4.2 $BCfEg(B (1998)

$BCfEg(B (1998) $B$O<>=aCGG.29EY8:N($H@EE*0BDjEY$r0J2<$N$h$&$KM?$($?(B. $B$?$@$7J*M}NL$r<($9J8;z$rJQ$($F$"$k(B.

$$\DD{T}{z} = - \frac{g}{{c_{p}^{\dagger}}_{d}} \left( \frac{ 1 + \frac{\lambda... ...lambda^{\dagger}}^{2} q}{R_{v}^{\dagger} {c_{p}^{\dagger}}_{d} T^{2}} } \right)$$ (63)

$$= - \frac{g}{{c_{p}^{\dagger}}_{d}} \left\{ 1 - \left( \frac{\lambd... ...\right) \frac{\lambda^{\dagger} q^{\dagger}}{{c_{p}^{\dagger}}_{d} T} \right\}.$$ (64)

$$N^{2} = \frac{g}{T} \left( \DD{T}{z} + \frac{g}{{c_{p}^{\dagger}}_{d}} \right) + g \left(\frac{M_{d}}{M_{v}} - 1 \right) \DP{ (rq)}{z},$$ (65)

$$\approx \frac{g^{2}}{{c_{p}^{\dagger}}_{d} T} \left( \frac{\lambda^{\dagg... ...r}}{{c_{p}^{\dagger}}_{d} T} + \left(1 - \frac{M_{d}}{M_{v}} \right) \right\} q$$ (66)

$B$?$@$7E:;z(B $\dagger$ $B$NIU$$$?NL$OC10L $R_{d}^{\dagger} = R/M_{d}$ $B$O4%[email protected],$NC10L $R_{v}^{\dagger} = R/M_{v}$ mail protected],(B $B$NC10L ${c_{p}^{\dagger}}_{d}=c_{p}/M_{d}$ $B$OC10L $\lambda^{\dagger}=\lambda/M_{v}$ $B$OC10L $B$O>e>:[email protected],$N:.9gHf$G$"$j(B, $B5$2t$N<~0O$NBg(B $B5$$N:.9gHf$r<>EY(B $r$ $B$rMQ$$$F(B $r q$ $B$H$7$?(B.

$B0J2<$G$O(B, $BA0@a$G5a$a$?<>=aCGG.29EY8:N($H@EE*0BDjEY$,(B, $B$=$l$>$l(B (63), (65) $B<0$GI=8=$5$l$k$3$H$r<($9(B. $B$^$?(B () $B$H(B (65) $B<0$rJQ7A$9$k$3$H$G(B (64) $B$H(B (66) $B<0$,$=$l$>$lF3$+$l$k$3$H$r<($9(B.

(63) $B<0$O(B (60) $B<0$K$*$$$F(B, $M \approx M_{d}, R^{\dagger}_{v} = R^{\dagger} / \varepsilon$ $B$H$9$k$3$H$GD>$A$K5a$^(B $B$k(B. mail protected],$N>/$J$$$H$9$k>r7o$,@.N)$9$k>l9g$K$O(B $1 \gg \frac{{\lambda^{\dagger}}^{2} q}{R_{v}^{\dagger} {c_{p}^{\dagger}}_{d} T^{2}}$ $B$H$J$k$N$G(B, (64) $B<0$O0J2<$N$h$&$KF3=P$5$l$k(B.

$$\DD{T}{z} = - \frac{g}{{c_{p}^{\dagger}}_{d}} \left( \frac{ 1 + \frac{\lambda... ...mbda^{\dagger}}^{2} q}{R_{v}^{\dagger} {c_{p}^{\dagger}}_{d} T^{2}} } \right) ,$$

$$\approx - \frac{g}{{c_{p}^{\dagger}}_{d}} \left( 1 + \frac{\lambda^{\dagg... ...\lambda^{\dagger}}^{2} q}{R_{v}^{\dagger} {c_{p}^{\dagger}}_{d} T^{2}} \right),$$

$$= - \frac{g}{{c_{p}^{\dagger}}_{d}} \left\{ 1 - \left( \frac{\lambd... ...\right) \frac{\lambda^{\dagger} q^{\dagger}}{{c_{p}^{\dagger}}_{d} T} \right\}.$$

$B$?$@$7(B $q$ $B$N(B 2 $Br7o$N>l9g(B, $B$3$N6a;w$,@.N)$9$k>r7o$O$*$*$h$=(B $q \ll 2.0 \times 10^{-2}$ $B$G$"$k(B.

