Role of cross helicity in magnetohydrodynamic turbulence

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.Comment: 4 pages, 4 figure

Weak and strong regimes of incompressible magnetohydrodynamic turbulence

It is shown that in the framework of the weak turbulence theory, the autocorrelation and cascade timescales are always of the same order of magnitude. This means that, contrary to the general belief, any model of turbulence which implies a large number of collisions among wave packets for an efficient energy cascade (such as the Iroshnikov-Kraichnan model) are not compatible with the weak turbulence theory.Comment: Accepted to Phys. Plasma

The Lagrangian frequency spectrum as a diagnostic for magnetohydrodynamic turbulence dynamics

For the phenomenological description of magnetohydrodynamic turbulence competing models exist, e.g. Boldyrev [Phys.Rev.Lett. \textbf{96}, 115002, 2006] and Gogoberidze [Phys.Plas. \textbf{14}, 022304, 2007], which predict the same Eulerian inertial-range scaling of the turbulent energy spectrum although they employ fundamentally different basic interaction mechanisms. {A relation is found that links} the Lagrangian frequency spectrum {with} the autocorrelation timescale of the turbulent fluctuations, $\tau_\mathrm{ac}$, and the associated cascade timescale, $\tau_{\mathrm{cas}}$. Thus, the Lagrangian energy spectrum can serve to identify weak ($\tau_\mathrm{ac}\ll\tau_{\mathrm{cas}}$) and strong ($\tau_\mathrm{ac}\sim\tau_{\mathrm{cas}}$) interaction mechanisms providing insight into the turbulent energy cascade. The new approach is illustrated by results from direct numerical simulations of two- and three-dimensional incompressible MHD turbulence.Comment: accepted for publication in PR

On the two-dimensional state in driven magnetohydrodynamic turbulence

The dynamics of the two-dimensional (2D) state in driven tridimensional (3D) incompressible magnetohydrodynamic turbulence is investigated through high-resolution direct numerical simulations and in the presence of an external magnetic field at various intensities. For such a flow the 2D state (or slow mode) and the 3D modes correspond respectively to spectral fluctuations in the plan $k_\parallel=0$ and in the area $k_\parallel>0$. It is shown that if initially the 2D state is set to zero it becomes non negligible in few turnover times particularly when the external magnetic field is strong. The maintenance of a large scale driving leads to a break for the energy spectra of 3D modes; when the driving is stopped the previous break is removed and a decay phase emerges with alfv\'enic fluctuations. For a strong external magnetic field the energy at large perpendicular scales lies mainly in the 2D state and in all situations a pinning effect is observed at small scales.Comment: 11 pages, 11 figure

Energy spectra stemming from interactions of Alfven waves and turbulent eddies

We present a numerical analysis of an incompressible decaying magnetohydrodynamic turbulence run on a grid of 1536^3 points. The Taylor Reynolds number at the maximum of dissipation is ~1100, and the initial condition is a superposition of large scale ABC flows and random noise at small scales, with no uniform magnetic field. The initial kinetic and magnetic energies are equal, with negligible correlation. The resulting energy spectrum is a combination of two components, each moderately resolved. Isotropy obtains in the large scales, with a spectral law compatible with the Iroshnikov-Kraichnan theory stemming from the weakening of nonlinear interactions due to Alfven waves; scaling of structure functions confirms the non-Kolmogorovian nature of the flow in this range. At small scales, weak turbulence emerges with a k_{\perp}^{-2} spectrum, the perpendicular direction referring to the local quasi-uniform magnetic field.Comment: 4 pages, 4 figure

MHD Turbulence Revisited

Kraichnan (1965) proposed that MHD turbulence occurs as a result of collisions between oppositely directed Alfv\'en wave packets. Recent work has generated some controversy over the nature of non linear couplings between colliding Alfv\'en waves. We find that the resolution to much of the confusion lies in the existence of a new type of turbulence, intermediate turbulence, in which the cascade of energy in the inertial range exhibits properties intermediate between those of weak and strong turbulent cascades. Some properties of intermediate MHD turbulence are: (i) in common with weak turbulent cascades, wave packets belonging to the inertial range are long lived; (ii) however, components of the strain tensor are so large that, similar to the situation in strong turbulence, perturbation theory is not applicable; (iii) the breakdown of perturbation theory results from the divergence of neighboring field lines due to wave packets whose perturbations in velocity and magnetic fields are localized, but whose perturbations in displacement are not; (iv) 3--wave interactions dominate individual collisions between wave packets, but interactions of all orders $n\geq 3$ make comparable contributions to the intermediate turbulent energy cascade; (v) successive collisions are correlated since wave packets are distorted as they follow diverging field lines; (vi) in common with the weak MHD cascade, there is no parallel cascade of energy, and the cascade to small perpendicular scales strengthens as it reaches higher wave numbers; (vii) For an appropriate weak excitation, there is a natural progression from a weak, through an intermediate, to a strong cascade.Comment: 25 pages, to appear in The Astrophysical Journa

