Shocks form the basis of our understanding for the density and velocity statistics of supersonic turbulent flows, such as those found in the cool interstellar medium (ISM). The variance of the density field, $σ^2_{ρ/ρ_0}$, is of particular interest for molecular clouds (MCs), the birthplaces of stars in the Universe. The density variance may be used to infer underlying physical processes in an MC, and parameterises the star formation (SF) rate of a cloud. However, models for $σ^2_{ρ/ρ_0}$ all share a common feature -- the variance is assumed to be isotropic. This assumption does not hold when a trans/sub-Alfvénic mean magnetic field, $\vec{B}_0$, is present in the cloud, which observations suggest is relevant for some MCs. We develop an anisotropic model for $σ_{ρ/ρ_0}^2$, using contributions from hydrodynamical and fast magnetosonic shocks that propagate orthogonal to each other. Our model predicts an upper bound for $σ_{ρ/ρ_0}^2$ in the high Mach number $(\mathcal{M})$ limit as small-scale density fluctuations become suppressed by the strong $\vec{B}_0$. The model reduces to the isotropic $σ_{ρ/ρ_0}^2-\mathcal{M}$ relation in the hydrodynamical limit. To validate our model, we calculate $σ_{ρ/ρ_0}^2$ from 12~high-resolution, three-dimensional, supersonic, sub-Alfvénic magnetohydrodynamical (MHD) turbulence simulations and find good agreement with our theory. We discuss how the two MHD shocks may be the bimodally oriented over-densities observed in some MCs and the implications for SF theory in the presence of a sub-Alfvénic $\vec{B}_0$. By creating an anisotropic, supersonic density fluctuation model, this study paves the way for SF theory in the highly anisotropic regime of interstellar turbulence.
The probability density function (PDF) of the logarithmic density contrast, $s=\ln (ρ/ρ_0)$, with gas density $ρ$ and mean density $ρ_0$, for hydrodynamical supersonic turbulence is well-known to have significant non-Gaussian (intermittent) features that monotonically increase with the turbulent Mach number, $\mathcal{M}$. By studying the mass- and volume-weighted $s$-PDF for an ensemble of 36 sub-to-trans-Alfvenic mean-field, supersonic, isothermal turbulence simulations with different modes of driving, relevant to molecular gas in the cool interstellar medium, we show that a more intricate p…
It is widely accepted that supersonic, magnetised turbulence plays a fundamental role for star formation in molecular clouds. It produces the initial dense gas seeds out of which new stars can form. However, the exact relation between gas compression, turbulent Mach number, and magnetic field strength is still poorly understood. Here, we introduce and test an analytical prediction for the relation between the density variance and the root-mean-square Mach number in supersonic, isothermal, magnetised turbulent flows. We approximate the density and velocity structure of the interstellar medium a…
Stars form in highly-magnetised, supersonic turbulent molecular clouds. Many of the tools and models that we use to carry out star formation studies rely upon the assumption of cloud isotropy. However, structures like high-density filaments in the presence of magnetic fields, and magnetosonic striations introduce anisotropies into the cloud. In this study we use the two-dimensional (2D) power spectrum to perform a systematic analysis of the anisotropies in the column density for a range of Alfvén Mach numbers ($\mathcal{M}_A=0.1$--$10$) and turbulent Mach numbers ($\mathcal{M}=2$--$20$), with …
We perform a comparison between the smoothed particle magnetohydrodynamics (SPMHD) code, Phantom, and the Eulerian grid-based code, Flash, on the small-scale turbulent dynamo in driven, Mach 10 turbulence. We show, for the first time, that the exponential growth and saturation of an initially weak magnetic field via the small-scale dynamo can be successfully reproduced with SPMHD. The two codes agree on the behaviour of the magnetic energy spectra, the saturation level of magnetic energy, and the distribution of magnetic field strengths during the growth and saturation phases. The main differe…
Supersonic turbulence plays an important role in a number of extreme astrophysical and terrestrial environments, yet its understanding remains rudimentary. We use data from a three-dimensional simulation of supersonic isothermal turbulence to reconstruct an exact fourth-order relation derived analytically from the Navier-Stokes equations (Galtier and Banerjee, Phys. Rev. Lett., vol. 107, 2011, p. 134501). Our analysis supports a Kolmogorov-like inertial energy cascade in supersonic turbulence previously discussed on a phenomenological level. We show that two compressible analogues of the four-…
Using data from a large-scale three-dimensional simulation of supersonic isothermal turbulence, we have tested the validity of an exact flux relation derived analytically from the Navier--Stokes equation by Falkovich, Fouxon and Oz [2010 New relations for correlation functions in Navier--Stokes turbulence. J. Fluid Mech. 644, 465]. That relation, for compressible barotropic fluids, was derived assuming turbulence generated by a large-scale force. However, compressible turbulence in simulations is usually initialized and maintained by a large-scale acceleration, as in gravity-driven astrophysic…
