Turbulence affects the structure and motions of nearly all temperature and density regimes in the interstellar gas. This two-part review summarizes the observations, theory, and simulations of interstellar turbulence and their implications for many fields of astrophysics. The first part begins with diagnostics for turbulence that have been applied to the cool interstellar medium, and highlights their main results. The energy sources for interstellar turbulence are then summarized along with numerical estimates for their power input. Supernovae and superbubbles dominate the total power, but many other sources spanning a large range of scales, from swing amplified gravitational instabilities to cosmic ray streaming, all contribute in some way. Turbulence theory is considered in detail, including the basic fluid equations, solenoidal and compressible modes, global inviscid quadratic invariants, scaling arguments for the power spectrum, phenomenological models for the scaling of higher order structure functions, the direction and locality of energy transfer and cascade, velocity probability distributions, and turbulent pressure. We emphasize expected differences between incompressible and compressible turbulence. Theories of magnetic turbulence on scales smaller than the collision mean free path are included, as are theories of magnetohydrodynamic turbulence and their various proposals for power spectra. Numerical simulations of interstellar turbulence are reviewed. Models have reproduced the basic features of the observed scaling relations, predicted fast decay rates for supersonic MHD turbulence, and derived probability distribution functions for density. Thermal instabilities and thermal phases have a new interpretation in a supersonically turbulent medium. Large-scale models with various combinations of self-gravity, magnetic fields, supernovae, and -2 -star formation are beginning to resemble the observed interstellar medium in morphology and statistical properties. The role of self-gravity in turbulent gas evolution is clarified, leading to new paradigms for the formation of star clusters, the stellar mass function, the origin of stellar rotation and binary stars, and the effects of magnetic fields. The review ends with a reflection on the progress that has been made in our understanding of the interstellar medium, and offers a list of outstanding problems.

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Observations suggest that star formation occurs in only one or two crossing times for a range of scales spanning a factor of D1000. These observations include (1) measurements of embedded cluster ages in comparison with the cloud core dynamical times, (2) measurements of the age di †erence versus separation for clusters in the Large Magellanic Clouds in comparison with the crossing time versus size correlation for molecular clouds, (3) the hierarchical structure of embedded young clusters, and (4) the high fraction of dense clouds that contain star formation.Such a short overall timescale for star formation implies that sources of turbulent energy or internal feedback are not required to explain or extend cloud lifetimes and that star and protostar interactions cannot be important for the stellar initial mass function. Stars appear in a cloud as if they freeze out of the gas, preserving the turbulent-driven gas structure in their birth locations. The Galaxy-wide star formation rate avoids the Zuckerman-Evans catastrophe, which has long been a concern for molecular clouds that evolve this quickly, because the multifractal structure of interstellar gas ensures that only a small fraction of the mass is able to form stars. Star formation on large scales operates more slowly than on small scales, but in most cases the whole process is over in only a few dynamical times.

Many galaxies at high redshift have peculiar morphologies dominated by 10 8 -10 9 M kpc-sized clumps. Using numerical simulations, we show that these ''clump clusters'' can result from fragmentation in gravitationally unstable primordial disks. They appear as ''chain galaxies'' when observed edge-on. In less than 1 Gyr, clump formation, migration, disruption, and interaction with the disk cause these systems to evolve from initially uniform disks into regular spiral galaxies with an exponential or double-exponential disk profile and a central bulge. The inner exponential is the initial disk size, and the outer exponential is from material flung out by spiral arms and clump torques. A nuclear black hole may form at the same time as the bulge from smaller black holes that grow inside the dense cores of each clump. The properties and lifetimes of the clumps in our models are consistent with observations of the clumps in high-redshift galaxies, and the stellar motions in our models are consistent with the observed velocity dispersions and lack of organized rotation in chain galaxies. We suggest that violently unstable disks are the first step in spiral galaxy formation. The associated starburst activity gives a short timescale for the initial stellar disk to form.