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$ p=400$%
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$ T=135$%
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$ p=90$%
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$ u$%
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$ T$%
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$\displaystyle \equiv$%
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$\displaystyle T \left( \frac{p_0}{p} \right)^{\frac{R}{c_{pv}}},
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$\displaystyle \Pi$%
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$\displaystyle \left( \frac{p}{p_0} \right)^{\frac{R}{c_{pv}}} =
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$ R$%
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$ c_{pv}$%
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$ R \simeq 188.9$%
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$ c_{pv} \simeq
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$ p_0 = 700$%
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$ \phi$%
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$ \phi^{\prime}$%
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$\displaystyle {\rho_s}^{\prime}(x,z,t). \Deqlab{ZE}$%
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$ ^{\prime}$%
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$ \overline{\Pi}$%
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$ _2$%
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$\displaystyle - u \DP{u}{x} - w \DP{u}{z} - c_{pv} \overline{\theta}
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$\displaystyle - u \DP{w}{x} - w \DP{w}{z} - c_{pv} \overline{\theta}
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$\displaystyle - u \DP{\theta^{\prime}}{x} - w \DP{\theta^{\prime}}{z}
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$\displaystyle - \frac{\overline{c}^2}{c_{pv} \overline{\rho} \overline{\theta}^2}
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$\displaystyle + \frac{\overline{c}^2}{c_{pv} \overline{\theta}^2}
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$\displaystyle - \DP{(\rho_s u)}{x} - \DP{(\rho_s w)}{z}
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$ \overline{c}$%
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$\displaystyle {\overline{c}}^2  = \frac{c_{pv}}{c_{vv}} R \overline{T} = \frac{c_{pv}}{c_{vv}} R \overline{\theta} \overline{\Pi}.   \Deqlab{Sound}$%
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$ c_{vv}$%
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$ c_{vv} \simeq 545.2$%
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$ D_u$%
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$ D_w$%
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$ D_{\theta}$%
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$ Q_{dis}$%
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$ L$%
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$ L \simeq 5.86 \times 10^5$%
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$\displaystyle + \frac{\overline{c}^2}{c_{pv} \overline{\rho} \overline{\theta}}
\left( \frac{L}{c_{pv} \overline{T}} - 1 \right) M_{cond}
+ \frac{\overline{c}^2}{c_{pv} \overline{\theta}^2 \overline{\Pi}}
( Q_{rad} + Q_{dis} ).
\Deqlab{AH}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3191}%
$ O(\overline{T}) \sim 150$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3203}%
$ L / (c_{pv} \overline{T}) > 1 $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3213}%
$\displaystyle \phi(x,z,t) = \phi(x+L,z,t) \Deqlab{BoundaryA}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3215}%
$ D$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3219}%
$ \psi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3224}%
$\displaystyle w$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3228}%
$\displaystyle 0, \quad \quad (z = 0, D) \Deqlab{boundaryB}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3232}%
$\displaystyle \DP{\psi}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3236}%
$\displaystyle 0, \quad \quad (z = 0, D) \Deqlab{boundaryC}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3249}%
$ D_\theta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3256}%
