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7168}%
$\displaystyle L_{\rm NH_4SH} = T \Delta s = RT^{2} \DP{K_{p}}{T}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7171}%
$\displaystyle L_{\rm NH_4SH} =  \frac{10834}{T^2} {R T^{2}} =  10834 R$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5587}%
$d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5589}%
$v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5593}%
$q_{x}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5595}%
$p_{x}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7180}%
$\displaystyle q_{x}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7182}%
$\displaystyle \frac{\rho_{x}}{\rho_{d}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7184}%
$\displaystyle \left(
       \frac{R_{d} T}{p} \frac{1/M_{d} + \sum_{v} q_{v}/M_{v}}{1/M_{d}}
      \right)
    \frac{p_{x}}{R_{x}T}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7186}%
$\displaystyle \frac{p_{x}}{p} M_{x} (1/M_{d} + \sum_{v} q_{v}/M_{v})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7187}%
$\displaystyle q_{x} \left(1 - \frac{p_{x}}{p} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7189}%
$\displaystyle \frac{p_{x}}{p} M_{x} (1/M_{d} + \sum_{v \neq x} q_{v}/M_{v})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7192}%
$\displaystyle \frac{p_{x}}{p}\frac{ M_{x} (1/M_{d} + \sum_{v \neq x} q_{v}/M_{v})  }
  {\left(1 - \frac{p_{x}}{p} \right) }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7195}%
$\displaystyle \frac{ p_{x} M_{x}  (1/M_{d} + \sum_{v \neq x} q_{v}/M_{v}) }{p - p_{x}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7198}%
$\displaystyle \frac{ p_{x} M_{x}  (1/M_{d} + \sum_{v \neq x} q_{v}/M_{v}) }
  {p_{0} \pi^{{c_{p}}_{d}/R_{d}} - p_{x}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5597}%
$x_{x}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7201}%
$\displaystyle q_{x} = 
  \frac{ x_{x} M_{x} (1/M_{d} + \sum_{v \neq x} q_{v}/M_{v})}{ 1 - x_{x} }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7205}%
$\displaystyle p_{x}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7207}%
$\displaystyle \frac{q_{x} p}{M_{x} (1/M_{d} + \sum_{v} q_{v}/M_{v})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7210}%
$\displaystyle \frac{q_{x}p_{0} \pi^{{c_{p}}_{d}/R_{d}}  }{M_{x} (1/M_{d} + \sum_{v} q_{v}/M_{v})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7213}%
$\displaystyle x_{x}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7215}%
$\displaystyle \frac{q_{x}}{M_{x} (1/M_{d} + \sum_{v} q_{v}/M_{v})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5585}%
\begin{displaymath}
  \mbox{dcstaff@gfd-dennou.org}
 \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}


\end{document}
</pre></body></html>