driving turbulence is not fully understood. As mentioned above, recent numerical simulations have found that the turbulence involving the TI is dynamical compared with the ZP69 picture that predicts very slow transition between CNM and WNM through the heat conduction. Moreover, in the shock compressed region, because of its high pressure, the bistable fluid cannot exist. The ZP69 picture cannot be applied directly to the TI in the shock compressed region.

In this paper, as a first step to understand the dynamical turbulent structure, we develop the works of ZP69 into a more dynamical transition front. In the steady solutions, there are two parameters, the pressure of the CNM and the mass flux across the front. ZP69 considered solutions only on a line in the parameter space. @Eetal92 found steady solutions with various mass flux. However, they used a simple cubic function of the cooling rate that enables them to investigate analytically, and they assumed spatially constant pressure. We systematically search steady solutions in larger parameter space even in the high pressure range where the bistable fluid does not exist by using a realistic cooling rate.

This paper is organized as follows: Basic equations and numerical methods are described in 