▪ Abstract 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 structu...

http://www.ifa.hawaii.edu/%7Ereipurth/reviews/elmegreen1_araa.pdf

Interstellar Turbulence I: Observations and Processes

This article reviews evidence concerning the cornerstone dissipation scaling of turbulence theory: � = CU 3 /L, with C� = const., � the dissipation rate of turbulent kinetic energy U 2 ,a ndL an integral length scale characterizing the energy-containing turbulent eddies. This scaling is intimately linked to the Richardson-Kolmogorov equilibrium cascade. Accumulating evidence shows that a significant nonequilibrium region exists in various turbulent flows in which the energy spectrum has Kolmogorov's −5/3 wave-number scaling over a wide wave-number range, yet C� ∼ Re m /Re n ,w ithm ≈ 1 ≈ n, Re I a global/inlet Reynolds number, and ReL a local turbulence Reynolds number.

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Dissipation in Turbulent Flows

The regions associated with high levels of vorticity and energy dissipation are studied in numerically simulated isotropic turbulence at Re λ = 168. Their geometry and spatial distribution are characterized by means of box-counting methods. No clear scaling is observed for the box counts of intense strain rate and vorticity sets, presumably due to the limited inertial range, but it is shown that, even in that case, the box-counting method can be refined to characterize the shape of the intense structures themselves, as well as their spatial distribution. The fractal dimension of the individual vorticity structures, D ω → 1.1 ± 0.1, suggests that they tend to form filamentary vortices in the limit of high vorticity threshold. On the other hand, the intense dissipation structures have dimensions D s ≃ 1.7 ± 0.1, with no noticeable dependence on the threshold, suggesting structures in the form of sheets or ribbons. Statistics of the associated aspect ratios for different thresholds support these observations. Finally box counting is used to characterize the spatial distribution of the baricentres of the structures

/pdf/geometry-and-clustering-of-intense-structures-in-isotropic-30bup8v7mn.pdf

Geometry and clustering of intense structures in isotropic turbulence

Context. Tens of light hydrides and small molecules have now been detected over several hundreds sightlines sampling the diffuse interstellar medium (ISM) in both the solar neighbourhood and the inner Galactic disk. They provide unprecedented statistics on the first steps of chemistry in the diffuse gas. Aims. These new data confirm the limitations of the traditional chemical pathways driven by the UV photons and the cosmic rays (CR) and the need for additional energy sources, such as turbulent dissipation, to open highly endoenergetic formation routes. The goal of the present paper is to further investigate the link between specific species and the properties of the turbulent cascade in particular its space-time intermittency. Methods. We have analysed ten different atomic and molecular species in the framework of the updated model of turbulent dissipation regions (TDR). We study the influence on the abundances of these species of parameters specific to chemistry (density, UV field, and CR ionisation rate) and those linked to turbulence (the average turbulent dissipation rate, the dissipation timescale, and the ion-neutral velocity drift in the regions of dissipation). Results. The most sensitive tracers of turbulent dissipation are the abundances of CH + and SH + , and the column densities of the J = 3, 4, 5 rotational levels of H2. The abundances of CO, HCO + , and the intensity of the 158 μm [CII] emission line are significantly enhanced by turbulent dissipation. The vast diversity of chemical pathways allows the independent determinations of free parameters never estimated before: an upper limit to the average turbulent dissipation rate, e 10 −23 erg cm −3 s −1 for nH = 20 cm −3 , from the CH + abundance; an upper limit to the ion-neutral velocity drift, υin 3. 5k m s −1 , from the SH + to CH + abundance ratio; and a range of dissipation timescales, 100 τV 1000 yr, from the CO to HCO + abundance ratio. For the first time, we reproduce the large abundances of CO observed on diffuse lines of sight, and we show that CO may be abundant even in regions with UV-shieldings as low as 5 × 10 −3 mag. The best range of parameters also reproduces the abundance ratios of OH, C2H, and H2 Ot o HCO + and are consistent with the known properties of the turbulent cascade in the Galactic diffuse ISM. Conclusions. Our results disclose an unexpected link between the dissipation of turbulence and the emergence of molecular richness in the diffuse ISM. Some species, such as CH + or SH + , turn out to be unique tracers of the energy trail in the ISM. In spite of some degeneracy, the properties of the turbulent cascade, down to dissipation, can be captured through specific molecular abundances.

