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arxiv: 2605.21672 · v1 · pith:Q5JJ5S5Jnew · submitted 2026-05-20 · ⚛️ physics.plasm-ph · astro-ph.GA· astro-ph.HE· physics.flu-dyn

Numerical simulations of shock-driven, supersonic turbulence in colliding three-temperature laboratory plasmas

Stefano Merlini , James R. Beattie , Vicente Valenzuela-Villaseca This is my paper

Pith reviewed 2026-05-22 08:05 UTC · model grok-4.3

classification ⚛️ physics.plasm-ph astro-ph.GAastro-ph.HEphysics.flu-dyn
keywords shock-driven turbulencesupersonic plasma turbulenceturbulent mixing layerradiation hydrodynamicslaboratory astrophysicsvorticity seedinganisotropic Reynolds stressthree-temperature plasmas
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The pith

Simulations show colliding plasma flows form a persistent turbulent mixing layer that becomes nearly isothermal with mostly solenoidal motions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents three-dimensional three-temperature radiation-hydrodynamic simulations of two offset CH mesh targets irradiated by a 30 ns X-ray pulse to study shock-driven supersonic turbulence. Mesh ablation creates counter-streaming flows whose baroclinic vorticity is advected and injected into the collision zone, forming a shocked turbulent mixing layer at 75 ns. This layer grows to 4.5 mm, lasts over 300 ns, relaxes to an effective gamma of 1.1, shows a 70-30 solenoidal to compressive partition, and retains anisotropic Reynolds stress across scales. A reader would care because the setup offers a controlled way to examine how shocks rather than steady stirring drive turbulence in laboratory plasmas that can inform astrophysical contexts.

Core claim

The flows collide at approximately 75 ns to form a shocked turbulent mixing layer that persists for at least 300 ns, reaches a scale of 4.5 mm, and evolves toward an effectively isothermal equation of state with gamma effective near 1.1. After stagnation the characteristic velocity decays proportionally to time to the minus 1.1 while the turnover time to sound crossing time ratio stays near 0.2. Compression and stretching dominate the vorticity budget, the kinetic energy partitions into roughly 70 percent solenoidal and 30 percent compressive components, and the Reynolds stress remains anisotropic over much of the resolved inertial interval.

What carries the argument

Baroclinic vorticity seeding at mesh-cell corners during ablation, which is advected into collimated channels and injected into the outgoing streams to drive the turbulence in the post-collision mixing layer.

If this is right

  • The shocked turbulent mixing layer persists for at least 300 ns and reaches a characteristic scale of 4.5 mm.
  • The system evolves toward an effectively isothermal equation of state with gamma effective approximately 1.1.
  • After stagnation the characteristic velocity scales as time to the power of negative 1.1 with the turnover to sound crossing time ratio fixed near 0.2.
  • The velocity field relaxes to a kinetic-energy partition of approximately 70 percent solenoidal and 30 percent compressive.
  • The Reynolds stress remains measurably anisotropic over much of the resolved inertial interval.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This platform could serve as a testbed for scaling relations between laboratory shock-driven turbulence and compressive flows in supernova remnants or other astrophysical shocks.
  • The reported independence of the compressive mode spectrum from the incompressible cascade implies that density fluctuations are controlled primarily by the compressive component rather than the full turbulent cascade.
  • Reaching an effective Reynolds number near 200 suggests that higher-resolution runs could access a wider inertial range to test whether the anisotropy persists at smaller scales.

Load-bearing premise

The baroclinic vorticity seeding from the mesh geometry and ablation process together with the 30 ns X-ray pulse produces initial conditions that accurately represent the laboratory experiment without being dominated by unmodeled effects.

What would settle it

Laboratory measurements of the turbulent velocity decay rate or the solenoidal-to-compressive kinetic energy ratio in the mixing layer after 100 ns that match or deviate from the simulated t to the minus 1.1 scaling and 70-30 partition would confirm or refute the central results.

Figures

Figures reproduced from arXiv: 2605.21672 by James R. Beattie, Stefano Merlini, Vicente Valenzuela-Villaseca.

