Annu. Rev. Astron. Astrophys. 2004. 42: 211-273
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In 1951, von Weizsäcker (1951) outlined a theory for interstellar matter (ISM) that is similar to what we believe today: cloudy objects with a hierarchy of structures form in interacting shock waves by supersonic turbulence that is stirred on the largest scale by differential galactic rotation and dissipated on small scales by atomic viscosity. The "clouds" disperse quickly because of turbulent motions, and on the largest scales they produce the flocculent spiral structures observed in galaxies. In the same year, von Hoerner (1951) noticed that rms differences in emission-line velocities of the Orion nebula increased with projected separation as a power law with a power alpha between 0.25 and 0.5, leading him to suggest that the gas was turbulent with a Kolmogorov energy cascade (for which alpha would be 0.33; Section 4.6). Wilson et al. (1959) later got a steeper function, alpha ~ 0.66, using better data, and proposed it resulted from compressible turbulence. Correlated motions with a Kolmogorov structure function (Section 2) in optical absorption lines were observed by Kaplan (1958). One of the first statistical models of a continuous and correlated gas distribution was by Chandrasekhar & Münch (1952), who applied it to extinction fluctuations in the Milky Way surface brightness. Minkowski (1955) called the ISM "an entirely chaotic mass ... of all possible shapes and sizes ... broken up into numerous irregular details."

These early proposals regarding pervasive turbulence failed to catch on. Interstellar absorption and emission lines looked too smooth to come from an irregular network of structures - a problem that is still with us today (Section 2). The extinction globules studied by Bok & Reilly (1947) looked too uniform and round, suggesting force equilibrium. Oort & Spitzer (1955) did not believe von Weizsäcker's model because they thought galactic rotational energy could not cascade down to the scale of cloud linewidths without severe dissipation in individual cloud collisions. Similar concerns about dissipation continue to be discussed (Sections 3, 5.3). Oort and Spitzer also noted that the ISM morphology appeared wrong for turbulence: "instead of more or less continuous vortices, we find concentrated clouds that are often separated by much larger spaces of negligible density." They expected turbulence to resemble the model of the time, with space-filling vortices in an incompressible fluid, rather than today's model with most of the mass compressed to a small fraction of the volume in shocks fronts. When a reddening survey by Scheffler (1967) used structure functions to infer power-law correlated structures up to 5° in the sky, the data were characterized by saying only that there were two basic cloud types, large (70 pc) and small (3 pc), the same categories popularized by Spitzer (1968) in his textbook.

Most of the interesting physical processes that could be studied theoretically at the time, such as the expansion of ionized nebulae and supernovae (SNe) and the collapse of gas into stars, could be modeled well enough with a uniform isothermal medium. Away from these sources, the ISM was viewed as mostly static, with discrete clouds moving ballistically. The discovery of broad emission lines and narrow absorption lines in H I at 21 cm reinforced this picture by suggesting a warm intercloud medium in thermal pressure balance with the cool clouds (Clark 1965). ISM models with approximate force equilibrium allowed an ease of calculation and conceptualization that was not present with turbulence. Supernovae were supposed to account for the energy, but mostly by heating and ionizing the diffuse phases (McCray & Snow 1979). Even after the discoveries of the hot intercloud (Bunner et al. 1971, Jenkins & Meloy 1974) and cold molecular media (Wilson et al. 1970), the observation of a continuous distribution of neutral hydrogen temperature (Dickey, Salpeter, & Terzian 1977), and the attribution of gas motions to supernovae (e.g., McKee & Ostriker 1977), there was no compelling reason to dismiss the basic cloud-intercloud model in favor of widespread turbulence. Instead, the list of ISM equilibrium "phases" was simply enlarged. Supersonic linewidths, long known from H I (e.g., McGee, Milton, & Wolfe 1966, Heiles 1970) and optical (e.g., Hobbs 1974) studies and also discovered in molecular regions at this time (see Zuckerman & Palmer 1974), were thought to represent magnetic waves in a uniform cloud (Arons & Max 1975), even though turbulence was discussed as another possibility in spite of problems with the rapid decay rate (Goldreich & Kwan 1974, Zuckerman & Evans 1974). A lone study by Baker (1973) found large-scale correlations in H I emission and presented them the context of ISM turbulence, deriving the number of "turbulent cells in the line of sight," instead of the number of "clouds." Mebold, Hachenberg & Laury-Micoulaut (1974) followed this with another statistical analysis of the H I emission. However, there was no theoretical context in which the Baker and Mebold et al. papers could flourish given the pervasive models about discrete clouds and two or three-phase equilibrium.