$\displaystyle D_u$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3260}%
$\displaystyle - \DP{}{x}
\left[ - \frac{2}{3} K_m \DP{u}{x} + \frac{2}{3} E_{turb} \right]
- \DP{}{x} \left[ - K_m \left( \DP{u}{x} + \DP{w}{z} \right) \right]
, \Deqlab{TurbA}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3264}%
$\displaystyle D_w$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3268}%
$\displaystyle - \DP{}{x} \left[ - K_m \left( \DP{w}{x} + \DP{u}{z} \right) \right]
- \DP{}{z}
\left[ - \frac{2}{3} K_m \DP{w}{x} + \frac{2}{3} E_{turb} \right]
, \Deqlab{TurbB}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3272}%
$\displaystyle D_{\theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3276}%
$\displaystyle - \DP{}{x} \left[ K_h \DP{\theta^{\prime}}{x} \right]
- \DP{}{z} \left[ K_h \DP{(\theta^{\prime} + \overline{\theta})}{z}
\right], \Deqlab{TurbC}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3280}%
$\displaystyle D_{\rho_s}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3284}%
$\displaystyle - \DP{}{x} \left[ K_h \DP{\rho_s}{x} \right]
- \DP{}{z} \left[ K_h \DP{\rho_s}{z}  \right] \Deqlab{TurbD}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3286}%
$ K_m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3288}%
$ K_h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3290}%
$ E_{turb}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3298}%
$\displaystyle E_{turb} = \left( \frac{K_m}{C_m l} \right)^2 \Deqlab{TurbE}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3300}%
$ l$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3302}%
$ \Delta x$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3304}%
$ \Delta z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3306}%
$ l = (\Delta x \Delta z)^{1/2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3308}%
$ C_m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3314}%
$\displaystyle K_h = 3 K_m \Deqlab{TurbF}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3319}%
$\displaystyle \DP{K_m}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3323}%
$\displaystyle - \left( u \DP{K_m}{x} + w \DP{K_m}{z} \right)
- \frac{3 g {C_m}^2 l^2}{2 \overline{\theta}}
\DP{\theta^{\prime}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3325}%
$\displaystyle + {C_m}^2 l^2 \left[ \left( \DP{u}{x} \right)^2 + \left( \DP{w}{z}
\right)^2 \right]
+ \frac{{C_m}^2 l^2}{2} \left( \DP{u}{z} + \DP{w}{x} \right)^2$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3327}%
$\displaystyle - \frac{K_m}{3} \left( \DP{u}{x} + \DP{w}{z} \right)
+ \Dinv{2} \left( \DP[2]{{K_m}^2}{x} + \DP[2]{{K_m}^2}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3331}%
$\displaystyle + \left( \DP{K_m}{x} \right)^2 + \left( \DP{K_m}{z} \right)^2
- \frac{C_{\varepsilon}}{2 C_m l^2} {K_m}^2.
\Deqlab{TurbG}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3333}%
$ C_{\varepsilon}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3335}%
$ C_m = C_{\varepsilon}
= 0.2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3341}%
$\displaystyle Q_{dis}  = \frac{C_{\varepsilon}}{c_{pv} l} E_{turb}^{3/2}  = \frac{C_{\varepsilon}}{c_{pv} l} \left( \frac{K_m}{C_m l} \right)^3  \Deqlab{TurbH}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3358}%
$ \mu$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3375}%
$\displaystyle M_{cond} = \frac{4 \pi r_d \overline{\rho} N^{*}}{R_h} (S - 1).   \Deqlab{CloudB}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3377}%
$ R_h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3379}%
$ S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3381}%
$ r_d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3386}%
$\displaystyle R_h$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3390}%
$\displaystyle \frac{L^2}{k R T^2} = \frac{L^2}{k R \theta^2 \Pi^2},
\Deqlab{CloudC}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3394}%
$\displaystyle S$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3398}%
$\displaystyle \frac{p}{p_{\ast}} = \frac{{p_0}^{\frac{c_{pv}}{R}} \Pi}{p_{\ast}}
\Deqlab{CloudE}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3402}%
$\displaystyle r_d$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3406}%
$\displaystyle \left(
r_{aero}^3 + \frac{3 \rho_s}{4 \rho_I \pi \overline{\rho} N^{*}}