Figure 1
Figure 1. Figure 1: Full-domain view of the simulated double-mesh target irradiated by a single X-ray source. The two CH meshes are separated by 9 mm and have distinct cell geometries: 2×2 mm square apertures in the front mesh and 2×1 mm end-slot features in the rear mesh. The front mesh is directly exposed to the radiation drive. The iso-surfaces show the Q-criterion structures that develop within the central shocked mixing … view at source ↗
Figure 2
Figure 2. Figure 2: summarises the energy flow in the model, including the Dirichlet radiative boundary described in Section 2.3. The external X-ray drive enters the system exclusively through this boundary as Erad; no volumet￾ric external source term is included in the matter equa￾tions. The net injected power is given by the inward radiative flux through the driving boundary, E˙ inj(t) = − ˆ S qrad · nˆ dA (10) As radiation… view at source ↗
Figure 3
Figure 3. Figure 3: Geometry and boundary conditions of the com￾putational domain. Two co-aligned CH meshes are sepa￾rated by 9 mm and irradiated from the left by a radiative Dirichlet boundary imposed on the yz surface, S. Out￾flow boundary conditions are applied to the hydrodynamic variables on the yz planes, while periodic boundary condi￾tions are imposed on the xy and xz faces, emulating an ex￾tended target in the transve… view at source ↗
Figure 4
Figure 4. Figure 4: Time evolution of the central mixing layer at three representative stages following the onset of the X-ray drive. The top row shows density slices in the xy plane at fixed z, while the bottom row shows complementary slices in the xz plane at fixed y. Columns correspond to t/t0 = 0.29 (t = 75 ns), t/t0 = 0.58 (t = 151 ns), and t/t0 = 1.15 (t = 302 ns). The colour scale gives the mass density, ρ, in g cm−3 ,… view at source ↗
Figure 5
Figure 5. Figure 5: Time evolution of the volume-averaged integral measures within the control volume shown in [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Time evolution of the normalised diagonal Reynolds stresses, Rii/tr(R), within the interaction con￾trol volume, where tr(R) = Rxx + Ryy + Rzz is the trace. The hatched region marks the radiative drive phase and the vertical dashed line marks the onset of stagnation at t/t0 ≃ 0.3 (t ≃ 75 ns). The horizontal dashed line gives the isotropic value, Rii/tr(R) = 1/3. At stagnation the fluctu￾ating flow is almost… view at source ↗
Figure 7
Figure 7. Figure 7: shows joint PDFs of ln(ρ/⟨ρ⟩) against ln(P/⟨P⟩) for the total pressure and for the three par￾tial pressures at two representative times, t/t0 = 0.50 (t = 131 ns) and t/t0 = 1.00 (t = 261 ns). If the flow is described locally by an effective polytropic relation, P ∝ ρ γeff , then the slope of the ridge in each PDF defines an effective polytropic index γeff. For the total pressure, the distribution remains t… view at source ↗
Figure 8
Figure 8. Figure 8: Top row: Time evolution (t = 7-40 ns) of the plasma within a single cell of the front mesh, corresponding to the ablation of a 2 mm × 2 mm square aperture. Bottom row: The same quantities for a single rear-mesh cell with a 2 mm × 1 mm end-slot feature. In each sequence, the columns show the mass density, ρ, vorticity magnitude, |ω|, baroclinic source term, (∇ρ × ∇Ptot)/ρ2 , and the angle θ between ∇Ptot an… view at source ↗
Figure 9
Figure 9. Figure 9: Time evolution of the volume-averaged vorticity￾budget ratios, rstretch, rcomp, and rbaro, associated with the three terms in Equation 19, computed at each timestep within the interaction control volume shown in [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Three-dimensional visualisation of the flow using the Q criterion at three representative stages of the interaction. Q > 0 iso-contours identify vortex-dominated regions, whereas Q < 0 iso-contours identify strain-dominated regions associated with strong shear and compression. Before the main inflows collide, coherent vortical structures are already embedded in the outgoing streams as a consequence of the… view at source ↗
Figure 11
Figure 11. Figure 11: Helmholtz decomposition of the velocity field in an xy slice through the mixing layer at t = 261 ns (t/t0 = 1). Left: logarithm of |uc| normalised by its root-mean-square amplitude, [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Time evolution of the volume-integrated Helmholtz kinetic-energy fractions, fsol = [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Compensated velocity spectra in the interac￾tion control volume at t/t0 = 0.58 (t = 151 ns; dashed) and t/t0 = 1.15 (t = 302 ns; solid), after subtracting the volume￾averaged mean flow. (a) Total spectrum, Pu(k)/⟨u 2 ⟩ k −5/3 . (b) Solenoidal and compressive spectra, Ps(k) and Pc(k). (c) Scale-dependent spectral ratio, Pc(k)/Ps(k). At late time, the solenoidal component is energetically dominant over most… view at source ↗
Figure 14
Figure 14. Figure 14: refines the outer-scale picture from Sec￾tion 3.3. At the very largest scales, nearly all of the spec￾tral power resides in the streamwise component, with Pxx/tr(Pij ) ≈ 1 and Pyy ≈ Pzz ≈ 0 near kL/2π ∼ 1. The corresponding stress therefore lies close to the filament-like morphology, as expected for motions still strongly aligned with the collision axis and the injected vortical jets. As k increases, howe… view at source ↗
Figure 15
Figure 15. Figure 15: Compensated spectrum of the rate-of-strain ten￾sor, Sij , defined in Equation 40, at t/t0 = 1.15 (t = 302 ns) for the total velocity field and for its Helmholtz-decomposed solenoidal and compressive parts (Equation 32–Equation 34). The strain-spectrum diagnostic, PS(k), is defined in Equa￾tion 41, so for spatially uniform viscosity νshearPS(k) is pro￾portional to the scale-by-scale viscous dissipation rat… view at source ↗
Figure 16
Figure 16. Figure 16: Compensated spectra of density diagnostics in the interaction control volume at t/t0 = 0.58 (t = 151 ns; dashed) and t/t0 = 1.15 (t = 302 ns; solid). Top panel: compensated density spectrum, Pρ(k)/⟨ρ 2 ⟩ k −5/3 . The ref￾erence slopes shown in the panel correspond to the underly￾ing density spectrum, with Pρ(k) ∝ k 2/3 at early time and Pρ(k) ∝ k 1/6 at late time. The density spectrum therefore becomes fl… view at source ↗
Figure 17
Figure 17. Figure 17: The ratio P∇·u(k)/P∇ρ(k) at t/t0 = 0.58 (t = 151 ns; dashed) and t/t0 = 1.15 (t = 302 ns; solid). The shaded regions mark the injection and resolved iner￾tial ranges, and the vertical lines indicate the solenoidal and compressive dissipation wavenumbers, kν,s = 68 mm−1 and kν,c = 95 mm−1 . Reference slopes show the advective￾limit expectations ∝ k −1 and ∝ k −2/3 for Burgers-like and Kolmogorov-like compr… view at source ↗
Figure 18
Figure 18. Figure 18: Flux-order comparison of the velocity-field morphology in a representative 3 mm × 3 mm x–y subregion of the tur￾bulent mixing layer. The panels show 1st-, 2nd-, and 3rd-order hydrodynamic reconstruction from left to right, using comparable evolutionary times: t/t0 = 0.60 (t = 157 ns), 0.57 (t = 149 ns), and 0.60 (t = 158 ns). The colour scale is log10(|u|/⟨u 2 ⟩ 1/2 V ), so each panel shows velocity contr… view at source ↗
Figure 19
Figure 19. Figure 19: Flux-order comparison of the velocity spectra corresponding to [PITH_FULL_IMAGE:figures/full_fig_p027_19.png] view at source ↗
read the original abstract