The presence of turbulence was more widely accepted for very small scales. Observations of interstellar scintillation at radio wavelengths implied there were correlated structures (Rickett 1970), possibly related to turbulence (Little & Matheson 1973), in the ionized gas at scales down to 109 cm or lower (Salpeter 1969; Interstellar Turbulence II, next chapter, this volume). This is the same scale at which cosmic rays (Interstellar Turbulence II) were supposed to excite magnetic turbulence by streaming instabilities (Wentzel 1968a). However, there was (and still is) little understanding of the physical connection between these small-scale fluctuations and the larger-scale motions in the cool neutral gas.

Dense structures on resolvable scales began to look more like turbulence after Larson (1981) found power-law correlations between molecular cloud sizes and linewidths that were reminiscent of the Kolmogorov scaling law. Larson's work was soon followed by more homogeneous observations that showed similar correlations (Myers 1983, Dame et al. 1986, Solomon et al. 1987). These motions were believed to be turbulent because of their power-law nature, despite continued concern with decay times, but there was little recognition that turbulence on larger scales could also form the same structures in which the linewidths were measured. Several reviews during this time reflect the pending transition (Dickey 1985, Dickman 1985, Scalo 1987, Dickey & Lockman 1990).

Perhaps the most widespread change in perception came when the Infrared Astronomical Satellite (IRAS) observed interstellar "cirrus" and other clouds in emission at 100 µ (Low et al. 1984). The cirrus clouds are mostly transparent at optical wavelengths, so they should be in the diffuse cloud category, but they were seen to be filamentary and criss-crossed, with little resemblance to "standard" clouds. Equally complex structures were present even in IRAS maps of "dark clouds," like Taurus, and they were observed in maps of molecular clouds, such as the Orion region (Bally et al. 1987). The wide field of view and good dynamic range of these new surveys finally allowed the diffuse and molecular clouds to reveal their full structural complexity, just as the optical nebulae and dark clouds did two decades earlier. Contributing to this change in perception was the surprising discovery by Crovisier & Dickey (1983) of a power spectrum for widespread H I emission that was comparable to the Kolmogorov power spectrum for velocity in incompressible turbulence. CO velocities were found to be correlated over a range of scales, too (Scalo 1984, Stenholm 1984). By the late 1980s, compression from interstellar turbulence was considered to be one of the main cloud-formation mechanisms (see review in Elmegreen 1991).

Here we summarize observations and theory of interstellar turbulence. This first review discusses the dense cool phases of the ISM, energy sources, turbulence theory, and simulations. Interstellar Turbulence II considers the effects of turbulence on element mixing, chemistry, cosmic ray scattering, and radio scintillation.

There are many reviews and textbooks on turbulence. A comprehensive review of magnetohydrodynamical (MHD) turbulence is in the recent book by Biskamp (2003), and a review of laboratory turbulence is in Sreenivasan & Antonia (1997). A review of incompressible MHD turbulence is in Chandran (2003). For the ISM, a collection of papers covering a broad range of topics is in the book edited by Franco & Carraminana (1999). Recent reviews of ISM turbulence simulations are in Vázquez-Semadeni et al. (2000), Mac Low (2003), and Mac Low & Klessen (2004), and a review of observations is in Falgarone, Hily-Blant & Levrier (2003). A review of theory related to the ISM is given by Vázquez-Semadeni (1999). Earlier work is surveyed by Scalo (1987). General discussions of incompressible turbulence can be found in Tennekes & Lumley (1972), Hinze (1975), Lesieur (1990), McComb (1990), Frisch (1995), Mathieu & Scott (2000), Pope (2000), and Tsinober (2001). The comprehensive two volumes by Monin & Yaglom (1975) remain extremely useful. Work on compressibility effects in turbulence at fairly low Mach numbers is reviewed by Lele (1994). Generally the literature is so large that we can reference only a few specific results on each topic; the reader should consult the most recent papers for citations of earlier work.

We have included papers that were available to us as of Dec. 2003. A complete bibliography including paper titles is available at:

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