We perform direct three-dimensional numerical simulations for magnetohydrodynamic (MHD) turbulence in a periodic box of size 2n threaded by strong uniform magnetic Ðelds. We use a pseudospectral code with hyperviscosity and hyperdi †usivity to solve the incompressible MHD equations. We analyze the structure of the eddies as a function of scale. A straightforward calculation of anisotropy in wavevector space shows that the anisotropy is scale independent. We discuss why this is not the true scaling law and how the curvature of large-scale magnetic Ðelds a †ects the power spectrum and leads to the wrong conclusion. When we correct for this e †ect, we Ðnd that the anisotropy of eddies depends on their size : smaller eddies are more elongated than larger ones along local magnetic Ðeld lines. The results are consistent with the scaling law recently proposed by Goldreich & Sridhar. Here (and arewavenumbers measured relative to the local magnetic Ðeld direction. However, we see some systematic deviations that may be a sign of limitations to the model or our inability to fully resolve the inertial range of turbulence in our simulations.

The nature and origin of turbulence and magnetic fields in the intergalactic space are important problems that are yet to be understood. We propose a scenario in which turbulent-flow motions are induced via the cascade of the vorticity generated at cosmological shocks during the formation of the large-scale structure. The turbulence in turn amplifies weak seed magnetic fields of any origin. Supercomputer simulations show that the turbulence is subsonic inside clusters and groups of galaxies, whereas it is transonic or mildly supersonic in filaments. Based on a turbulence dynamo model, we then estimated that the average magnetic field strength would be a few microgauss (microG) inside clusters and groups, approximately 0.1 muG around clusters and groups, and approximately 10 nanogauss in filaments. Our model presents a physical mechanism that transfers the gravitational energy to the turbulence and magnetic field energies in the large-scale structure of the universe.

We present numerical simulations and explore scalings and anisotropy of compressible magnetohydrodynamic (MHD) turbulence. Our study covers both gas‐pressure‐dominated (high β) and magnetic‐pressure‐dominated (low β) plasmas at different Mach numbers. In addition, we present results for super‐Alfvénic turbulence and discuss in what way it is similar to sub‐Alfvénic turbulence. We describe a technique of separating different magnetohydrodynamic modes (slow, fast and Alfvén) and apply it to our simulations. We show that, for both high‐ and low‐β cases, Alfvén and slow modes reveal a Kolmogorov k−5/3 spectrum and scale‐dependent Goldreich–Sridhar anisotropy, while fast modes exhibit a k−3/2 spectrum and isotropy. We discuss the statistics of density fluctuations arising from MHD turbulence in different regimes. Our findings entail numerous astrophysical implications ranging from cosmic ray propagation to gamma ray bursts and star formation. In particular, we show that the rapid decay of turbulence reported by earlier researchers is not related to compressibility and mode coupling in MHD turbulence. In addition, we show that magnetic field enhancements and density enhancements are marginally correlated. Addressing the density structure of partially ionized interstellar gas on astronomical‐unit scales, we show that the viscosity‐damped regime of MHD turbulence that we reported earlier for incompressible flows persists for compressible turbulence and therefore may provide an explanation for these mysterious structures.

We analyze three-dimensional numerical simulations of driven incompressible magnetohydrodynamic (MHD) turbulence in a periodic box threaded by a moderately strong external magnetic Ðeld. We sum over nonlinear interactions within Fourier wave bands and Ðnd that the timescale for the energy cascade is consistent with the Goldreich-Sridhar model of strong MHD turbulence. Using higher order longitudinal structure functions, we show that the turbulent motions in the plane perpendicular to the local mean magnetic Ðeld are similar to ordinary hydrodynamic turbulence, while motions parallel to the Ðeld are consistent with a scaling correction that arises from the eddy anisotropy. We present the structure tensor describing velocity statistics of and turbulence. Finally, we conÐrm that an Alfve nic pseudo-Alfve nic imbalance of energy moving up and down magnetic Ðeld lines leads to a slow decay of turbulent motions, and speculate that this imbalance is common in the interstellar medium, where injection of energy is intermittent both in time and space.