We conduct a systematic numerical study of passive scalar structures in supersonic turbulent flows. We find that the degree of intermittency in the scalar structures increases only slightly as the flow changes from transonic to highly supersonic, while the velocity structures become significantly more intermittent. This difference is due to the absence of shock-like discontinuities in the scalar field. The structure functions of the scalar field are well described by the intermittency model of She and Lévêque [Phys. Rev. Lett. 72, 336 (1994)], and the most intense scalar structures are found t…
I present a review of incompressible magnetohydrodynamic (MHD) turbulence in a strongly magnetised plasma. The approach is phenomenological even where a more rigorous theory is available, so that a reader armed with paper, pencil and some determination may be able to work through most of the physics. The focus is on the inertial-range spectra for very large (fluid and magnetic) Reynolds numbers. These theories of the inertial-range are built on two important facts: (i) Kraichnan's insight that the turbulent cascades are a result of nonlinear interactions between oppositely directed wavepackets…
The properties of supersonic isothermal turbulence influence a variety of astrophysical phenomena, including the structure and evolution of star forming clouds. This work presents a simple model for the structure of dense regions in turbulence in which the density distribution behind isothermal shocks originates from rough hydrostatic balance between the pressure gradient behind the shock and its deceleration from ram pressure applied by the background fluid. Using simulations of supersonic isothermal turbulence and idealized waves moving through a background medium, we show that the structura…
The interstellar turbulence is magnetized and thus anisotropic. The anisotropy of turbulent magnetic fields and velocities is imprinted in the related observables, rotation measures (RMs), and velocity centroids (VCs). This anisotropy provides valuable information on both the direction and strength of the magnetic field. However, its measurement is difficult especially in highly supersonic turbulence in cold interstellar phases due to the distortions by isotropic density fluctuations. By using 3D simulations of supersonic and sub-Alfvénic magnetohydrodynamic(MHD) turbulence, we find that the p…
The role of supersonic turbulence in structuring the interstellar medium (ISM) remains an unsettled question. Here, this problem is investigated using a newexact law of compressible isothermal hydrodynamic turbulence, which involves two-point correlations in physical space. The new law is shown to have a compact expression that contains a single flux term reminiscent of the incompressible case and a source term with a simple expression whose sign is given by the divergence of the velocity. The law is then used to investigate the properties of such a turbulence at integral Mach number $4$ produ…
Understanding the physics of turbulence is crucial for many applications, including weather, industry, and astrophysics. In the interstellar medium (ISM), supersonic turbulence plays a crucial role in controlling the gas density and velocity structure, and ultimately the birth of stars. Here we present a simulation of interstellar turbulence with a grid resolution of 10048^3 cells that allows us to determine the position and width of the sonic scale (l_s) - the transition from supersonic to subsonic turbulence. The simulation simultaneously resolves the supersonic and subsonic cascade, v(l) ~ …
We present collapse simulations of strongly magnetised, turbulent molecular cloud cores with masses ranging from 2.6 to 1000 M_sun in order to study the influence of the initial conditions on the turbulence-induced disc formation mechanism proposed recently by Seifried et al. 2012. We find that Keplerian discs are formed in all cases independently of the core mass, the strength of turbulence, or the presence of global rotation. The discs appear within a few kyr after the formation of the protostar, are 50 - 150 AU in size, and have masses between 0.05 and a few 0.1 M_sun. During the formation …
We present results of large-scale three-dimensional simulations of weakly magnetized supersonic turbulence at grid resolutions up to 1024^3 cells. Our numerical experiments are carried out with the Piecewise Parabolic Method on a Local Stencil and assume an isothermal equation of state. The turbulence is driven by a large-scale isotropic solenoidal force in a periodic computational domain and fully develops in a few flow crossing times. We then evolve the flow for a number of flow crossing times and analyze various statistical properties of the saturated turbulent state. We show that the energ…
Based on ideas by Woodward et al., a subgrid scale model that is applicable to highly compressible turbulence is presented. Applying the subgrid scale model in large eddy simulations of forced supersonic turbulence, the bottleneck effect is largely reduced and, thereby, approximate scaling laws can be obtained at relatively low numerical resolution. In agreement with previous results from PPM simulations without explicit subgrid scale model, it is found that the energy spectrum function for the velocity field with fractional density-weighing, rho^(1/3)u, varies substantially with the forcing, …
We use three-dimensional simulations to study the statistics of supersonic turbulence in molecular clouds. Our numerical experiments describe driven turbulent flows with an isothermal equation of state, Mach numbers around 10, and various degrees of magnetization. We first support the so-called 1/3-rule of Kritsuk et al. 2007 with our new data from a larger 2048^3 simulation. We then attempt to extend the 1/3-rule to supersonic MHD turbulence and get encouraging preliminary results based on a set of 512^3 simulations. Our results suggest an interesting new approach to tackle universal scaling …