\right)^{1/3}
\Deqlab{CloudA}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3408}%
$ k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3410}%
$ p_{\ast}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3414}%
$ \rho_I$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3420}%
$ r_{aero}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3422}%
$ N^{*}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3424}%
$ \rho_I = 1.565 \times 10^3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3426}%
$ ^3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3436}%
$\displaystyle p_{\ast} \simeq \exp \left( A_{ant} - \frac{B_{ant}}{T} \right)  \Deqlab{CloudG}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3438}%
$ A_{ant}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3440}%
$ B_{ant}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3444}%
$ A_{ant} = 27.4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3446}%
$ B_{ant} = 3103$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3456}%
$ V_{term}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3460}%
$\displaystyle M_{fall} = \DP{}{z} \left( \rho_s V_{term} \right) \Deqlab{CloudI}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3464}%
$\displaystyle V_{term} = C_{sc} \frac{2 r_d^2 g \rho_I}{9 \eta} \Deqlab{CloudJ}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3466}%
$ \eta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3470}%
$\displaystyle \eta   =   \eta_{ref}   \left( \frac{T_{ref} + C_{CO_2}}{\overline{T} + C_{CO_2}} \right)  \left( \frac{\overline{T}}{T_{ref}} \right)^{3/2}   =   \eta_{ref}   \left(    \frac{T_{ref} + C_{CO_2}}{\overline{\theta} \overline{\Pi} + C_{CO_2}}   \right)  \left(    \frac{\overline{\theta} \overline{\Pi}}{T_{ref}}   \right)^{3/2}   \Deqlab{CloudM}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3472}%
$ \eta_{ref}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3474}%
$ T_{ref}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3476}%
$ C_{CO_2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3480}%
$ \eta_{ref} = 1.47 \times
10^{-5}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3482}%
$ \cdot$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3484}%
$ T_{ref} = 293$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3486}%
$ C_{CO_2} = 240$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3488}%
$ C_{sc}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3492}%
$\displaystyle C_{sc}   = 1 + \frac{4}{3} K_n  \Deqlab{CloudK}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3494}%
$ K_n \equiv \lambda / r_d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3497}%
$\displaystyle C_{sc} = 1 + 1.255 K_n$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3499}%
$\displaystyle C_{sc}   = 1 + K_n     \left[       1.257 + 0.400 \exp \left( - \frac{1.10}{K_n} \right)     \right].$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3501}%
$ \lambda$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3507}%
$\displaystyle \lambda   =    \frac{k_B \overline{T}}{\sqrt{2} \pi \sigma^2 \overline{p}}   =    \frac{k_B \overline{\theta}}   {\sqrt{2} \pi \sigma^2 p_0 \overline{\Pi}^{c_{vv}/R}}   \Deqlab{CloudL}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3509}%
$ k_B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3511}%
$ \sigma$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3515}%
$ k_B =
1.38 \times 10^{-23}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3517}%
$ ^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3519}%
$ ^{-2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3523}%
$ \sigma =
3.3 \times 10^{-10}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3525}%
$ T \sim 150$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3527}%
$ p \sim 400$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3529}%
$ T \sim 135$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3531}%
$ p \sim 90$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure542}%
\begin{figure} \begin{center}
\Depsf[][][width=6.0cm,angle=270]{ps/radius-dens.ps}

 \end{center}
  \end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure550}%
\begin{figure} \begin{center}
\Depsf[][][width=6.0cm,angle=270]{ps/Vterm.ps}

