Strong incompressible three-dimensional magnetohydrodynamic turbulence is investigated by means of high resolution direct numerical simulations. The simulations show that the configuration space is characterized by regions of positive and negative cross-helicity, corresponding to highly aligned or anti-aligned velocity and magnetic field fluctuations, even when the average cross-helicity is zero. To elucidate the role of cross-helicity, the spectra and structure of turbulence are obtained in imbalanced regions where cross-helicity is non-zero. When averaged over regions of positive and negative cross-helicity, the result is consistent with the simulations of balanced turbulence. An analytical explanation for the obtained results is proposed.
We present numerical simulations and explore scalings and anisotropy of compressible magnetohydrodynamic (MHD) turbulence. Our study covers both gas pressure dominated (high beta) and magnetically dominated (low beta) plasmas at different Mach numbers. In addition, we present results for superAlfvenic turbulence and discuss in what way it is similar to the subAlfvenic turbulence. We describe a technique of separating different magnetohydrodynamic (MHD) modes (slow, fast and Alfven) and apply it to our simulations. We show that, for both high and low beta cases, Alfven and slow modes reveal the…
A novel model of incompressible magnetohydrodynamic turbulence in the presence of a strong external magnetic field is proposed for explanation of recent numerical results. According to the proposed model, in the presence of the strong external magnetic field, incompressible magnetohydrodynamic turbulence becomes nonlocal in the sense that low frequency modes cause decorrelation of interacting high frequency modes from the inertial interval. It is shown that the obtained nonlocal spectrum of the inertial range of incompressible magnetohydrodynamic turbulence represents an anisotropic analogue o…
Motivated by recent analytic predictions, we report numerical evidence showing that in driven incompressible magnetohydrodynamic turbulence the magnetic- and velocity-field fluctuations locally tend to align the directions of their polarizations. This dynamic alignment is stronger at smaller scales with the angular mismatch between the polarizations decreasing with the scale λapproximately as θ_λ~ λ^{1/4}. This can naturally lead to a weakening of the nonlinear interactions and provide an explanation for the energy spectrum E(k) ~ k^{-3/2} that is observed in numerical experiments of strongly …
The evolution of the magnetic helicity tensor for a nonzero mean magnetic field and for large magnetic Reynolds numbers in an anisotropic turbulence is studied. It is shown that the isotropic and anisotropic parts of the magnetic helicity tensor have different characteristic times of evolution. The time of variation of the isotropic part of the magnetic helicity tensor is much larger than the correlation time of the turbulent velocity field. The anisotropic part of the magnetic helicity tensor changes for the correlation time of the turbulent velocity field. The mean turbulent flux of the magn…
Recent numerical and observational studies contain conflicting reports on the spectrum of magnetohydrodynamic turbulence. In an attempt to clarify the issue we investigate anisotropic incompressible magnetohydrodynamic turbulence with a strong guide field $B_0$. We perform numerical simulations of the reduced MHD equations in a special setting that allows us to elucidate the transition between weak and strong turbulent regimes. Denote $k_{\|}$, $k_\perp$ characteristic field-parallel and field-perpendicular wavenumbers of the fluctuations, and $b_λ$ the fluctuating field at the scale $λ\sim 1/…
We report the results of an extensive set of direct numerical simulations of forced, incompressible, magnetohydrodynamic turbulence with a strong guide field. The aim is to resolve the controversy regarding the power law exponent (α, say) of the field perpendicular energy spectrum E(k_\perp) \propto k_\perp ^ α. The two main theoretical predictions, α=-3/2 and α=-5/3, have both received some support from numerical simulations carried out by different groups. Our simulations have a resolution of 512^3 mesh points, a strong guide field, an anisotropic simulation domain, and implement a broad ran…
We propose a phenomenological model for incompressible magnetohydrodynamic turbulence. We argue that nonlinear-wave interaction weakens as the energy cascade proceeds to small scales, however, the anisotropy of fluctuations along the large-scale magnetic field increases, which makes turbulence strong at all scales. To explain the weakening of the interaction, we propose that small-scale fluctuations of the velocity and magnetic fields become increasingly dynamically aligned as their scale decreases, so that turbulent eddies become locally anisotropic in the plane perpendicular to the large-sca…
A gauge invariant and hence physically meaningful definition of magnetic helicity density for random fields is proposed, using the Gauss linking formula, as the density of correlated field line linkages. This definition is applied to the random small scale field in weakly inhomogeneous turbulence, whose correlation length is small compared with the scale on which the turbulence varies. For inhomogeneous systems, with or without boundaries, our technique then allows one to study the local magnetic helicity density evolution in a gauge independent fashion, which was not possible earlier. This ev…
Biskamp and Schwarz [Phys. Plasmas, 8, 3282 (2001)] have reported that the energy spectrum of two-dimensional magnetohydrodynamic turbulence is proportional to $k^{-3/2}$, which is a prediction of Iroshnikov-Kraichnan phenomenology. In this comment we report some earlier results which conclusively show that for two-dimensional magnetohydrodynamic turbulence, Kolmogorov-like phenomenology (spectral index 5/3) is better model than Iroshnikov-Kraichnan phenomenology; these results are based on energy flux analysis.