Recent observations of column densities in molecular clouds find lognormal distributions with power-law high-density tails. These results are often interpreted as indications that supersonic turbulence dominates the dynamics of the observed clouds. We calculate and present the column-density distributions of three clouds, modeled with very different techniques, none of which is dominated by supersonic turbulence. The first star-forming cloud is simulated using smoothed particle hydrodynamics (SPH); in this case gravity, opposed only by thermal-pressure forces, drives the evolution. The second …
The probabilistic approach to turbulence is applied to investigate density fluctuations in supersonic turbulence. We derive kinetic equations for the probability distribution function (PDF) of the logarithm of the density field, $s$, in compressible turbulence in two forms: a first-order partial differential equation involving the average divergence conditioned on the flow density, $\langle \nabla \cdot {\bs u} | s\rangle$, and a Fokker-Planck equation with the drift and diffusion coefficients equal to $-\langle {\bs u} \cdot \nabla s | s\rangle$ and $\langle {\bs u} \cdot \nabla s | s\rangle$…
Coagulation driven by supersonic turbulence is primarily an astrophysical problem because coagulation processes on Earth are normally associated with incompressible fluid flows at low Mach numbers, while dust aggregation in the interstellar medium (ISM) for instance is an example of the opposite regime. We study coagulation of inertial particles in compressible turbulence using high-resolution direct and shock-capturing numerical simulations with a wide range of Mach numbers from nearly incompressible to moderately supersonic. The particle dynamics is simulated by representative particles and …
We show that the growth rate of dust grains in cold molecular clouds is enhanced by the high degree of compressibility of a turbulent, dilute gas. By means of high resolution (10243) numerical simulations, we confirm the theory that the spatial mean growth rate is proportional to the gas-density variance. This also results in broadening of the grain-size distribution (GSD) due to turbulence-induced variation of the grain-growth rate. We show, for the first time in a detailed numerical simulation of hydrodynamic turbulence, that the GSD evolves towards a shape which is a reflection of the gas-d…
Supersonic isothermal turbulence establishes a network of transient dense shocks that sweep up material and have a density profile described by balance between ram pressure of the background fluid versus the magnetic and gas pressure gradient behind the shock. These rare, densest regions of a turbulent environment can become Jeans unstable and collapse to form pre-stellar cores. Using numerical simulations of magneto-gravo-turbulence, we describe the structural properties of dense shocks, which are the seeds of gravitational collapse, as a function of magnetic field strength. In the regime of …
The hot intracluster medium (ICM) is thought to be quiescent with low observed velocity dispersions. Surface brightness fluctuations of the ICM also suggest that its turbulence is subsonic with a Kolmogorov scaling relation, indicating that the viscosity is suppressed and the kinetic energy cascades to small scales unscathed. However, recent observations of the cold gas filaments in galaxy clusters find that the scaling relations are steeper than that of the hot plasma, signaling kinetic energy losses and the presence of supersonic flows. In this work we use high-resolution simulations to expl…
We propose a model for the density statistics in supersonic turbulence, which play a crucial role in star-formation and the physics of the interstellar medium (ISM). Motivated by [Hopkins, MNRAS, 430, 1880 (2013)], the model considers the density to be arranged into a collection of strong shocks of width $\sim\! \mathcal{M}^{-2}$, where $\mathcal{M}$ is the turbulent Mach number. With two physically motivated parameters, the model predicts all density statistics for $\mathcal{M}>1$ turbulence: the density probability distribution and its intermittency (deviation from log-normality), the densit…
Supersonic flows in the interstellar medium (ISM) are believed to be a key driver of the molecular cloud formation and evolution. Among molecular clouds' properties, the ratio between the solenoidal and compressive modes of turbulence plays important roles in determining the star formation efficiency. We use numerical simulations of supersonic converging flows of the warm neutral medium (WNM) resolving the thermal instability to calculate the early phase of molecular cloud formation, and investigate the turbulence structure and the density probability distribution function (density PDF) of the…
The probability distribution of density in isothermal, supersonic, turbulent gas is approximately lognormal. This behaviour can be traced back to the shock waves travelling through the medium, which randomly adjust the density by a random factor of the local sonic Mach number squared. Provided a certain parcel of gas experiences a large number of shocks, due to the central limit theorem, the resulting distribution for density is lognormal. We explore a model in which parcels of gas undergo finite number of shocks before relaxing to the ambient density, causing the distribution for density to d…