 \end{center}
  \end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3583}%
$ \bf {107}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3585}%
$ \bf {108(E7)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3587}%
$ \bf {24}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3589}%
$ \bf {83}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3591}%
$ \bf {57}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3593}%
$ \bf {29}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3595}%
$ \bf {45}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3599}%
$ \bf {160}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3601}%
$ \bf {162}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3603}%
$ \bf {66}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3605}%
$ \bf {10}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3607}%
$ \bf {35}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3611}%
$ \bf {110}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3613}%
$ \bf {102}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3615}%
$ \bf {36}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3617}%
$ \bf {30}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3619}%
$ \bf {9}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3623}%
$ \bf {164}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\setcounter{equation}{0}
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\renewcommand{\thechapter}{\Alph{chapter}}

\renewcommand{\theequation}{\thechapter .\arabic{equation}}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3630}%
$ \rho_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3635}%
$\displaystyle \frac{D u}{D t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3639}%
$\displaystyle - \Dinv{\rho} \DP{p}{x} + D_u, \Deqlab{EOM1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3643}%
$\displaystyle \frac{D w}{D t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3647}%
$\displaystyle - \Dinv{\rho} \DP{p}{z} - g + D_w \Deqlab{EOM2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3649}%
$ \rho \equiv \rho_v + \rho_s$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3658}%
$\displaystyle - \Dinv{\rho} \DP{p}{x_i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3662}%
$\displaystyle - \frac{\rho_v}{\rho} \Dinv{\rho_v} \DP{p}{x_i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3666}%
$\displaystyle - \frac{\rho_v}{\rho} \frac{R \theta \Pi}{p}
\DP{}{x_i} \left[ p_0 \Pi^{c_{pv} / R} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3670}%
$\displaystyle - \frac{\rho_v}{\rho} \frac{R \theta \Pi}{p}
\frac{p_0 c_{pv}}{R} \Pi^{(c_{pv} / R) - 1} \DP{\Pi}{x_i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3674}%
$\displaystyle - \frac{\rho_v}{\rho} \frac{R \theta \Pi}{p}
p_0 \Pi^{c_{pv} / R} \frac{c_{pv}}{R \Pi} \DP{\Pi}{x_i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3678}%
$\displaystyle - \frac{\rho_v}{\rho} \frac{R \theta \Pi}{p}
p \frac{c_{pv}}{R \Pi} \DP{\Pi}{x_i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3684}%
$\displaystyle - \frac{\rho_v}{\rho} c_{pv} \theta \DP{\Pi}{x_i}
\Deqlab{EOM3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3686}%
$ p = \rho_v R T = \rho_v R \theta \Pi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3695}%
$\displaystyle - \frac{\rho_v}{\rho} c_{pv} \theta \DP{\Pi}{x}
+ D_u, \Deqlab{EOM4}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3703}%
$\displaystyle - \frac{\rho_v}{\rho} c_{pv} \theta \DP{\Pi}{z}
- g + D_w \Deqlab{EOM5}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3705}%
$ \overline{\rho} = \overline{\rho_v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3707}%
$ \rho^{\prime} = \rho_v^{\prime} + \rho_s^{\prime}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3709}%
$ \rho = \overline{\rho_v} + \rho_v^{\prime} + \rho_s^{\prime}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3712}%
$\displaystyle \DP{u}{t} + u \DP{u}{x} + w \DP{u}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3716}%
$\displaystyle - \frac{\overline{\rho_v} + \rho_v^{\prime}}
{\overline{\rho} + \rho^{\prime}}
c_{pv} (\overline{\theta} + \theta^{\prime})
\DP{\Pi^{\prime}}{x} + D_{u}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3720}%
$\displaystyle - \frac{\overline{\rho_v} + \rho_v^{\prime}}
