The turbulent interstellar medium: Generalizing to a scale-dependent phase continuum

We discuss the likely sources of turbulence in the ISM and explicitly calculate the detailed grand source function for the conventional sources of turbulence from supernovae, superbubbles, stellar winds, and H II regions. We find that the turbulent pumping due to the grand source function is broadband, consequently expanding the inertial range of the cascade. We investigate the general properties of the turbulent spectrum using a simple approach based on a spectral transfer equation derived from the hydrodynamic Kovasznay approximation. There are two major findings in this paper: (1) the turbulent pressure calculated from the grand source function is given by p(turb) similar to 10-100p(th); (2) with the scale-dependent energy dissipation from a turbulent cascade, the multiphase medium concept can be generalized to a more natural continuum description, in which density and temperature are functions of scale. Approximate power-law behavior is seen over a large dynamic range. We discuss some of the implications of models for the ISM, in particular, addressing the energy balance of the warm neutral phase. However, this paper is not concerned with the detailed structure of the ISM of the Galaxy. Rather, we attempt here to broaden our approach to the global turbulent structure of the ISM and also to move from the current many-phase description to a more natural scale-dependent continuum of phases.