We report a laser-plasma experiment that was carried out at the LMJ-PETAL facility and realized the first magnetized, turbulent, supersonic plasma with a large magnetic Reynolds number ($\mathrm{Rm} \approx 45$) in the laboratory. Initial seed magnetic fields were amplified, but only moderately so, and did not become dynamically significant. A notable absence of magnetic energy at scales smaller than the outer scale of the turbulent cascade was also observed. Our results support the notion that moderately supersonic, low-magnetic-Prandtl-number plasma turbulence is inefficient at amplifying ma…
We present three-dimensional, adaptive mesh simulations of dwarf galaxy out- flows driven by supersonic turbulence. Here we develop a subgrid model to track not only the thermal and bulk velocities of the gas, but also its turbulent velocities and length scales. This allows us to deposit energy from supernovae directly into supersonic turbulence, which acts on scales much larger than a particle mean free path, but much smaller than resolved large-scale flows. Unlike previous approaches, we are able to simulate a starbursting galaxy modeled after NGC 1569, with realistic radiative cooling throu…
An example of a cold massive core, JCMT 18354-0649S, a possible high mass analogue to a low mass star forming core is studied. Line and continuum observations from JCMT, Mopra Telescope and Spitzer are presented and modelled in detail using a 3D molecular line radiative transfer code. In almost every way JCMT 18354-0649S is a scaled-up version of a typical low mass core with similar temperatures, chemical abundances and densities. The difference is that both the infall velocity and the turbulent width of the line profiles are an order of magnitude larger. While the higher infall velocity is ex…
We investigate the clustering and dynamics of nano-sized particles (nano-dust) in high-resolution ($1024^3$) simulations of compressible isothermal hydrodynamic turbulence. It is well-established that large grains will decouple from a turbulent gas flow, while small grains will tend to trace the motion of the gas. We demonstrate that nano-sized grains may cluster in a turbulent flow (fractal small-scale clustering), which increases the local grain density by at least a factor of a few. In combination with the fact that nano-dust grains may be abundant in general, and the increased interaction …
Stable, accurate, divergence-free simulation of magnetized supersonic turbulence is a severe test of numerical MHD schemes and has been surprisingly difficult to achieve due to the range of flow conditions present. Here we present a new, higher order-accurate, low dissipation numerical method which requires no additional dissipation or local "fixes" for stable execution. We describe PPML, a local stencil variant of the popular PPM algorithm for solving the equations of compressible ideal magnetohydrodynamics. The principal difference between PPML and PPM is that cell interface states are evolv…
We present a simulation of isothermal supersonic (rms Mach number $\mathcal{M}_{\rm rms} \sim 3$) turbulent gas with inertial particles (dust) and self-gravity in statistical steady-state, which we compare with a corresponding simulation without self-gravity. The former is in steady state, but close to gravitationally unstable, since we match the scale of the simulation box with Jeans wavelength, which provides the strongest influence of gravity on the dynamics of gas and dust without causing irreversible gravitational collapses. We find that self-gravity does not cause any significant increas…
We examine the relation between the density variance and the mean-square Mach number in supersonic, isothermal turbulence, assumed in several recent analytic models of the star formation process. From a series of calculations of supersonic, hydrodynamic turbulence driven using purely solenoidal Fourier modes, we find that the `standard' relationship between the variance in the log of density and the Mach number squared, i.e., sigma^2_(ln rho/rhobar)=ln (1+b^2 M^2), with b = 1/3 is a good fit to the numerical results in the supersonic regime up to at least Mach 20, similar to previous determina…
The slope of the power spectrum of the density field in isothermal supersonic compressible turbulence
ENS de Lyon, CRAL UMR5574, Universite Claude Bernard Lyon 1, CNRS（里昂高等师范学校，CRAL UMR5574，克洛德·贝尔纳里昂大学，法国国家科学研究中心）；School of Physics, University of Exeter（埃克塞特大学物理学院）
Filaments are an ubiquitous feature of molecular clouds, and appear to play a critical role in assembling the material to form stars. The dominant filaments are observed to have a rather narrow range of widths around $\sim 0.1$ pc, and to be preferentially aligned perpendicularly to the direction of the local magnetic field. We have previously argued that the observed filament widths can be explained if filaments are formed by converging, mildly supersonic flows, resulting from large-scale turbulent motions in the parent molecular cloud. Here we demonstrate that the introduction of a magnetic …
Shock bound interaction zones (SBIZs) are ubiquitous in astrophysics. We present numerical results for 2D and 3D, plane-parallel, infinitely extended SBIZs. Isothermal settings and parameterized cooling are considered. We highlight and compare characteristic of such zones. We emphasize the mutual coupling between the turbulence within the SBIZ and the confining shocks, point out potential differences to 3D periodic box studies of supersonic turbulence, and contemplate on possible effects on the X-ray emission of such zones.