{\overline{\rho}}
\Dinv{1 + (\rho^{\prime} / \overline{\rho})}
c_{pv} (\overline{\theta} + \theta^{\prime})
\DP{\Pi^{\prime}}{x} + D_{u}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3722}%
$\displaystyle \simeq$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3724}%
$\displaystyle - \frac{\overline{\rho_v} + \rho_v^{\prime}}
{\overline{\rho}}
\left( 1 - \frac{\rho^{\prime}}{\overline{\rho}} \right)
c_{pv} (\overline{\theta} + \theta^{\prime})
\DP{\Pi^{\prime}}{x} + D_{u}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3728}%
$\displaystyle - \frac{\overline{\rho_v} + \rho_v^{\prime}}
{\overline{\rho_v}}
\left( 1 - \frac{\rho^{\prime}}{\overline{\rho}} \right)
c_{pv} (\overline{\theta} + \theta^{\prime})
\DP{\Pi^{\prime}}{x} + D_{u}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3732}%
$\displaystyle - \left( 1 + \frac{\rho_v^{\prime}}{\overline{\rho_v}} \right)
\left( 1 - \frac{\rho^{\prime}}{\overline{\rho}} \right)
c_{pv} (\overline{\theta} + \theta^{\prime})
\DP{\Pi^{\prime}}{x} + D_{u}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3736}%
$\displaystyle -  c_{pv} \overline{\theta} \DP{\Pi^{\prime}}{x} + D_{u},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3744}%
$\displaystyle - u \DP{u}{x} - w \DP{u}{z}
- c_{pv} \overline{\theta} \DP{\Pi^{\prime}}{x} + D_{u}
\Deqlab{EOM6}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3749}%
$\displaystyle 0 = - c_{pv} \overline{\theta} \DP{\overline{\Pi}}{z} - g
\Deqlab{EOM7}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3752}%
$\displaystyle \DP{w}{t} + u \DP{w}{x} + w \DP{w}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3756}%
$\displaystyle - \frac{\overline{\rho_v} + \rho_v^{\prime}}
{\overline{\rho} + \rho^{\prime}}
c_{pv} (\overline{\theta} + \theta^{\prime})
\left( \DP{\overline{\Pi}}{z} + \DP{\Pi^{\prime}}{z} \right)
- g + D_{w}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3760}%
$\displaystyle - \left( 1 + \frac{\rho_v^{\prime}}{\overline{\rho_v}} \right)
\left( 1 - \frac{\rho^{\prime}}{\overline{\rho}} \right)
c_{pv} (\overline{\theta} + \theta^{\prime})
\left( \DP{\overline{\Pi}}{z} + \DP{\Pi^{\prime}}{z} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3762}%
$\displaystyle - g + D_{w}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3766}%
$\displaystyle -  c_{pv} \overline{\theta} \DP{\overline{\Pi}}{z}
-  c_{pv} \overline{\theta} \DP{\Pi^{\prime}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3768}%
$\displaystyle -  \frac{\rho_v^{\prime}}{\overline{\rho_v}}
c_{pv} \overline{\theta} \DP{\overline{\Pi}}{z}
+  \frac{\rho^{\prime}}{\overline{\rho}}
c_{pv} \overline{\theta} \DP{\overline{\Pi}}{z}
-  c_{pv} \theta^{\prime} \DP{\overline{\Pi}}{z}
- g + D_{w}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3772}%
$\displaystyle -  c_{pv} \overline{\theta} \DP{\Pi^{\prime}}{z}
-  \frac{\rho_v^{\prime}}{\overline{\rho}}
c_{pv} \overline{\theta} \DP{\overline{\Pi}}{z}
+  \frac{\rho^{\prime}}{\overline{\rho}}
c_{pv} \overline{\theta} \DP{\overline{\Pi}}{z}
-  c_{pv} \theta^{\prime} \DP{\overline{\Pi}}{z}
+ D_{w}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3776}%
$\displaystyle -  c_{pv} \overline{\theta} \DP{\Pi^{\prime}}{z}
+  \frac{\rho_s^{\prime}}{\overline{\rho}}
c_{pv} \overline{\theta} \DP{\overline{\Pi}}{z}
-  c_{pv} \theta^{\prime} \DP{\overline{\Pi}}{z}
+ D_{w}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3780}%
$\displaystyle -  c_{pv} \overline{\theta} \DP{\Pi^{\prime}}{z}
-  \frac{\rho_s^{\prime}}{\overline{\rho}}  g
+  \frac{ \theta^{\prime}}{\overline{\theta}} g
+ D_{w}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3784}%
$\displaystyle -  c_{pv} \overline{\theta} \DP{\Pi^{\prime}}{z}
+ g
\left(
\frac{\theta^{\prime}}{\overline{\theta}}
- \frac{R \overline{\theta}}{p_0 \overline{\Pi}^{c_{vv}/R}}
\rho_s^{\prime}
\right)
+ D_{w},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3791}%
$\displaystyle - u \DP{w}{x} - w \DP{w}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3795}%
$\displaystyle -  c_{pv} \overline{\theta} \DP{\Pi^{\prime}}{z}
+ g
\left(
\frac{\theta^{\prime}}{\overline{\theta}}
- \frac{R \overline{\theta}}{p_0 \overline{\Pi}^{c_{vv}/R}}
\rho_s^{\prime}
\right)
+ D_{w}