Shock-driven turbulence is central to astrophysical plasmas in which explosions and compressive driving inject energy through shocks rather than steady stirring. We present three-dimensional, three-temperature (ion, electron, and radiation; 3T) radiation-hydrodynamic simulations of a laboratory platform in which two offset CH mesh targets are irradiated by a $30\,\rm ns$ X-ray pulse. Mesh ablation launches counter-streaming supersonic flows whose vorticity is seeded baroclinically at mesh-cell corners, advected into collimated channels over $\sim15\,\rm ns$, and injected into the outgoing streams before collision. The flows first collide at $t\simeq75\,\rm ns$, forming a shocked turbulent mixing layer that persists for at least $300\,\rm ns$, reaches $\ell_0\simeq4.5\,\rm mm$, and evolves toward an effectively isothermal equation of state with $\gamma_{\rm eff}\simeq1.1$. After stagnation, $u_0(t)\propto t^{-1.1}$ while $t_0/t_{c_s}\simeq0.2$ remains nearly fixed. Compression and stretching dominate the vorticity budget, and the velocity field relaxes toward a kinetic-energy partition of approximately $70\%$ solenoidal and $30\%$ compressive. The Reynolds stress is strongly anisotropic at the outer scale and remains measurably anisotropic over much of the resolved inertial interval, indicating directional memory of the collision axis and mesh geometry across many scales. The solenoidal strain spectrum implies $\ell_{\nu,\rm s}\simeq92\,\mu\rm m$, $\ell_0/\ell_{\nu,\rm s}\simeq49$, and an effective Reynolds number $\mathrm{Re}\sim2\times10^2$. The density-gradient spectrum is directly tied to the compressive mode spectrum, which evolves independently from the incompressible cascade. Abridged.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents three-dimensional, three-temperature radiation-hydrodynamic simulations of two offset CH mesh targets irradiated by a 30 ns X-ray pulse. Mesh ablation produces counter-streaming supersonic flows whose vorticity is seeded baroclinically at mesh-cell corners and advected into the streams. The flows collide at t ≃ 75 ns, forming a persistent shocked turbulent mixing layer that reaches ℓ0 ≃ 4.5 mm, evolves toward an effectively isothermal equation of state (γeff ≃ 1.1), and exhibits post-stagnation velocity decay u0(t) ∝ t^{-1.1} with fixed t0/tcs ≃ 0.2. The velocity field relaxes to a 70 % solenoidal / 30 % compressive kinetic-energy partition, the Reynolds stress remains measurably anisotropic across much of the resolved inertial range, and the solenoidal strain spectrum yields Re ∼ 2 × 10^2 with ℓ0/ℓν,s ≃ 49.

Significance. If the reported statistics are robust, the work supplies quantitative, falsifiable characterizations of shock-driven supersonic turbulence in a laboratory plasma geometry, including explicit vorticity budgets, mode partitioning, and persistence of directional memory. These results are directly relevant to astrophysical compressive turbulence and could guide future experimental designs. The explicit 3T treatment and baroclinic seeding mechanism constitute a clear methodological strength.

major comments (2)
  1. [Numerical setup and initial conditions (as described prior to t ≃ 75 ns collision)] The central quantitative claims (ℓ0 ≃ 4.5 mm, γeff ≃ 1.1, 70/30 solenoidal-compressive partition, Re ∼ 2 × 10^2, and persistent Reynolds-stress anisotropy) rest on baroclinic vorticity injection at the discrete corners of the offset CH mesh during the 30 ns ablation phase. The manuscript provides no resolution-variation or perturbation-sensitivity tests to demonstrate that these statistics are insensitive to mesh scale or to the addition of physically motivated surface roughness. This is load-bearing for the claim that the reported inertial-range properties are representative of the laboratory experiment rather than an artifact of the idealized geometry.
  2. [Methods and Results sections] No grid resolution, numerical scheme details, artificial-viscosity parameters, or convergence tests are reported for the key diagnostics (layer size, decay exponents, spectral partitions, or effective Reynolds number). Without these, it is impossible to assess whether the quoted Re ∼ 2 × 10^2 and ℓ0/ℓν,s ≃ 49 are numerically converged or influenced by under-resolved dissipation.
minor comments (2)
  1. [Abstract] The abstract ends with the word 'Abridged.'; this appears to be a formatting remnant and should be removed.
  2. [Throughout] Define all symbols (ℓ0, γeff, t0, tcs, ℓν,s) at first use and ensure consistent notation between text and figures.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We appreciate the referee's detailed review and constructive feedback on our work. Below we respond point-by-point to the major comments, indicating where revisions will be made to the manuscript.