We study effects of kinetic helicity fluctuations in a turbulence with large-scale shear using two different approaches: the spectral tau-approximation and the second order correlation approximation (or first-order smoothing approximation). These two approaches demonstrate that homogeneous kinetic helicity fluctuations alone with zero mean value in a sheared homogeneous turbulence cannot cause large-scale dynamo. Mean-field dynamo can be possible when kinetic helicity fluctuations are inhomogeneous which cause a nonzero mean alpha effect in a sheared turbulence. On the other hand, shear-curren…
In this review article we will describe recent developments in statistical theory of magnetohydrodynamic (MHD) turbulence. Kraichnan and Iroshnikov first proposed a phenomenology of MHD turbulence where Alfven time-scale dominates the dynamics, and the energy spectrum E(k) is proportional to k^{-3/2}. In the last decade, many numerical simulations show that spectral index is closer to 5/3, which is Kolmogorov's index for fluid turbulence. We review recent theoretical results based on anisotropy and Renormalization Groups which support Kolmogorov's scaling for MHD turbulence. Energy transfer am…
We present numerical studies of 3-dimensional magnetohydrodynamic (MHD) turbulence in a strongly magnetized medium in the extremely relativistic limit, in which the inertia of the charge carriers can be neglected. We have focused on strong Alfvenic turbulence in the limit. We have found the following results. First, the energy spectrum is consistent with a Kolmogorov spectrum: $E(k)\sim k^{-5/3}$. Second, turbulence shows a Goldreich-Sridhar type anisotropy: $k_{\|} \propto k_{\perp}^{2/3}$, where $k_{\|}$ and $k_{\perp}$ are wavenumbers along and perpendicular to the local mean magnetic field…
We perform direct numerical simulations of three-dimensional freely decaying magnetohydrodynamic (MHD) turbulence. For helical magnetic fields an inverse cascade effect is observed in which power is transfered from smaller scales to larger scales. The magnetic field reaches a scaling regime with self-similar evolution, and power law behavior at high wavenumbers. We also find power law decay in the magnetic and kinematic energies, and power law growth in the characteristic length scale of the magnetic field.
Fast particles diffusing along magnetic field lines in a turbulent plasma can diffuse through and then return to the same eddy many times before the eddy is randomized in the turbulent flow. This leads to an enhancement of particle acceleration by large-scale compressible turbulence relative to previous estimates in which isotropic particle diffusion is assumed.
This Letter presents a calculation of the power spectra of weakly turbulent Alfven waves and fast magnetosonic waves ("fast waves") in low-beta plasmas. It is shown that three-wave interactions transfer energy to high-frequency fast waves and, to a lesser extent, high-frequency Alfven waves. MHD turbulence is thus a promising mechanism for producing the high-frequency waves needed to explain the anisotropic heating of minor ions in the solar corona.
This paper proposes a new phenomenology for strong incompressible MHD turbulence with nonzero cross helicity. This phenomenology is then developed into a quantitative Fokker-Planck model that describes the time evolution of the anisotropic power spectra of the fluctuations propagating parallel and anti-parallel to the background magnetic field. It is found that in steady state the power spectra of the magnetic field and total energy are steeper than a Kolmogorov spectrum and become increasingly steep as C/E increases, where C is the cross helicity and E is the fluctuation energy. Increasing C …
The effect of shear on the growth of large scale magnetic fields in helical turbulence is investigated. The resulting large-scale magnetic field is also helical and continues to evolve, after saturation of the small scale field, on a slow resistive time scale. This is a consequence of magnetic helicity conservation. Because of shear, the time scale needed to reach an equipartition-strength large scale field is shortened proportionally to the ratio of the resulting toroidal to poloidal large scale fields.
