The Mach number error bar is a consequence of uncertainties in the measurement of the thermodynamic conditions of the plasma see Fig. The error bars for the density spectral index show the variation across the four regions of the plasma highlighted in Fig. For context, we have also plotted in Fig.

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All these results fall within the error bars of our experimentally measured spectral exponents. The effect of the magnetic field on the dynamics of MCs is a topic of active research Although magnetohydrodynamic simulations predict changes in the density power spectrum with increasing magnetic field 31 , this is beyond the scope of this work.

In Fig. For the velocity power spectrum, our results appear to agree with the numerical ones obtained for 3-D hydrodynamic, compressible turbulence by Kritsuk et al. However, the experimental slopes are shallower than those predicted by Konstandin et al. Thus, we have demonstrated that supersonic compressible turbulence, with a duration many times the outer-scale turnover time, can be investigated experimentally by arranging a collision of two laser-driven high-velocity plasma jets.

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Statistical measures of the turbulence such as the density and velocity power spectra are extracted, along with the thermodynamic properties of the plasma. Such experiments are able to provide information in addition to astrophysical observations as well as rigorous tests of numerical simulations. This opens up an avenue for the study of supersonic turbulent plasmas.

Future experimental work is planned to explore the role of dynamically important magnetic fields in supersonic turbulence. Further details on the magnetic-field configuration are presented below. Therefore, the magnetic field is expected to penetrate fully into the plasma during the initial stages of the experiment. The grids are misaligned so that the centers of the apertures in one grid face the vertices of the other.

The misalignment of the two ETFE grids, as well as instabilities present during the collision, make the outer-scale motions as chaotic as possible, giving rise to vigorous turbulence. This suggests that small fields are generated in the plasma by the laser-target interaction and, perhaps, by Biermann battery However, we expect that the analysis performed does not depend on the exact source of the magnetic field.

The Schlieren imaging was performed with a vertically aligned knife edge, i.

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The data that support the findings of this study are available from the corresponding author upon reasonable request. Ingenito, A. Physics and regimes of supersonic combustion. AIAA J. Ogden, D. Effects of vent overpressure on buoyant eruption columns: implications for plume stability. Earth Planet. Papamoschou, D. Evidence of shocklets in a counterflow supersonic shear layer. Fluids 7 , — Padoan, P. Protostars and Planets VI , pp. Miniati, F.

The matryoshka run. Time-dependent turbulence statistics, stochastic particle acceleration, and microphysics impact in a massive galaxy cluster.

Larson, R. Turbulence and star formation in molecular clouds. The stellar initial mass function from turbulent fragmentation. Kritsuk, A. The statistics of supersonic isothermal turbulence. Elmegreen, B. Interstellar turbulence I: observations and processes.

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Scalo, J. Interstellar turbulence II: implications and effects. Burgers, J. A mathematical model illustrating the theory of turbulence. Boldyrev, S. Supersonic turbulence and structure of interstellar molecular clouds. Scaling relations of supersonic turbulence in star-forming molecular clouds. Saichev, A. Density fields in burgers and KdV-burgers turbulence. SIAM J.

Orkisz, J. Turbulence and star formation efficiency in molecular clouds: solenoidal versus compressive motions in Orion B.

## Plasma and Fluid Turbulence: Theory and Modelling - CRC Press Book

Deshpande, A. Power spectrum of the density of cold atomic gas in the galaxy toward Cassiopeia A and Cygnus A. Kim, J. Density power spectrum of compressible hydrodynamic turbulent flows. Federrath, C. Magnetic field amplification in turbulent astrophysical plasmas. Plasma Phys. On the universality of supersonic turbulence. Gordeyev, S. Aero-optical effects of supersonic boundary layers. Meinecke, J. Turbulent amplification of magnetic fields in laboratory laser-produced shock waves.

Developed turbulence and nonlinear amplification of magnetic fields in laboratory and astrophysical plasmas. Natl Acad. USA , — Goldsmith, P. Molecular cooling and thermal balance of dense interstellar clouds. Kolmogorov, A. Golitsyn, G. Fluctuations of the magnetic field and current density in a turbulent flow of a weakly conducting fluid. Schekochihin, A. Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers.

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New J. Zhuravleva, I. The relation between gas density and velocity power spectra in galaxy clusters: qualitative treatment and cosmological simulations. The power spectrum of supersonic turbulence In Perseus. Comparing the statistics of interstellar turbulence in simulations and observations. Solenoidal versus compressive turbulence forcing. Two regimes of turbulent fragmentation and the stellar initial mass function from primordial to present-day star formation. Squire, J. The distribution of density in supersonic turbulence.

Konstandin, L. Mach number study of supersonic turbulence: the properties of the density field. Download references. The authors would like to thank Prof. Steve Cowley for a useful discussion. Awards of computer time were provided by the U. This material is partially based upon work supported by the U. This project was conceived by A. Keywords: plasma turbulence , transport , structure formation , toroidal confinement , bifurcation , meso-scale structure , nonlinear interaction , statistical theory , multiple scale lengths , nonlinear instability , transition probability , turbulence transition , nonlinear noise.

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