layer can be evaluated by $|v|\simeq l_\mathrm{F}/t_\mathrm{c}$, where $t_\mathrm{c}$ is the cooling timescale [@FS93]. Since this value is very small in the actual ISM, ZP69 suggested that the transition front is almost static.

Figure \[fig:j0\](a) represents properties of the ZP solution for $P_\mathrm{c}/k_\mathrm{B}=3000$ K cm$^{-3}$. The corresponding mass flux is as large as $j_\mathrm{ZP}=-3.2\times10^{-3}m_\mathrm{H}$ km s$^{-1}
(v_\mathrm{w}=4.7\times10^{-3}$ km s$^{-1}$). The first row of figure \[fig:j0\] shows trajectories of solutions with various boundary conditions in the phase diagram $(\theta,d\theta/dx)$. There are three stationary points, which are indicated by the filled circles. The CNM and WNM are denoted by ‘C’ and ‘W’, respectively. As mentioned in section \[sec:numerical\], the CNM and WNM correspond to saddle points. On the other hand, the stationary point at the intermediate $\theta$ corresponds to the unstable phase denoted by ‘U’ in figure \[fig:j0\](a), and it is spiral point [@Eetal92; @FS93]. The solutions starting from the CNM are denoted by the thick solid line. The ZP solution connects two saddle points ‘C’ and ‘W’. The second row of figure \[fig:j0\](a) represents the temperature profile. The trajectory of the ZP solution in the $(n,P)$ plane is shown in the third row of figure \[fig:j0\](a).

Dynamical Transition Layers {#sec:dynamical}
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