In this paper a procedure for large-eddy simulation (LES) has been devised for fluid and magnetohydrodynamic turbulence in Fourier space using the renormalized parameters. The parameters calculated using field theory have been taken from recent papers by Verma [Phys. Rev. E, 2001; Phys. Plasmas, 2001]. We have carried out LES on $64^3$ grid. These results match quite well with direct numerical simulations of $128^3$. We show that proper choice of parameter is necessary in LES.
Recent advances in understanding of magnetohydrodynamic (MHD) turbulence call for substantial revisions in our understanding of cosmic ray transport. In this paper we use gyroresonance recently obtained scaling laws for MHD modes to calculate the scattering frequency for cosmic rays in the ISM. We consider gyroresonance with MHD modes (Alfvenic, slow and fast) and transit-time damping (TTD) by fast modes. We conclude that the gyroresonance with fast modes is the dominant contribution to cosmic ray scattering for the typical interstellar conditions. In contrast to earlier studies, we find that …
Warped, precessing accretion discs appear in a range of astrophysical systems, for instance the X-ray binary Her X-1 and in the active nucleus of NGC4258. In a warped accretion disc there are horizontal pressure gradients that drive an epicyclic motion. We have studied the interaction of this epicyclic motion with the magnetohydrodynamic turbulence in numerical simulations. We find that the turbulent stress acting on the epicyclic motion is comparable in size to the stress that drives the accretion, however an important ingredient in the damping of the epicyclic motion is its parametric decay …
The nonlinear mean-field dynamo due to a shear-current effect in a nonhelical homogeneous turbulence with a mean velocity shear is discussed. The transport of magnetic helicity as a dynamical nonlinearity is taken into account. The shear-current effect is associated with the ${\bf W} {\bf \times} {\bf J}$ term in the mean electromotive force, where ${\bf W}$ is the mean vorticity due to the large-scale shear motions and ${\bf J}$ is the mean electric current. This effect causes the generation of large-scale magnetic field in a turbulence with large hydrodynamic and magnetic Reynolds numbers. T…
A self-consistent renormalization (RG) scheme has been applied to nonhelical magnetohydrodynamic turbulence with zero cross helicity. Kolmogorov's 5/3 powerlaw has been shown to be a consistent solution for $d \ge d_c \approx 2.2$. For Kolmogorov's solution, both renormalized viscosity and resistivity are positive for the whole range of parameters. Various cascade rate and Kolmogorov's constant for MHD turbulence have been calculated by solving the flux equation to the first order in perturbation series. We find that the magnetic energy cascades forward. The Kolmogorov's constant for $d=3$ doe…
We investigate field-line separation in strong MHD turbulence using direct numerical simulations. We find that in the static-magnetic-field approximation the thermal conductivity in galaxy clusters is reduced by a factor of about 50 relative to the Spitzer thermal conductivity of a non-magnetized plasma. This value is too small for heat conduction to balance radiative cooling in clusters.
We study the evolution of magnetic fields in freely decaying magnetohydrodynamic turbulence. By quasi-linearizing the Navier-Stokes equation, we solve analytically the induction equation in quasi-normal approximation. We find that, if the magnetic field is not helical, the magnetic energy and correlation length evolve in time respectively as E_B \propto t^{-2(1+p)/(3+p)} and ξ_B \propto t^{2/(3+p)}, where p is the index of initial power-law spectrum. In the helical case, the magnetic helicity is an almost conserved quantity and forces the magnetic energy and correlation length to scale as E_B …
Energy cascade rates and Kolmogorov's constant for nonhelical steady magnetohydrodynamic turbulence have been calculated by solving the flux equations to the first order in perturbation. For zero cross helicity and space dimension $d=3$, magnetic energy cascades from large length-scales to small length-scales (forward cascade). In addition, there are energy fluxes from large-scale magnetic field to small-scale velocity field, large-scale velocity field to small-scale magnetic field, and large-scale velocity field to large-scale magnetic field. Kolmogorov's constant for magnetohydrodynamics is …
