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Register a new userMagnetic field fluctuations in anisotropic, supersonic turbulence
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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, $vec{delta B}$, over a wide range of turbulent Mach numbers, $mathcal{M} = 2 - 20$ (i.e., from weak to strong compressibility), and Alfven Mach numbers, $mathcal{M}_{text{A}0} = 0.1 - 100$ (i.e., from strong to weak magnetic mean fields, $B_0$). We derive a compressible quasi-static fluctuation model from the magnetohydrodynamical (MHD) equations and show that velocity gradients parallel to the mean magnetic field give rise to compressible modes in sub-Alfvenic flows, which prevents the flow from becoming two-dimensional, as is the case in incompressible MHD turbulence. We then generalise an analytical model for the magnitude of the magnetic fluctuations to include $mathcal{M}$, and find $|vec{delta B}| = delta B = c_ssqrt{pirho_0}mathcal{M}mathcal{M}_{text{A}0}$, where $c_s$ is the sound speed and $rho_0$ is the mean density of gas. This new relation fits well in the strong $B$-field regime. We go on to study the anisotropy between the perpendicular ($ B_{perp}$) and parallel ($ B_{parallel}$) fluctuations and the mean-normalised fluctuations, which we find follow universal scaling relations, invariant of $mathcal{M}$. We provide a detailed analysis of the morphology for the $delta B_{perp}$ and $delta B_{parallel}$ probability density functions and find that eddies aligned with $B_0$ cause parallel fluctuations that reduce $B_{parallel}$ in the most anisotropic simulations. We discuss broadly the implications of our fluctuation models for magnetised gases in the interstellar medium.
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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 of dynamical processes on the PDF, showing that the nonlinear term in the divergence equation amplifies the right tail of the PDF and reduces the left one, the pressure term reduces both the right and left tails, and the viscosity term, counter-intuitively, broadens the right tail of the PDF. Despite the inaccuracy of the velocity divergence from the Riemann runs, as found in our previous work, we show that the density PDF from the Riemann runs is consistent with that from the N-S runs. Taking advantage of their much higher effective resolution, we then use the Riemann runs to study the dependence of the PDF on the Mach number, $mathcal{M}$, up to $mathcal{M}sim30$. The PDF width, $sigma_{s}$, follows the relation $sigma_{s}^2 = ln (1+b^2 {mathcal M}^2)$, with $bapprox0.38$. However, the PDF exhibits a negative skewness that increases with increasing $mathcal{M}$, so much of the growth of $sigma_{s}$ is accounted for by the growth of the left PDF tail, while the growth of the right tail tends to saturate. Thus, the usual prescription that combines a lognormal shape with the standard variance-Mach number relation greatly overestimates the right PDF tail at large $mathcal{M}$, which may have a significant impact on theoretical models of star formation.
The magnetorotational instability (MRI) is the most promising mechanism by which angular momentum is efficiently transported outwards in astrophysical discs. However, its application to protoplanetary discs remains problematic. These discs are so poorly ionised that they may not support magnetorotational turbulence in regions referred to as `dead zones. It has recently been suggested that the Hall effect, a non-ideal magnetohydrodynamic (MHD) effect, could revive these dead zones by enhancing the magnetically active column density by an order of magnitude or more. We investigate this idea by performing local, three-dimensional, resistive Hall-MHD simulations of the MRI in situations where the Hall effect dominates over Ohmic dissipation. As expected from linear stability analysis, we find an exponentially growing instability in regimes otherwise linearly stable in resistive MHD. However, instead of vigorous and sustained magnetorotational turbulence, we find that the MRI saturates by producing large-scale, long-lived, axisymmetric structures in the magnetic and velocity fields. We refer to these structures as zonal fields and zonal flows, respectively. Their emergence causes a steep reduction in turbulent transport by at least two orders of magnitude from extrapolations based upon resistive MHD, a result that calls into question contemporary models of layered accretion. We construct a rigorous mean-field theory to explain this new behaviour and to predict when it should occur. Implications for protoplanetary disc structure and evolution, as well as for theories of planet formation, are briefly discussed.
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 functions for the dynamo {alpha} effect, diamagnetic pumping, and turbulent diffusivity, which are compared with theoretical expectations. At late times, we observe the suppression of the vertical wind. Because this potentially affects the removal of small-scale magnetic helicity, new concerns arise about circumventing constraints imposed by the conservation of magnetic helicity at high magnetic Reynolds numbers. While present results cannot safely rule out this possibility, the issue only becomes important at late stages and is absent when the dynamo is quenched by the wind itself.
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 magnetic fields.
We study the spatio-temporal behavior of the Elsasser variables describing magnetic and velocity field fluctuations, using direct numerical simulations of three-dimensional magnetohydrodynamic turbulence. We consider cases with relatively small, intermediate, and large values of a mean background magnetic field, and with null, small, and high cross-helicity (correlations between the velocity and the magnetic field). Wavenumber-dependent time correlation functions are computed for the different simulations. From these correlation functions, the decorrelation time is computed and compared with different theoretical characteristic times: the local non-linear time, the random-sweeping time, and the Alfvenic time. It is found that decorrelation times are dominated by sweeping effects for low values of the mean magnetic field and for low values of the cross-helicity, while for large values of the background field or of the cross-helicity and for wave vectors sufficiently aligned with the guide field, decorrelation times are controlled by Alfvenic effects. Finally, we observe counter-propagation of Alfvenic fluctuations due to reflections produced by inhomogeneities in the total magnetic field. This effect becomes more prominent in flows with large cross-helicity, strongly modifying the propagation of waves in turbulent magnetohydrodynamic flows.
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