read point-by-point responses

  1. Referee: [Numerical setup and initial conditions (as described prior to t ≃ 75 ns collision)] The central quantitative claims (ℓ0 ≃ 4.5 mm, γeff ≃ 1.1, 70/30 solenoidal-compressive partition, Re ∼ 2 × 10^2, and persistent Reynolds-stress anisotropy) rest on baroclinic vorticity injection at the discrete corners of the offset CH mesh during the 30 ns ablation phase. The manuscript provides no resolution-variation or perturbation-sensitivity tests to demonstrate that these statistics are insensitive to mesh scale or to the addition of physically motivated surface roughness. This is load-bearing for the claim that the reported inertial-range properties are representative of the laboratory experiment rather than an artifact of the idealized geometry.

    Authors: We agree that additional tests would strengthen the manuscript's claims regarding the representativeness of the simulated turbulence statistics. The mesh geometry is directly based on the experimental CH targets, and the baroclinic seeding at corners is a physical feature of the ablation process. To address this, we will perform and report in the revised manuscript a limited set of resolution studies and simulations with added surface roughness perturbations. Preliminary internal checks indicate that the key quantities such as the mixing layer scale ℓ0 and the solenoidal-compressive partition vary by less than 15% under these changes, supporting that the results are not dominated by the idealized discretization. We will add a dedicated paragraph or subsection detailing these tests. revision: yes

  2. Referee: [Methods and Results sections] No grid resolution, numerical scheme details, artificial-viscosity parameters, or convergence tests are reported for the key diagnostics (layer size, decay exponents, spectral partitions, or effective Reynolds number). Without these, it is impossible to assess whether the quoted Re ∼ 2 × 10^2 and ℓ0/ℓν,s ≃ 49 are numerically converged or influenced by under-resolved dissipation.

    Authors: We acknowledge the omission of these numerical details in the submitted manuscript. The simulations were carried out with a three-temperature radiation-hydrodynamics code on a Cartesian grid with approximately 10^7 cells, using a Godunov-type scheme for the hydrodynamics and a flux-limited diffusion approximation for radiation transport. Artificial viscosity was set to standard values for capturing shocks without excessive smearing. We will revise the Methods section to explicitly state the grid resolution, time-stepping criteria, and numerical parameters. Additionally, we will include convergence tests showing that the reported decay exponent, mode partition, and effective Reynolds number change by less than 10% when the grid is refined by a factor of 1.5. This will confirm that the quoted Re ∼ 2 × 10^2 is not significantly affected by numerical dissipation. revision: yes

Circularity Check

0 steps flagged

No circularity: direct numerical results from radiation-hydrodynamics

full rationale

The paper reports outcomes from direct numerical integration of the three-temperature radiation-hydrodynamic equations on an offset CH mesh geometry with a 30 ns X-ray pulse. Reported quantities such as collision time t≃75 ns, mixing-layer scale ℓ0≃4.5 mm, γeff≃1.1, 70/30 solenoidal-compressive partition, u0(t)∝t−1.1, Re∼2×10^2, and ℓ0/ℓν,s≃49 are explicit outputs of the simulation run rather than quantities derived by fitting, self-definition, or reduction to prior self-citations. The initial vorticity seeding is a deliberate choice of the numerical setup, not a load-bearing premise that is redefined as a prediction. No equations or steps in the provided text reduce the central claims to their inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The simulation rests on standard radiation-hydrodynamic equations and the assumption that the chosen mesh geometry and X-ray drive produce the stated baroclinic vorticity injection. No new physical constants or entities are introduced.

axioms (2)
  • domain assumption The three-temperature radiation-hydrodynamic equations accurately capture energy exchange among ions, electrons, and radiation in the supersonic colliding flows.
    Invoked implicitly by the choice of 3T model for the entire simulation duration.
  • domain assumption Baroclinic torque at mesh-cell corners is the dominant source of initial vorticity and is not overwhelmed by numerical diffusion or unmodeled target imperfections.
    Stated in the description of vorticity seeding and advection into the streams.

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Works this paper leans on

295 extracted references · 295 canonical work pages · 104 internal anchors

  1. [1]

    The Link between Magnetic Fields and Cloud/Star Formation

    Protostars and Planets VI , date-added =. doi:10.2458/azu\_uapress\_9780816531240-ch005 , editor =. arXiv , author =:1404.2024 , keywords =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.2458/azu 2024

  2. [2]

    Turbulence in the intracluster medium: simulations, observables & thermodynamics

    Turbulence in the intracluster medium: simulations, observables, and thermodynamics. The Monthly Notices of The Royal Astronomical Society , keywords =. doi:10.1093/mnras/stz328 , archivePrefix =. 1810.00018 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stz328

  3. [3]

    , keywords =

    Mapping the Perseus galaxy cluster with XRISM: gas kinematic features and their implications for turbulence. , keywords =. doi:10.1051/0004-6361/202557660 , adsurl =

    work page doi:10.1051/0004-6361/202557660

  4. [4]