/pdf/chemical-probes-of-turbulence-in-the-diffuse-medium-the-tdr-2t65x0xwwo.pdf

Chemical probes of turbulence in the diffuse medium: the TDR model

Context. Tens of light hydrides and small molecules have now been detected over several hundreds sight lines sampling the diffuse interstellar medium (ISM) in both the Solar neighbourhood and the inner Galactic disk. They provide unprecedented statistics on the first steps of chemistry in the diffuse gas. Aims. These new data confirm the limitations of the traditional chemical pathways driven by the UV photons and the cosmic rays (CR) and the need for additional energy sources, such as turbulent dissipation, to open highly endoenergetic formation routes. The goal of the present paper is to further investigate the link between specific species and the properties of the turbulent cascade in particular its space-time intermittency. Methods. We have analysed ten different atomic and molecular species in the framework of the updated model of turbulent dissipation regions (TDR). We study the influence on the abundances of these species of parameters specific to chemistry (density, UV field, and CR ionisation rate) and those linked to turbulence (the average turbulent dissipation rate, the dissipation timescale, and the ion neutral velocity drift in the regions of dissipation). Results. The most sensitive tracers of turbulent dissipation are the abundances of CH+ and SH+, and the column densities of the J = 3, 4, 5 rotational levels of H2 . The abundances of CO, HCO+, and the intensity of the 158 $\mu$m [CII] emission line are significantly enhanced by turbulent dissipation. The vast diversity of chemical pathways allows the independent determinations of free parameters never estimated before: an upper limit to the average turbulent dissipation rate, $\overline{\varepsilon}$ < 10$^{-23}$ erg cm$^{-3}$ s$^{-1}$ for $n_H$=20 cm$^{-3}$, from the CH+ abundance; an upper limit to the ion-neutral velocity drift, $u_{in}$ < 3.5 km s$^{-1}$, from the SH+ to CH+ abundance ratio; and a range of dissipation timescales, 100 < $\tau_V$ < 1000 yr, from the CO to HCO+ abundance ratio. For the first time, we reproduce the large abundances of CO observed on diffuse lines of sight, and we show that CO may be abundant even in regions with UV-shieldings as low as $5 \times 10^{-3}$ mag. The best range of parameters also reproduces the abundance ratios of OH, C2H, and H2O to HCO+ and are consistent with the known properties of the turbulent cascade in the Galactic diffuse ISM. Conclusions. Our results disclose an unexpected link between the dissipation of turbulence and the emergence of molecular richness in the diffuse ISM. Some species, such as CH+ or SH+, turn out to be unique tracers of the energy trail in the ISM. In spite of some degeneracy, the properties of the turbulent cascade, down to dissipation, can be captured through specific molecular abundances.

/pdf/chemical-probes-of-turbulence-in-the-diffuse-medium-the-tdr-3k54w98qtu.pdf

The probability density function (PDF) of velocity fluctuations is studied experimentally for grid turbulence in a systematical manner. At small distances from the grid, where the turbulence is still developing, the PDF is sub-Gaussian. At intermediate distances, where the turbulence is fully developed, the PDF is Gaussian. At large distances, where the turbulence has decayed, the PDF is hyper-Gaussian. The Fourier transforms of the velocity fluctuations always have Gaussian PDFs. At intermediate distances from the grid, the Fourier transforms are statistically independent of each other. This is the necessary and sufficient condition for Gaussianity of the velocity fluctuations. At small and large distances, the Fourier transforms are dependent.

Probability density function of turbulent velocity fluctuations.

Vortical structures of turbulence, i.e., vortex tubes and sheets, are studied using one-dimensional velocity data obtained in laboratory experiments for duct flows and boundary layers at microscale Reynolds numbers from 332 to 1934. We study the mean velocity profile of intense vortical structures. The contribution from vortex tubes is dominant. The radius scales with the Kolmogorov length. The circulation velocity scales with the rms velocity fluctuation. We also study the spatial distribution of intense vortical structures. The distribution is self-similar over small scales and is random over large scales. Since these features are independent of the microscale Reynolds number and of the configuration for turbulence production, they appear to be universal.

Laboratory experiments for intense vortical structures in turbulence velocity fields

Kolmogorov’s theory for turbulence, proposed in 1941, is based on a hypothesis that small-scale statistics are uniquely determined by the kinematic viscosity and the mean rate of energy dissipation. Landau remarked that the local rate of energy dissipation should fluctuate in space over large scales and hence should affect small-scale statistics. Experimentally, we confirm the significance of this large-scale fluctuation, which is comparable to the mean rate of energy dissipation at the typical scale for energy-containing eddies. The significance is independent of the Reynolds number and the configuration for turbulence production. With an increase of scale r above the scale of largest energy-containing eddies, the fluctuation comes to have the scaling r−1∕2 and becomes close to Gaussian. We also confirm that the large-scale fluctuation affects small-scale statistics.

On Landau's prediction for large-scale fluctuation of turbulence energy dissipation

The probability density function of single-point velocity fluctuations in turbulence is studied systematically using Fourier coefficients in the energy-containing range. In ideal turbulence where energy-containing motions are random and independent, the Fourier coefficients tend to Gaussian and independent of each other. Velocity fluctuations accordingly tend to Gaussian. However, if energy-containing motions are intermittent or contaminated with bounded-amplitude motions such as wavy wakes, the Fourier coefficients tend to non-Gaussian and dependent of each other. Velocity fluctuations accordingly tend to non-Gaussian. These situations are found in our experiment of a rough-wall boundary layer.

Probability density function of turbulent velocity fluctuations in a rough-wall boundary layer.

The streamwise and transverse velocities are measured simultaneously in isotropic grid turbulence at relatively high Reynolds numbers ${\mathrm{Re}}_{\ensuremath{\lambda}}\ensuremath{\simeq}110--330.$ Using a conditional averaging technique, we extract typical intermittency patterns that are consistent with velocity profiles of a model for a vortex tube, i.e., Burgers vortex. The radii of the vortex tubes are several of the Kolmogorov length, regardless of the Reynolds number. Using the distribution of an interval between successive enhancements of a small-scale velocity increment, we study the spatial distribution of vortex tubes. The vortex tubes tend to cluster together. This tendency is increasingly significant with the Reynolds number. Using statistics of velocity increments, we also study the energetical importance of vortex tubes as a function of the scale. The vortex tubes are important over the background flow at small scales especially below the Taylor microscale. At a fixed scale, the importance is increasingly significant with the Reynolds number.

Yoshihide Kawashima

Papers

Probability density function of turbulent velocity fluctuations.

Laboratory experiments for intense vortical structures in turbulence velocity fields

On Landau's prediction for large-scale fluctuation of turbulence energy dissipation

Probability density function of turbulent velocity fluctuations in a rough-wall boundary layer.

Vortex tubes in velocity fields of laboratory isotropic turbulence: dependence on the Reynolds number.