Bimodal Behavior and Convergence Requirement in Macroscopic Properties
  of the Multiphase Interstellar Medium Formed by Atomic Converging Flows
  We systematically perform hydrodynamics simulations of 20 km s^-1 converging
flows of the warm neutral medium (WNM) to calculate the formation of the cold
neutral medium (CNM), especially focusing on the mean properties of the
multiphase interstellar medium (ISM), such as the average shock front position
and the mean density on a 10 pc scale. Our results show that the convergence in
those mean properties requires 0.02 pc spatial resolution that resolves the
cooling length of the thermally unstable neutral medium (UNM) to follow the
dynamical condensation from the WNM to CNM. We also find that two distinct
post-shock states appear in the mean properties depending on the amplitude of
the upstream WNM density fluctuation (= sqrt(<drho^2>)/rho_0). When the
amplitude > 10 %, the interaction between shocks and density inhomogeneity
leads to a strong driving of the post-shock turbulence of > 3 km s^-1, which
dominates the energy budget in the shock-compressed layer. The turbulence
prevents the dynamical condensation by cooling and the following CNM formation,
and the CNM mass fraction remains as ~ 45 %. In contrast, when the amplitude <=
10 %, the shock fronts maintain an almost straight geometry and CNM formation
efficiently proceeds, resulting in the CNM mass fraction of ~ 70 %. The
velocity dispersion is limited to the thermal-instability mediated level of 2 -
3 km s^-1 and the layer is supported by both turbulent and thermal energy
equally. We also propose an effective equation of state that models the
multiphase ISM formed by the WNM converging flow as a one-phase ISM.