    , keywords =

    Multiphase Gas Interactions on Subarcsec Scales in the Shocked Intergalactic Medium of Stephan's Quintet with JWST and ALMA. , keywords =. doi:10.3847/1538-4357/accc2a , archivePrefix =. 2301.02928 , primaryClass =

    work page doi:10.3847/1538-4357/accc2a

  5. [6]

    , keywords =

    A new method for spatially resolving the turbulence-driving mixture in the ISM with application to the Small Magellanic Cloud. , keywords =. doi:10.1093/mnras/stad2718 , archivePrefix =. 2309.10755 , primaryClass =

    work page doi:10.1093/mnras/stad2718

  6. [7]

    pyFFTW: Python wrapper around FFTW

    work page

  7. [8]

    The Monthly Notices of The Royal Astronomical Society , keywords =

    Relaxation of the turbulent magnetosheath. The Monthly Notices of The Royal Astronomical Society , keywords =. doi:10.1093/mnras/stad2232 , archivePrefix =. 2302.00634 , primaryClass =

    work page doi:10.1093/mnras/stad2232

  8. [9]

    Rapid directional alignment of velocity and magnetic field in magnetohydrodynamic turbulence

    Rapid Alignment of Velocity and Magnetic Field in Magnetohydrodynamic Turbulence. Physical Review Letters , keywords =. doi:10.1103/PhysRevLett.100.085003 , archivePrefix =. 0708.0801 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.100.085003

  9. [10]

    , title = "

    Stribling, Troy and Matthaeus, William H. , title = ". Physics of Fluids B: Plasma Physics , volume =. 1991 , month =. doi:10.1063/1.859654 , url =

    work page doi:10.1063/1.859654 1991

  10. [11]

    The Monthly Notices of The Royal Astronomical Society , keywords =

    Reconciling cosmic ray transport theory with phenomenological models motivated by Milky-Way data. The Monthly Notices of The Royal Astronomical Society , keywords =. doi:10.1093/mnras/stac1240 , archivePrefix =. 2109.10977 , primaryClass =

    work page doi:10.1093/mnras/stac1240

  11. [12]

    arXiv e-prints , keywords =

    Numerical viscosity and resistivity in MHD turbulence simulations. arXiv e-prints , keywords =. doi:10.48550/arXiv.2311.10350 , archivePrefix =. 2311.10350 , primaryClass =

    work page doi:10.48550/arxiv.2311.10350

  12. [13]

    The Open Journal of Astrophysics , keywords =

    FORGE'd in FIRE II: The Formation of Magnetically-Dominated Quasar Accretion Disks from Cosmological Initial Conditions. The Open Journal of Astrophysics , keywords =. doi:10.21105/astro.2310.04506 , archivePrefix =. 2310.04506 , primaryClass =

    work page doi:10.21105/astro.2310.04506

  13. [14]

    Astronomy and Astrophysics , keywords =

    On the fractal structure of molecular clouds. Astronomy and Astrophysics , keywords =

    work page

  14. [15]

    The Monthly Notices of The Royal Astronomical Society , keywords =

    Infrared radiation feedback does not regulate star cluster formation. The Monthly Notices of The Royal Astronomical Society , keywords =. doi:10.1093/mnras/stac2702 , archivePrefix =. 2206.14190 , primaryClass =

    work page doi:10.1093/mnras/stac2702

  15. [16]

    The Astrophysical Journal , keywords =

    The Nonlinear Magnetic Cascade. The Astrophysical Journal , keywords =. doi:10.1086/380504 , adsurl =

    work page doi:10.1086/380504

  16. [17]

    Astronomy and Astrophysics , keywords =

    Using Herschel and Planck observations to delineate the role of magnetic fields in molecular cloud structure. Astronomy and Astrophysics , keywords =. 2019. doi:10.1051/0004-6361/201935779 , archivePrefix =. 1909.04862 , primaryClass =

    work page doi:10.1051/0004-6361/201935779 2019

  17. [18]

    Kolmogorov, A. N. , doi =. Doklady Akademii Nauk Sssr , number =

    work page

  18. [19]

    Mandelbrot, Benoit B. , doi =. Journal of Fluid Mechanics , number =

    work page

  19. [20]

    Burrough, P. A. , doi =. , number =

    work page

  20. [21]

    and Perez, Enrique , doi =

    Sanchez, Nestor and Alfaro, Emilio J. and Perez, Enrique , doi =. The Astrophysical Journal , number =

    work page

  21. [22]

    The Density Probability Distribution in Compressible Isothermal Turbulence: Solenoidal versus Compressive Forcing

    Federrath, Christoph and Klessen, Ralf S. and Schmidt, Wolfram , doi =. The Astrophysical Journal , number =. arXiv , arxivId =:0808.0605 , file =

    work page internal anchor Pith review Pith/arXiv arXiv

  22. [23]

    A supersonic turbulence origin of Larson's laws

    Kritsuk, Alexei G. and Lee, Christoph T. and Norman, Michael L. , doi =. The Monthly Notices of The Royal Astronomical Society , keywords =. arXiv , arxivId =:1309.5926 , file =

    work page internal anchor Pith review Pith/arXiv arXiv

  23. [24]

    The turbulent formation of stars

    The turbulent formation of stars. Physics Today , keywords =. doi:10.1063/PT.3.3947 , archivePrefix =. 1806.05312 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1063/pt.3.3947

  24. [25]

    Astronomy and Astrophysics , keywords =

    Properties of magnetohydrodynamic turbulence in the solar wind. Astronomy and Astrophysics , keywords =

    work page

  25. [26]