\Deqlab{EOM8}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\setcounter{chapter}{2}
\setcounter{equation}{0}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3805}%
$\displaystyle \rho_v
= \frac{p}{R T}
= \frac{ p_0 \Pi^{c_{pv}/R}}{R \Pi \theta}
= \frac{p_0}{R} \frac{\Pi^{c_{vv} / R}}{\theta}
\Deqlab{Peq1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3808}%
$\displaystyle \frac{D \rho_v}{D t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3812}%
$\displaystyle \frac{D}{D t}
\left( \frac{p_0}{R} \frac{\Pi^{c_{vv} / R}}{\theta} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3816}%
$\displaystyle \frac{p_0 c_{vv}}{R^2}
\frac{ \Pi^{c_{vv}/R - 1}}{\theta} \frac{D \Pi}{D t}
- \frac{p_0}{R}
\frac{\Pi^{c_{vv}/R}}{\theta^2} \frac{D \theta}{D t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3820}%
$\displaystyle \frac{c_{vv}}{R \Pi}
\left( \frac{p_0}{R} \frac{\Pi^{c_{vv} / R}}{\theta} \right)
\frac{D \Pi}{D t}
-
\Dinv{\theta}
\left( \frac{p_0}{R} \frac{\Pi^{c_{vv} / R}}{\theta} \right)
\frac{D \theta}{D t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3826}%
$\displaystyle \frac{c_{vv} \rho_v}{R \Pi} \frac{D \Pi}{D t}
- \frac{\rho_v}{\theta} \frac{D \theta}{D t}
\Deqlab{Peq2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3830}%
$\displaystyle \frac{D \rho_v}{D t}  = - \rho_v \nabla \cdot \Dvect{u} - M_{cond}  \Deqlab{Peq3}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3834}%
$\displaystyle \frac{D \theta}{D t}  =    \Dinv{\Pi}    \left( Q_{cond} + Q_{dis} + Q_{rad} \right) \Deqlab{Peq4}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3837}%
$\displaystyle \frac{D \Pi}{D t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3841}%
$\displaystyle \frac{R \Pi}{c_{vv}}
\left(
\Dinv{\rho_v} \frac{D \rho_v}{D t}
+ \Dinv{\theta} \frac{D \theta}{D t}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3845}%
$\displaystyle \frac{R \Pi}{c_{vv}}
\left[
- \nabla \cdot \Dvect{u}
- \Dinv{\rho_v} M_{cond}
+ \Dinv{\theta \Pi}
\left( Q_{cond} + Q_{dis} + Q_{rad} \right)
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3849}%
$\displaystyle \frac{c^2}{c_{pv} \theta}
\left[
- \nabla \cdot \Dvect{u}
- \Dinv{\rho_v} M_{cond}
+ \Dinv{\theta \Pi}
\left( Q_{cond} + Q_{dis} + Q_{rad} \right)
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3855}%
$\displaystyle - \frac{c^2}{c_{pv} \theta} \nabla \cdot \Dvect{u}
- \frac{c^2}{c_{pv} \rho_v \theta} M_{cond}
+ \frac{c^2 }{c_{pv} \theta^2 \Pi}
\left( Q_{cond} + Q_{dis} + Q_{rad} \right)
\Deqlab{Peq5}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3857}%
$ c$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3861}%
$\displaystyle c^2   = \frac{c_{pv}}{c_{vv}} R \theta \Pi   \Deqlab{Peq6}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3865}%
$ Q_{*}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3872}%
$\displaystyle - w^{\prime} \DP{\overline{\Pi}}{z}
- \frac{\overline{c^2}}{c_{pv} \overline{\theta}}
\nabla \cdot \Dvect{u}^{\prime}
- \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}}
M_{cond}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3876}%
$\displaystyle + \frac{\overline{c^2} }{c_{pv} \overline{\theta}^2 \overline{\Pi}}
\left( Q_{cond + }Q_{dis} + Q_{rad} \right)
\Deqlab{Peq7}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3881}%
$\displaystyle \overline{\rho} \overline{\theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3885}%
$\displaystyle \frac{p_0}{R} \overline{\Pi}^{c_{vv}/R}
\Deqlab{Peq8}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3889}%
$\displaystyle \overline{c^2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3893}%
$\displaystyle \frac{c_{pv}}{c_{vv}} R \overline{\theta} \overline{\Pi}
\Deqlab{Peq9}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3896}%
$\displaystyle \DP{}{z} \left( \overline{\rho} \overline{\theta} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3900}%
$\displaystyle \DP{}{z}
\left( \frac{p_0}{R} \overline{\Pi}^{c_{vv}/R} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3904}%
$\displaystyle \frac{c_{vv}}{R} \frac{p_0}{R} \overline{\Pi}^{c_{vv}/R - 1}
\DP{\overline{\Pi}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3908}%
$\displaystyle \frac{c_{vv}}{R}
\frac{\overline{\rho} \overline{\theta}}{\overline{\Pi}}
\DP{\overline{\Pi}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3914}%