We present a model for compressible sub-Alfvénic isothermal magnetohydrodynamic (MHD) turbulence in low- beta plasmas and numerically test it. We separate MHD fluctuations into three distinct families: Alfvén, slow, and fast modes. We find that production of slow and fast modes by Alfvénic turbulence is suppressed. As a result, Alfvén modes in compressible regime exhibit scalings and anisotropy similar to those in incompressible regime. Slow modes passively mimic Alfvén modes. However, fast modes show isotropy and a scaling similar to acoustic turbulence.

We construct a magnetic helicity conserving dynamo theory which incorporates a calculated magnetic helicity current. In this model the fluid helicity plays a small role in large scale magnetic field generation. Instead, the dynamo process is dominated by a new quantity, derived from asymmetries in the second derivative of the velocity correlation function, closely related to the `twist and fold' dynamo model. The turbulent damping term is, as expected, almost unchanged. Numerical simulations with a spatially constant fluid helicity and vanishing resistivity are not expected to generate large scale fields in equipartition with the turbulent energy density. The prospects for driving a fast dynamo under these circumstances are uncertain, but if it is possible, then the field must be largely force-free. On the other hand, there is an efficient analog to the $\alpha-\Omega$ dynamo. Systems whose turbulence is driven by some anisotropic local instability in a shearing flow, like real stars and accretion disks, and some computer simulations, may successfully drive the generation of strong large scale magnetic fields, provided that $\partial_r\Omega< \partial_\theta v_z\omega_\theta>>0$. We show that this criterion is usually satisfied. Such dynamos will include a persistent, spatially coherent vertical magnetic helicity current with the same sign as $-\partial_r\Omega$, that is, positive for an accretion disk and negative for the Sun. We comment on the role of random magnetic helicity currents in storing turbulent energy in a disordered magnetic field, which will generate an equipartition, disordered field in a turbulent medium, and also a declining long wavelength tail to the power spectrum. As a result, calculations of the galactic `seed' field are largely irrelevant.Comment: 28 pages, accepted by The Astrophysical Journa

We present numerical studies of 3-dimensional electron magnetohydrodynamic (EMHD) turbulence. We investigate cascade timescale and anisotropy of freely decaying strong EMHD turbulence with zero electron skin depth. Cascade time scales with k −4/3 . Our numerical results clearly show scaledependent anisotropy. We discuss that the observed anisotropy is consistent with k ∝ kwhere k and k ⊥ are wave numbers parallel and perpendicular to (local) mean magnetic field, respectively.

We consider stochastic reconnection in a magnetized, partially ionized medium. Stochastic reconnection is a generic effect that results from field line wandering, in which the speed of reconnection is determined by the ability of ejected plasma to diffuse away from the current sheet along magnetic field lines, rather than by the details of current sheet structure. As in earlier work, in which we dealt with a fully ionized plasma, we consider the limit of weak stochasticity, so that the mean magnetic field energy density is greater than either the turbulent kinetic energy density or the energy density associated with the fluctuating component of the field. For specificity, we consider field line stochasticity generated through a turbulent cascade, which leads us to consider the effect of neutral drag on the turbulent cascade of energy. In a collisionless plasma, neutral particle viscosity and ionneutral drag will damp midscale turbulent motions, but the power spectrum of the magnetic perturbations extends below the viscous cutoff scale. We give a simple physical picture of the magnetic field structure below this cutoff, consistent with numerical experiments. We provide arguments for the reemergence of the turbulent cascade well below the viscous cutoff scale and derive estimates for field line diffusion on all scales. We note that this explains the persistence of a single power-law form for the turbulent power spectrum of the interstellar medium (ISM), from scales of tens of parsecs down to thousands of kilometers. We find that under typical conditions in the ISM stochastic reconnection speeds are reduced by the presence of neutrals, but by no more than an order of magnitude. However, neutral drag implies a steep dependence on the Mach number of the turbulence. In the dense cores of H 2 regions the reconnection speed is probably determined by tearing-mode instabilities.