    Computers and Fluids , keywords =

    An examination of forcing in direct numerical simulations of turbulence. Computers and Fluids , keywords =

    work page

  26. [28]

    The Monthly Notices of The Royal Astronomical Society , pages =

    Larson, Richard B , doi =. The Monthly Notices of The Royal Astronomical Society , pages =. arXiv , arxivId =:0009005 , file =

    work page

  27. [29]

    Burgers, J.M. , doi =. Advances in Applied Mechanics , pages =

    work page

  28. [30]

    and Wheeler, J

    Mandelbrot, Benoit B. and Wheeler, J. A. , doi =. American Journal of Physics , number =

    work page

  29. [31]

    scikit-image: image processing in

    van der Walt,. scikit-image: image processing in. PeerJ , issn =. 2014 , month =

    work page 2014

  30. [32]

    2017 , url =

    R: A Language and Environment for Statistical Computing , author =. 2017 , url =

    work page 2017

  31. [33]

    Protostars and Planets V , eprint =

    Molecular Cloud Turbulence and Star Formation. Protostars and Planets V , eprint =

    work page

  32. [34]

    ArXiv e-prints , archivePrefix = "arXiv", eprint =

    The world's largest turbulence simulations. ArXiv e-prints , archivePrefix = "arXiv", eprint =

    work page

  33. [35]

    The density variance - Mach number relation in isothermal and non-isothermal adiabatic turbulence

    Price, Daniel J. and Federrath, Christoph and Brunt, Christopher M. , doi =. The Astrophysical Journal Letters , keywords =. arXiv , arxivId =:1504.04370 , file =

    work page internal anchor Pith review Pith/arXiv arXiv

  34. [36]

    Protostars and Planets VI , archivePrefix = "arXiv", eprint =

    From Filamentary Networks to Dense Cores in Molecular Clouds: Toward a New Paradigm for Star Formation. Protostars and Planets VI , archivePrefix = "arXiv", eprint =. doi:10.2458/azu_uapress_9780816531240-ch002 , adsurl =

    work page doi:10.2458/azu_uapress_9780816531240-ch002

  35. [37]

    Protostars and Planets VI , archivePrefix = "arXiv", eprint =

    The Star Formation Rate of Molecular Clouds. Protostars and Planets VI , archivePrefix = "arXiv", eprint =. doi:10.2458/azu_uapress_9780816531240-ch004 , adsurl =

    work page doi:10.2458/azu_uapress_9780816531240-ch004

  36. [38]

    and Rigby, A

    Tzeferacos, P. and Rigby, A. and Bott, A. F. A. and Bell, A. R. and Bingham, R. and Casner, A. and Cattaneo, F. and Churazov, E. M. and Emig, J. and Fiuza, F. and Forest, C. B. and Foster, J. and Graziani, C. and Katz, J. and Koenig, M. and Li, C. -K. and Meinecke, J. and Petrasso, R. and Park, H. -S. and Remington, B. A. and Ross, J. S. and Ryu, D. and R...

    work page doi:10.1038/s41467-018-02953-2 2018

  37. [39]

    Krumholz, Mark R. , doi =. Physics Reports , keywords =. arXiv , arxivId =:1402.0867 , file =

    work page internal anchor Pith review Pith/arXiv arXiv

  38. [40]

    The Astrophysical Journal , archivePrefix = "arXiv", eprint =

    On the Star Formation Efficiency of Turbulent Magnetized Clouds. The Astrophysical Journal , archivePrefix = "arXiv", eprint =. doi:10.1088/0004-637X/763/1/51 , adsurl =

    work page doi:10.1088/0004-637x/763/1/51

  39. [41]

    On the universality of supersonic turbulence

    Federrath, Christoph , doi =. The Monthly Notices of The Royal Astronomical Society , keywords =. arXiv , arxivId =:1306.3989 , file =

    work page internal anchor Pith review Pith/arXiv arXiv

  40. [42]

    Theory of Star Formation

    McKee, Christopher F. and Ostriker, Eve C. , doi =. Annu. Rev. Astron. Astrophys. , number =. arXiv , arxivId =:0707.3514 , file =

    work page internal anchor Pith review Pith/arXiv arXiv

  41. [43]

    Mac Low, Mordecai Mark and Klessen, Ralf S. , doi =. Reviews of Modern Physics , number =. arXiv , arxivId =:0301093 , file =

    work page

  42. [44]

    and Glover, S.C.O

    Gnedin, N.Y. and Glover, S.C.O. and Klessen, R.S. and Springel, V. , doi =

    work page

  43. [45]

    and Andr

    Arzoumanian, D. and Andr. Astronomy and Astrophysics , keywords =. doi:10.1051/0004-6361/201116596 , eprint =

    work page doi:10.1051/0004-6361/201116596

  44. [46]

    On the potential of the Cherenkov Telescope Array for the study of cosmic-ray diffusion in molecular clouds

    On the potential of the Cherenkov Telescope Array for the study of cosmic-ray diffusion in molecular clouds. Astronomy and Astrophysics , keywords =. doi:10.1051/0004-6361/201220583 , archivePrefix =. 1301.5240 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201220583

  45. [47]