$\displaystyle \frac{c_{pv} \overline{\rho} \overline{\theta}^2}{\overline{c^2}}
\DP{\overline{\Pi}}{z}
\Deqlab{Peq10}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3917}%
$\displaystyle - w^{\prime} \DP{\overline{\Pi}}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3921}%
$\displaystyle - \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}^2}
w^{\prime}
\DP{}{z} \left( \overline{\rho} \overline{\theta} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3927}%
$\displaystyle - \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}^2}
\Dvect{u}^{\prime} \cdot \nabla
\left( \overline{\rho} \overline{\theta} \right)
\Deqlab{Peq11}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3934}%
$\displaystyle - \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}^2}
\Dvect{u}^{\prime} \cdot \nabla
\left( \overline{\rho} \overline{\theta} \right)
- \frac{\overline{c^2}}{c_{pv} \overline{\theta}}
\nabla \cdot \Dvect{u}^{\prime}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3936}%
$\displaystyle + \frac{\overline{c^2} }{c_{pv}^2 \overline{\theta}^2 \overline{\Pi}}
\left( Q_{cond} + Q_{dis} + Q_{rad} \right)
- \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}}
M_{cond}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3940}%
$\displaystyle - \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}^2}
\left[
\Dvect{u}^{\prime} \cdot \nabla
\left( \overline{\rho} \overline{\theta} \right)
+ \overline{\rho} \overline{\theta}
\nabla \cdot \Dvect{u}^{\prime}
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3946}%
$\displaystyle - \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}^2}
\nabla \cdot
\left( \overline{\rho} \overline{\theta} \Dvect{u}^{\prime} \right)
+ \frac{\overline{c^2} }{c_{pv} \overline{\theta}^2 \overline{\Pi}}
\left( Q_{cond} + Q_{dis} + Q_{rad} \right)
- \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}}
M_{cond}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3950}%
$\displaystyle \Deqlab{Peq12}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3954}%
$\displaystyle Q_{cond} = \frac{L M_{cond}}{c_{pv} \overline{\rho}}   \Deqlab{Peq13}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3963}%
$\displaystyle - \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}^2}
\nabla \cdot
\left( \overline{\rho} \overline{\theta} \Dvect{u}^{\prime} \right)
+ \frac{\overline{c^2} }{c_{pv} \overline{\theta}^2 \overline{\Pi}}
\left(
\frac{L M_{cond}}{c_{pv} \overline{\rho}}  + Q_{dis} + Q_{rad}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3965}%
$\displaystyle - \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}}
M_{cond}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3971}%
$\displaystyle + \frac{\overline{c^2} }{c_{pv} \overline{\theta}^2 \overline{\Pi}}
\left( Q_{dis} + Q_{rad} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3975}%
$\displaystyle - \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}^2}
\nabla \cdot
\left( \overline{\rho} \overline{\theta} \Dvect{u}^{\prime} \right)
+ \frac{\overline{c^2} }{c_{pv} \overline{\rho} \overline{\theta}}
\left(
\frac{L}{c_{pv} \overline{\theta} \overline{\Pi}} - 1
\right)  M_{cond}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3981}%
$\displaystyle - \frac{\overline{c^2}}{c_{pv} \overline{\rho} \overline{\theta}^2}
\nabla \cdot
\left( \overline{\rho} \overline{\theta} \Dvect{u}^{\prime} \right)
+ \frac{\overline{c^2} }{c_{pv} \overline{\rho} \overline{\theta}}
\left( \frac{L}{c_{pv} \overline{T}} - 1 \right)  M_{cond}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3985}%
$\displaystyle + \frac{\overline{c^2} }{c_{pv} \overline{\theta}^2 \overline{\Pi} }
\left( Q_{dis} + Q_{rad} \right)
\Deqlab{Peq14}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\setcounter{chapter}{3}
\setcounter{equation}{0}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3988}%
$ m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3993}%
$\displaystyle \DD{m}{t} = 4 \pi r_d^2 D \DP{\rho}{r}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3995}%
$ r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4004}%
$\displaystyle \DD{m}{t} = - 4 \pi r_d D (\rho_{r_d} - \rho_{\infty})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4006}%