The tight correlation between turbulence and luminosity in Giant HII Regions is not well understood. While the luminosity is due to the UV radiation from the massive stars in the ionizing clusters, it is not clear what powers the turbulence. Observations of the two prototypical Giant HII Regions in the local Universe, 30 Doradus and NGC604, show that part of the kinetic energy of the nebular gas comes from the combined stellar winds of the most massive stars - the cluster winds, but not all. We present a study of the kinematics of 30 Doradus based on archival VLT FLAMES/GIRAFFE data and new hi…
In many astrophysical environments, mixing of heavy elements occurs in the presence of a supersonic turbulent velocity field. Here we carry out the first systematic numerical study of such passive scalar mixing in isothermal supersonic turbulence. Our simulations show that the ratio of the scalar mixing timescale, $τ_{\rm c}$, to the flow dynamical time, $τ_{\rm dyn}$ (defined as the flow driving scale divided by the rms velocity), increases with the Mach number, $M$, for $M \lsim3$, and becomes essentially constant for $M \gsim3.$ This trend suggests that compressible modes are less efficient…
We revisit the origin of Larson's scaling laws describing the structure and kinematics of molecular clouds. Our analysis is based on recent observational measurements and data from a suite of six simulations of the interstellar medium, including effects of self-gravity, turbulence, magnetic field, and multiphase thermodynamics. Simulations of isothermal supersonic turbulence reproduce observed slopes in linewidth-size and mass-size relations. Whether or not self-gravity is included, the linewidth-size relation remains the same. The mass-size relation, instead, substantially flattens below the …
In major galaxy mergers, the orbits of stars are violently perturbed, and gas is torqued to the centre, diluting the gas metallicity and igniting a starburst. In this paper, we study the gas dynamics in and around merging galaxies using a series of cosmological magneto-hydrodynamical (MHD) zoom-in simulations. We find that the gas bridge connecting the merging galaxies pre-coalescence is dominated by turbulent pressure, with turbulent Mach numbers peaking at values of 1.6-3.3. This implies that bridges are dominated by supersonic turbulence, and are thus ideal candidates for studying the impac…
The rich structure that we observe in molecular clouds is due to the interplay between strong magnetic fields and supersonic (turbulent) velocity fluctuations. The velocity fluctuations interact with the magnetic field, causing it too to fluctuate. Using numerical simulations, we explore the nature of such magnetic field fluctuations, $\vec{δB}$, over a wide range of turbulent Mach numbers, $\mathcal{M} = 2 - 20$ (i.e., from weak to strong compressibility), and Alfvén Mach numbers, $\mathcal{M}_{\text{A}0} = 0.1 - 100$ (i.e., from strong to weak magnetic mean fields, $B_0$). We derive a compre…
The emergence of large-scale magnetic fields observed in the diffuse interstellar medium is explained by a turbulent dynamo. The underlying transport coefficients have previously been extracted from numerical simulations. So far, this was restricted to the kinematic regime, but we aim to extend our analysis into the realm of dynamically important fields. This marks an important step on which derived mean-field models rely to explain observed equipartition strength fields. As in previous work, we diagnose turbulent transport coefficients by means of the test-field method. We derive quenching fu…
Observations reveal the presence of supermassive black holes (SMBH) as early as ~700 million years after the Big Bang. Their formation path is still subject to current debate. We explore the influence of magnetic fields, which are strongly amplified via the turbulent small-scale dynamo, on the formation of SMBH seeds within the direct collapse scenario. In this study, we perform for the first time cosmological magnetohydrodynamic large eddy simulations that employ a model for unresolved, compressible MHD turbulence. In total we perform 36 simulations for 9 haloes each with two different initia…