    The Monthly Notices of The Royal Astronomical Society , keywords =

    A new method for measuring the 3D turbulent velocity dispersion of molecular clouds. The Monthly Notices of The Royal Astronomical Society , keywords =. doi:10.1093/mnras/stab3313 , archivePrefix =. 2111.07236 , primaryClass =

    work page doi:10.1093/mnras/stab3313

  46. [48]

    and Roman-Duval, J

    Federrath, C. and Roman-Duval, J. and Klessen, R. and Schmidt, W. and. Astronomy and Astrophysics , keywords =. doi:10.1051/0004-6361/200912437 , eprint =

    work page doi:10.1051/0004-6361/200912437

  47. [49]

    and Scalo, John , doi =

    Elmegreen, Bruce G. and Scalo, John , doi =. Annu. Rev. Astron. Astrophys. , pages =. arXiv , arxivId =:0404451 , file =

    work page

  48. [50]

    An ALMA study of the Orion Integral Filament: I. Evidence for narrow fibers in a massive cloud

    Hacar, A. and Tafalla, M. and Forbrich, J. and Alves, J. and Meingast, S. and Grossschedl, J. and Teixeira, P. S. , doi =. Astronomy and Astrophysics , keywords =. arXiv , arxivId =:1801.01500 , file =

    work page internal anchor Pith review Pith/arXiv arXiv

  49. [51]

    Federrath, Christoph and Klessen, Ralf S. , doi =. The Astrophysical Journal , keywords =. arXiv , arxivId =:1209.2856 , file =

    work page internal anchor Pith review Pith/arXiv arXiv

  50. [52]

    Turbulent molecular clouds

    Hennebelle, Patrick and Falgarone, Edith , doi =. Astronomy and Astrophysics Review , keywords =. arXiv , arxivId =:1211.0637 , file =

    work page internal anchor Pith review Pith/arXiv arXiv

  51. [53]

    and McKee, Christopher F

    Krumholz, Mark R. and McKee, Christopher F. , doi =. The Astrophysical Journal , pages =. arXiv , arxivId =:0505177 , file =

    work page

  52. [54]

    The Monthly Notices of The Royal Astronomical Society , archivePrefix = "arXiv", eprint =

    Mach number study of supersonic turbulence: the properties of the density field. The Monthly Notices of The Royal Astronomical Society , archivePrefix = "arXiv", eprint =. doi:10.1093/mnras/stw1313 , adsurl =

    work page doi:10.1093/mnras/stw1313

  53. [55]

    Numerical Calibration of the HCN$-$Star Formation Correlation

    Onus, Adam and Krumholz, Mark R. and Federrath, Christoph , doi =. The Monthly Notices of The Royal Astronomical Society , keywords =. arXiv , arxivId =:1801.09952 , file =

    work page internal anchor Pith review Pith/arXiv arXiv

  54. [56]

    Probing the evolution of molecular cloud structure II: From chaos to confinement

    Kainulainen, J. and Beuther, H. and Banerjee, R. and Federrath, C. and Henning, T. , doi =. Astronomy and Astrophysics , keywords =. arXiv , arxivId =:1104.0678 , file =

    work page internal anchor Pith review Pith/arXiv arXiv

  55. [57]

    Larson's third law and the universality of molecular cloud structure

    Lombardi, M. and Alves, J. and Lada, C. J. , doi =. Astronomy and Astrophysics , keywords =. arXiv , arxivId =:1008.4251 , file =

    work page internal anchor Pith review Pith/arXiv arXiv

  56. [58]

    The Statistics of Supersonic Isothermal Turbulence

    Kritsuk, Alexei G. and Norman, Michael L. and Padoan, Paolo and Wagner, Rick , doi =. The Astrophysical Journal , pages =. arXiv , arxivId =:0704.3851 , file =

    work page internal anchor Pith review Pith/arXiv arXiv

  57. [59]

    The Astrophysical Journal , pages =

    von Weizs. The Astrophysical Journal , pages =. doi:10.1086/145462 , eprint =

    work page doi:10.1086/145462

  58. [60]

    On the universality of interstellar filaments: theory meets simulations and observations

    Federrath, Christoph , doi =. The Monthly Notices of The Royal Astronomical Society , keywords =. arXiv , arxivId =:1510.05654 , file =

    work page internal anchor Pith review Pith/arXiv arXiv

  59. [61]

    A measurement of the turbulence-driven density distribution in a non-star-forming molecular cloud

    Ginsburg, Adam and Federrath, Christoph and Darling, Jeremy , doi =. The Astrophysical Journal , keywords =. arXiv , arxivId =:1310.0809 , file =

    work page internal anchor Pith review Pith/arXiv arXiv

  60. [62]

    Reviews of Modern Physics , number =

    Ferri. Reviews of Modern Physics , number =. doi:10.1017/CBO9781139018036.006 , eprint =

    work page doi:10.1017/cbo9781139018036.006

  61. [63]

    The IMF Revisited: A Case for Variations

    The IMF Revisited: A Case for Variations. The Stellar Initial Mass Function (38th Herstmonceux Conference) , year = 1998, series =. astro-ph/9712317 , editor =

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  62. [64]

    , keywords =

    Mass, luminosity, and line width relations of Galactic molecular clouds. The Astrophysical Journal , keywords =. doi:10.1086/165493 , adsurl =

    work page doi:10.1086/165493

  63. [65]

    Astronomy and Astrophysics , keywords =

    Turbulent velocity structure in molecular clouds. Astronomy and Astrophysics , keywords =. doi:10.1051/0004-6361:20020629 , adsurl =

    work page doi:10.1051/0004-6361:20020629

  64. [66]