The Spectral Slope and Kolmogorov Constant of MHD turbulence

The spectral slope of strong MHD turbulence has recently been a matter of controversy. While Goldreich-Sridhar model (1995) predicts Kolmogorov's -5/3 slope of turbulence, shallower slopes were often reported by numerical studies. We argue that earlier numerics was affected by driving due to a diffuse locality of energy transfer in MHD case. Our highest-resolution simulation (3072^2x1024) has been able to reach the asymptotic -5/3 regime of the energy slope. Additionally, we found that so-called dynamic alignment, proposed in the model with -3/2 slope, saturates and therefore can not affect asymptotic slope. The observation of the asymptotic regime allowed us to measure Kolmogorov constant C_KA=3.2+-0.2 for purely Alfv\'enic turbulence and C_K=4.1+-0.3 for full MHD turbulence. These values are much higher than the hydrodynamic value of 1.64. The larger value of Kolmogorov constant is an indication of a fairly inefficient energy transfer and, as we show in this Letter, is in theoretical agreement with our observation of diffuse locality. We also explain what has been missing in numerical studies that reported shallower slopes.Comment: 5 pages 3 figure

Is nonhelical hydromagnetic turbulence peaked at small scales?

Nonhelical hydromagnetic turbulence without an imposed magnetic field is considered in the case where the magnetic Prandtl number is unity. The magnetic field is entirely due to dynamo action. The magnetic energy spectrum peaks at a wavenumber of about 5 times the minimum wavenumber in the domain, and not at the resistive scale, as has previously been argued. Throughout the inertial range the spectral magnetic energy exceeds the kinetic energy by a factor of about 2.5, and both spectra are approximately parallel. At first glance, the total energy spectrum seems to be close to k^{-3/2}, but there is a strong bottleneck effect and it is suggested that the asymptotic spectrum is k^{-5/3}. This is supported by the value of the second order structure function exponent that is found to be \zeta_2=0.70, suggesting a k^{-1.70} spectrum.Comment: 6 pages, 6 figure

A numerical study of the alpha model for two-dimensional magnetohydrodynamic turbulent flows

We explore some consequences of the ``alpha model,'' also called the ``Lagrangian-averaged'' model, for two-dimensional incompressible magnetohydrodynamic (MHD) turbulence. This model is an extension of the smoothing procedure in fluid dynamics which filters velocity fields locally while leaving their associated vorticities unsmoothed, and has proved useful for high Reynolds number turbulence computations. We consider several known effects (selective decay, dynamic alignment, inverse cascades, and the probability distribution functions of fluctuating turbulent quantities) in magnetofluid turbulence and compare the results of numerical solutions of the primitive MHD equations with their alpha-model counterparts' performance for the same flows, in regimes where available resolution is adequate to explore both. The hope is to justify the use of the alpha model in regimes that lie outside currently available resolution, as will be the case in particular in three-dimensional geometry or for magnetic Prandtl numbers differing significantly from unity. We focus our investigation, using direct numerical simulations with a standard and fully parallelized pseudo-spectral method and periodic boundary conditions in two space dimensions, on the role that such a modeling of the small scales using the Lagrangian-averaged framework plays in the large-scale dynamics of MHD turbulence. Several flows are examined, and for all of them one can conclude that the statistical properties of the large-scale spectra are recovered, whereas small-scale detailed phase information (such as e.g. the location of structures) is lost.Comment: 22 pages, 20 figure

Strong Imbalanced Turbulence

We consider stationary, forced, imbalanced, or cross-helical MHD Alfvenic turbulence where the waves traveling in one direction have higher amplitudes than the opposite waves. This paper is dedicated to so-called strong turbulence, which cannot be treated perturbatively. Our main result is that the anisotropy of the weak waves is stronger than the anisotropy of a strong waves. We propose that critical balance, which was originally conceived as a causality argument, has to be amended by what we call a propagation argument. This revised formulation of critical balance is able to handle the imbalanced case and reduces to old formulation in the balanced case. We also provide phenomenological model of energy cascading and discuss possibility of self-similar solutions in a realistic setup of driven turbulence.Comment: this is shorter, 5 page version of what is to appear in ApJ 682, Aug. 1, 200