mechanism of the corrugation instability is analogous to the Darriues-Landau instability [@LL87]. Taking into account magnetic field perpendicular to the normal of the front, @SZ10 investigated linear stability of transition layers.

In the above-mentioned theoretical works with respect to the bistable fluid, the phase transition proceeds in a quasi-static manner through the heat conduction. However, recent multidimensional numerical simulations show more a dynamical turbulent structure. @KN02 have investigated the non-linear development of the TI in the three-dimensional hydrodynamical simulations with periodic boundary condition without any external forcing. As the initial condition, they set the hot ionized medium ($T=2\times 10^6$ K) where cooling dominates heating. The gas is quickly decomposed into two stable phases (CNM and WNM) and the intermediate unstable phase. In the multiphase medium, the supersonic turbulence is developed by conversion from the thermal energy to the kinetic energy. They found that turbulence decays on a dynamical timescale. This decaying timescale is larger than that in supersonic isothermal turbulence of one-phase medium where it is smaller or comparable to the flow crossing time [@Setal98]. @KI06 have done similar calculations on a much longer timescale. As the initial condition, they set an unstable gas in thermal equilibrium state with density 