$B@EE*0BDjEY$N<0(B (65) $B$O(B, $B@EE*0BDjEY$N<0(B (55) $B$K$*$$$F(B, $BC10L%b%kEv$?$j$N(B $BNL$rC10L/$J$$>r7o2<$G$N%b%kHf$H:.9gHf$N4X78<0(B (61) $B$*$h$SJ,;RNL$N4X78(B (62) $B$rMQ$$$k$3$H$G5a$^$k(B.

$$N^{2} = \frac{g}{T} \left( \Gamma_{m} + \frac{M g}{{c_{p}^{\dagger}}_{d} M} \right) - g \left( \frac{r (M_{v} - M_{d})}{M} \DD{X}{z} \right)$$

$$= \frac{g}{T} \left( \Gamma_{m} + \frac{ g}{{c_{p}^{\dagger}}_{d}} ... ... g \left( \frac{r (M_{v} - M_{d})}{M_{d}} \frac{M_{d}}{M_{v}} \DD{q}{z} \right)$$

$$= \frac{g}{T} \left( \Gamma_{m} + \frac{ g}{{c_{p}^{\dagger}}_{d}} \right) + g \left( \frac{M_{d}}{M_{v}} - 1 \right) \DD{(r q)}{z}$$

$B$?$@$7(B $dT/dz = \Gamma_{m}$ $B$H$7$?(B. $B$5$i$K(B (65) $B<0$NJQ7A$r(B $B9T$&(B. (31) $B<0$r(B $dq/dz$ $B$N<0$K=q$-49$($k$H(B,

$$\DD{ ( r q )}{z} = \left( \frac{ \lambda^{\dagger} M_{v} }{ R^{\dagger}_{d} M_{d} T^{2}} \DD{T}{z} + \frac{M g }{ R^{\dagger}_{d} M T} \right) (r q) ,$$

$$= \left( - \frac{ \lambda^{\dagger} }{ R^{\dagger}_{v} T^{2}} \frac{g}{{c_{p}^{\dagger}}_{d}} + \frac{g }{ R^{\dagger}_{d} T} \right) (r q) ,$$

$$= \frac{g}{{c_{p}^{\dagger}}_{d} T} \left( \frac{ {c_{p}^{\dagger}}... ...\dagger}_{d} } - \frac{ \lambda^{\dagger} }{ R^{\dagger}_{v} T} \right) (r q) .$$ (67)

$B$H$J$k(B. $B$?$@$7(B $q$ $B$O>.$5$$$N$G(B, $dT/dz \approx - g /{c_{p}^{\dagger}}_{d}$ $B$H$7$?(B. (67) $B<0$H(B (64) $B<0$r(B (65) $B<0$K(B $BBeF~$9$k$3$H$G(B, (66) $B<0$,F@$i$l$k(B.

$$N^{2} = \frac{g}{T} \left( \Gamma_{m} + \frac{ g}{{c_{p}^{\dagger}}_{d}} \right) + g \left( \frac{M_{d}}{M_{v}} - 1 \right) \DD{(r q)}{z}$$

$$= \frac{g}{T} \left[ \frac{g}{{c_{p}^{\dagger}}_{d}} \left\{ \left(... ...{d} } - \frac{ \lambda^{\dagger} }{ R^{\dagger}_{v} T} \right) (r q) \right\} ,$$

$$= \frac{g^{2}}{{c_{p}^{\dagger}}_{d} T} \left( \frac{\lambda^{\dagg... ...{c_{p}^{\dagger}}_{d} T} + r \left( 1 - \frac{M_{d}}{M_{v}} \right) \right\} q.$$