We present the results of eighteen magnetohydrodynamical calculations of the collapse of a molecular cloud core to form a protostar. Some calculations include radiative transfer in the flux-limited diffusion approximation while others employ a barotropic equation of state. We cover a wide parameter space, with mass-to-flux ratios ranging from $μ= 5$ to $20$; initial turbulent amplitudes ranging from a laminar calculation (i.e. where the Mach number, $\mathscr{M} = 0$) to transonic $\mathscr{M} = 1$; and initial rotation rates from $β_\mathrm{rot} = 0.005$ to $0.02$. We first show that using a …
This work presents a new physical model of the star formation rate (SFR), verified with an unprecedented set of large numerical simulations of driven, supersonic, self-gravitating, magneto-hydrodynamic (MHD) turbulence, where collapsing cores are captured with accreting sink particles. The model depends on the relative importance of gravitational, turbulent, magnetic, and thermal energies, expressed through the virial parameter, alpha_vir, the rms sonic Mach number, M_S,0, and the ratio of mean gas pressure to mean magnetic pressure, beta_0. The SFR is predicted to decrease with increasing alp…
We study density fluctuations in supersonic turbulence using both theoretical methods and numerical simulations. A theoretical formulation is developed for the probability distribution function (PDF) of the density at steady state, connecting it to the conditional statistics of the velocity divergence. Two sets of numerical simulations are carried out, using either a Riemann solver to evolve the Euler equations or a finite-difference method to evolve the Navier-Stokes (N-S) equations. After confirming the validity of our theoretical formulation with the N-S simulations, we examine the effects …
We compare the statistics of driven, supersonic turbulence at high Mach number using FLASH a widely used Eulerian grid-based code and PHANTOM, a Lagrangian SPH code at resolutions of up to 512^3 in both grid cells and SPH particles. We find excellent agreement between codes on the basic statistical properties: a slope of k^-1.95 in the velocity power spectrum for hydrodynamic, Mach 10 turbulence, evidence in both codes for a Kolmogorov-like slope of k^-5/3 in the variable rho^1/3 v as suggested by Kritsuk et al. and a log-normal PDF with a width that scales with Mach number and proportionality…
Magnetic fields in several astrophysical objects are amplified and maintained by a dynamo mechanism, which is the conversion of the turbulent kinetic energy to magnetic energy. A dynamo that amplifies magnetic fields at scales $<$ the driving scale of turbulence is known as the fluctuation dynamo. We study the properties of the fluctuation dynamo in supersonic turbulent plasmas, which is of relevance to the ISM, structure formation, and lab experiments of laser-plasma turbulence. Using simulations, we explore the properties of the exponentially growing and saturated state of the fluctuation dy…
Turbulence in compressible plasma plays a key role in many areas of astrophysics and engineering. The extreme plasma parameters in these environments, e.g. high Reynolds numbers, supersonic and super-Alfvenic flows, however, make direct numerical simulations computationally intractable even for the simplest treatment -- magnetohydrodynamics (MHD). To overcome this problem one can use subgrid-scale (SGS) closures -- models for the influence of unresolved, subgrid-scales on the resolved ones. In this work we propose and validate a set of constant coefficient closures for the resolved, compressib…
We conduct numerical experiments to determine the density probability distribution function (PDF) produced in supersonic, isothermal, self-gravitating turbulence of the sort that is ubiquitous in star-forming molecular clouds. Our experiments cover a wide range of turbulent Mach number and virial parameter, allowing us for the first time to determine how the PDF responds as these parameters vary, and we introduce a new diagnostic, the dimensionless star formation efficiency versus density ($ε_{\rm ff}(s)$) curve, which provides a sensitive diagnostic of the PDF shape and dynamics. We show that…
A model, which is widely used for inertial rang statistics of supersonic turbulence in the context of molecular clouds and star formation, expresses (measurable) relative scaling exponents Z_p of two-point velocity statistics as a function of two parameters, beta and Delta. The model relates them to the dimension D of the most dissipative structures, D=3-Delta/(1-beta). While this description has proved most successful for incompressible turbulence (beta=Delta=2/3, and D=1), its applicability in the highly compressible regime remains debated. For this regime, theoretical arguments suggest D=2 …