$ r=r_d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4008}%
$ \rho = \rho_{r_d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4010}%
$ r\rightarrow \infty$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4012}%
$ \rho \rightarrow \rho_{\infty}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4014}%
$ p = \rho R T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4019}%
$\displaystyle \DD{m}{t} = - 4 \pi r_d D
\left(\frac{p_*(T_{r_d})}{RT_{r_d}}
- \frac{p_{\infty}}{RT_{\infty}}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4021}%
$ p*(T_{\infty})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4024}%
$\displaystyle \frac{1}{p_*(T_{\infty})} \DD{m}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4028}%
$\displaystyle - \frac{4 \pi r_d D}{R} \left(\frac{p_*(T_{r_d})}{p_*(T_{r_d})T_{r_d}}
- \frac{p_{\infty}}{p_*(T_{r_d})T_{\infty}}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4034}%
$\displaystyle - \frac{4 \pi r_d D}{RT_{\infty}} \left(\frac{p_*(T_{r_d})}{p_*(T_{\infty})}
- \frac{p_{\infty}}{p_*(T_{\infty})}\right)
\Deqlab{±ÀÎ³¼ÁÎÌ¤Î»þ´ÖÊÑ²½}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4036}%
$ (T_{r_d}-T_{\infty})/T_{\infty} \ll 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4041}%
$\displaystyle L \DD{m}{t} = - 4 \pi r^2 k \DD{T}{r}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4048}%
$\displaystyle L \DD{m}{t} = 4 \pi r k (T_{r_d} - T_{\infty})
\Deqlab{ÀøÇ®¤Î»þ´ÖÊÑ²½}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4052}%
$ T = T_{r_d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4056}%
$ T \rightarrow T_{\infty}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4059}%
$\displaystyle \DD{p_*}{T} = \frac{L p_*}{R T^2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4062}%
$\displaystyle \ln \frac{p_*(T_{r_d})}{p_*(T_{\infty})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4066}%
$\displaystyle \frac{L}{R}\frac{T_{r_d} - T_{\infty}}{T_{r_d}T_{\infty}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4070}%
$\displaystyle \sim$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4072}%
$\displaystyle \frac{L}{R}\frac{T_{r_d} - T_{\infty}}{T_{\infty}^2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4075}%
$\displaystyle \frac{p_*(T_{r_d})}{p_*(T_{\infty})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4079}%
$\displaystyle \exp\left(\frac{L}{R}\frac{T_{r_d} - T_{\infty}}{T_{r_d}T_{\infty}}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4083}%
$\displaystyle 1 + \frac{L}{R}\frac{T_{r_d} - T_{\infty}}{T_{\infty}^2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4089}%
$\displaystyle 1 + \frac{L^2}{4 \pi r_d k R T_{\infty}^2} \DD{m}{t}
\Deqlab{Ë°ÏÂ¾øµ¤°µÈæ¤Î¼°}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4094}%
$\displaystyle \DD{m}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4098}%
$\displaystyle - \frac{4 \pi r D p_*(T_{\infty})}{RT_{\infty}}
\left(1 + \frac{L^2}{4 \pi r_d k R T_{\infty}^2} \DD{m}{t}
- \frac{p_{\infty}}{p_*(T_{\infty})}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4103}%
$\displaystyle \left( \frac{RT_{\infty}}{D p_*(T_{\infty})}
+ \frac{L^2}{k R T_{\infty}^2} \right) \DD{m}{t}
= 4 \pi r_d \left(\frac{p_{\infty}}{p_*(T_{\infty})} - 1 \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4106}%
$\displaystyle R_m$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4110}%
$\displaystyle \frac{RT_{\infty}}{D p_*(T_{\infty})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4116}%
$\displaystyle \frac{L^2}{k R T_{\infty}^2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4122}%
$\displaystyle \frac{p_{\infty}}{p_*(T_{\infty})}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4127}%
$\displaystyle \DD{m}{t} = \frac{4 \pi r_d}{R_m + R_h} (S - 1)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4129}%
$ R_m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4135}%
$ N$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4142}%
$\displaystyle M_{cond} = N \DD{m}{t} = \frac{4 \pi r_d N}{R_m + R_h} (S - 1)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4144}%
$ R_m \ll R_h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4149}%
$\displaystyle M_{cond} \sim \frac{4 \pi r_d N}{R_h} (S - 1)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}


\end{document}