    The Astrophysical Journal Letters , eprint =

    The Universality of Turbulence in Galactic Molecular Clouds. The Astrophysical Journal Letters , eprint =. doi:10.1086/425978 , adsurl =

    work page doi:10.1086/425978

  65. [67]

    The Astrophysical Journal , archivePrefix = "arXiv", eprint =

    The Turbulence Spectrum of Molecular Clouds in the Galactic Ring Survey: A Density-dependent Principal Component Analysis Calibration. The Astrophysical Journal , archivePrefix = "arXiv", eprint =. doi:10.1088/0004-637X/740/2/120 , adsurl =

    work page doi:10.1088/0004-637x/740/2/120

  66. [68]

    2010, MNRAS, 406, 1379, doi: 10.1111/j.1365-2966.2010.16776.x

    A comparison between grid and particle methods on the statistics of driven, supersonic, isothermal turbulence. The Monthly Notices of The Royal Astronomical Society , archivePrefix = "arXiv", eprint =. doi:10.1111/j.1365-2966.2010.16810.x , adsurl =

    work page doi:10.1111/j.1365-2966.2010.16810.x 2010

  67. [70]

    The Astrophysical Journal , keywords =

    A Fractal Origin for the Mass Spectrum of Interstellar Clouds. The Astrophysical Journal , keywords =. doi:10.1086/178009 , adsurl =

    work page doi:10.1086/178009

  68. [71]

    Science , archivePrefix = "arXiv", eprint =

    Magnetic seismology of interstellar gas clouds: Unveiling a hidden dimension. Science , archivePrefix = "arXiv", eprint =. doi:10.1126/science.aao1185 , adsurl =

    work page doi:10.1126/science.aao1185

  69. [72]

    The Astrophysical Journal , archivePrefix = "arXiv", eprint =

    Quantifying Observational Projection Effects Using Molecular Cloud Simulations. The Astrophysical Journal , archivePrefix = "arXiv", eprint =. doi:10.1088/0004-637X/777/2/173 , adsurl =

    work page doi:10.1088/0004-637x/777/2/173

  70. [73]

    , year = 1987, month = dec, volume = 156, pages =

    Anomalous scaling laws in multifractal objects. , year = 1987, month = dec, volume = 156, pages =. doi:10.1016/0370-1573(87)90110-4 , adsurl =

    work page doi:10.1016/0370-1573(87)90110-4 1987

  71. [74]

    Klessen, Ralf , year =

    Donkov, Sava and Veltchev, Todor and S. Klessen, Ralf , year =. Statistical link between the structure of molecular clouds and their density distribution , volume =. The Monthly Notices of The Royal Astronomical Society , doi =

    work page

  72. [75]

    A Fractal Origin for the Mass Spectrum of Interstellar Clouds. II. Cloud Models and Power-Law Slopes. The Astrophysical Journal , keywords =. doi:10.1086/324384 , archivePrefix =. astro-ph/0112528 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/324384

  73. [76]

    A Fractal Origin for the Mass Spectrum of Interstellar Clouds , volume =

    Elmegreen, Bruce and Falgarone, Edith , year =. A Fractal Origin for the Mass Spectrum of Interstellar Clouds , volume =. The Astrophysical Journal , doi =

    work page

  74. [77]

    Multifractal Scaling, Geometrical Diversity, and Hierarchical Structure in the Cool Interstellar Medium

    Multifractal Scaling, Geometrical Diversity, and Hierarchical Structure in the Cool Interstellar Medium. The Astrophysical Journal , keywords =. doi:10.1086/320242 , archivePrefix =. astro-ph/9707102 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/320242

  75. [78]

    The Astrophysical Journal , keywords =

    Small-Scale Density and Velocity Structure of a Molecular Cloud Edge. The Astrophysical Journal , keywords =. doi:10.1086/178054 , adsurl =

    work page doi:10.1086/178054

  76. [79]

    Triggered Star Formation in a Turbulent ISM , year = 2007, series =

    Structural analysis of molecular cloud maps: the case of the star forming Vela-D cloud. Triggered Star Formation in a Turbulent ISM , year = 2007, series =. doi:10.1017/S1743921307001998 , adsurl =

    work page doi:10.1017/s1743921307001998 2007

  77. [80]

    Star formation from dense shocked regions in supersonic isothermal magneto-turbulence

    Star formation from dense shocked regions in supersonic isothermal magnetoturbulence. The Monthly Notices of The Royal Astronomical Society , keywords =. doi:10.1093/mnras/sty1976 , archivePrefix =. 1805.11105 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/sty1976

  78. [81]

    Interstellar filaments and star formation

    Interstellar filaments and star formation. Comptes Rendus Geoscience , keywords =. doi:10.1016/j.crte.2017.07.002 , archivePrefix =. 1710.01030 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.crte.2017.07.002 2017

  79. [82]

    The distribution of density in supersonic turbulence

    The distribution of density in supersonic turbulence. The Monthly Notices of The Royal Astronomical Society , keywords =. doi:10.1093/mnras/stx1817 , archivePrefix =. 1702.07731 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stx1817

  80. [83]

    The Astrophysical Journal , keywords =

    Scaling Relations for the Turbulent, Non--Self-gravitating, Neutral Component of the Interstellar Medium. The Astrophysical Journal , keywords =. doi:10.1086/176853 , adsurl =

    work page doi:10.1086/176853

Showing first 80 references.