Scaling Relations for Turbulence in Multiphase Interstellar Medium

We simulate the dynamics of phase transition in radiatively cooling interstellar gas in three dimensions with a high order hydrodynamic method. We have previously shown (Kritsuk & Norman 2002a) in simulations with non-equilibrium initial conditions that thermal instability induces supersonic turbulence as a by-product of the phase transition which leads to formation of multiphase medium. We rely on a generalization of the She & Lévêque (1994) model to study velocity scaling relations in this decaying turbulence and compare those with analogous results for compressible isothermal turbulence. Since radiative cooling promotes nonlinear instabilities in highly supersonic flows, turbulence in our simulations tends to be more intermittent than in the isothermal case. Hausdorff dimension of the most singular dissipative structures, D, can be as high as 2.3, while in supersonic isothermal turbulence D is limited by a more primitive nature of dissipation (shocks): D ≤ 2. We also show that single-phase velocity statistics carry only incomplete information on turbulent cascade in a multiphase medium. We discuss possible implications of these results to hierarchical structure of molecular clouds and star formation. Subject headings: hydrodynamics — instabilities — ISM: structure — turbulence