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A high-order method to evolve in time electromagnetic and velocity fields in conducting fluids with non-periodic boundaries is presented. The method has a small overhead compared with fast FFT-based pseudospectral methods in periodic domains. It uses the magnetic vector potential formulation for accurately enforcing the null divergence of the magnetic field, and allowing for different boundary conditions including perfectly conducting walls or vacuum surroundings, two cases relevant for many astrophysical, geophysical, and industrial flows. A spectral Fourier continuation method is used to accurately represent all fields and their spatial derivatives, allowing also for efficient solution of Poisson equations with different boundaries. A study of conducting flows at different Reynolds and Hartmann numbers, and with different boundary conditions, is presented to study convergence of the method and the accuracy of the solenoidal and boundary conditions.

We study the spatio-temporal behavior of the Els\"asser 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 Alfv\'enic 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 Alfv\'enic effects. Finally, we observe counter-propagation of Alfv\'enic 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., Comment: 16 pages, 40 figures

Using spatio-temporal spectra we show direct evidence of excitation of magnetosonic and Alfv\'en waves in three-dimensional compressible magnetohydrodynamic turbulence at small Mach numbers. For the plasma pressure dominated regime, or high $\beta$ regime (with $\beta$ the ratio between fluid and magnetic pressure), and for the magnetic pressure dominated regime, or low $\beta$ regime, we study magnetic field fluctuations parallel and perpendicular to a guide magnetic field $\textbf{B}_0$. In the low $\beta$ case we find excitation of compressible and incompressible fluctuations, with a transfer of energy towards Alfv\'enic modes and to a lesser extent towards magnetosonic modes. In particular, we find signatures of the presence of fast magnetosonic waves in a scenario compatible with that of weak turbulence. In the high $\beta$ case, fast and slow magnetosonic waves are present, with no clear trace of Alfv\'en waves, and a significant part of the energy is carried by two-dimensional turbulent eddies.

In this paper we analyze the effect of dynamical three-dimensional MHD turbulence on test particle acceleration, and compare how this evolving system affects particle energization by current sheets interaction, against frozen-in-time fields. To do this we analize the ensamble particle acceleration for static electromagnetic fields extracted from direct numerical simulations of the MHD equations, and compare with the dynamical fields. We show that a reduction in particle acceleration in the dynamical model results from the particle trapping in the field lines, which forces the particles to remain in a moving current sheet that suppress the longer exposure at the strong electric field gradients located between structures, which is an efficient particle acceleration mechanism. In addition, we analize the effect of anisotropy caused by the mean magnetic field. It is well known that for sufficiently strong external fields, the system suffers a transition towards a two-dimensional flow. This causes an increment in the size of the coherent structures, resulting in a magnetized state of the particles and the reduction of the particle energization., Comment: 13 pages,7 figures

Using direct numerical simulations of three-dimensional magnetohydrodynamic (MHD) turbulence the spatio-temporal behavior of magnetic field fluctuations is analyzed. Cases with relatively small, medium and large values of a mean background magnetic field are considered. The (wavenumber) scale dependent time correlation function is directly computed for different simulations, varying the mean magnetic field value. From this correlation function the time decorrelation is computed and compared with different theoretical times, namely, the local non-linear time, the random sweeping time, and the Alfv\'enic time, the latter being a wave effect. It is observed that time decorrelations are dominated by sweeping effects, and only at large values of the mean magnetic field and for wave vectors mainly aligned with this field time decorrelations are controlled by Alfv\'enic effects., Comment: 12 pages, 13 figures

We study the transition in dimensionality of a three-dimensional magnetohydrodynamic flow forced only mechanically, when the strength of a magnetic guiding field is gradually increased. We use numerical simulations to consider cases in which the mechanical forcing injects (or not) helicity in the flow. As the guiding field is increased, the strength of the magnetic field fluctuations decrease as a power law of the guiding field intensity. We show that for strong enough guiding fields, the helical magnetohydrodynamic flow can become almost two-dimensional. In this case, the mechanical energy can undergo a process compatible with an inverse cascade, being transferred preferentially towards scales larger than the forcing scale. The presence of helicity changes the spectral scaling of the small magnetic field fluctuations, and affects the statistics of the velocity field and of the velocity gradients. Moreover, at small scales the dynamics of the flow becomes dominated by a direct cascade of helicity, which can be used to derive scaling laws for the velocity field., Comment: 11 pages, 11 figures

The effect of compressibility in charged particle energization by magnetohydrodynamic (MHD) fields is studiedin the context of test particle simulations. This problem is relevant to the solar wind and the solar corona due to the compressible nature of the flow in those astrophysical scenarios. We consider turbulent electromagnetic fields obtained from direct numerical simulations of the MHD equations with a strong background magnetic field. In order to explore the flow compressibilty effect over the particle dynamics we performed different numerical experiments: an incompressible case, and two weak compressible cases with Mach number M = 0.1 and M = 0.25. We analyze the behavior of protons and electrons in those turbulent fields, which are well known to form aligned current sheets in the direction of the guide magnetic field. What we call protons and electrons are test particles with scales comparable to (for protons) and much smaller than (for electrons) the dissipative scale of MHD turbulence, maintaining the correct mass ratio me /mi. For these test particles we show that compressibility enhances the efficiency of proton acceleration, and that the energization is caused by perpendicular electric fields generated between currents sheets. On the other hand, electrons remain magnetized and display an almost adiabatic motion, with no effect of compressibility observed. Another set of numerical experiments takes into account two fluid modifications, namely electric field due to Hall effect and electron pressure gradient. We show that the electron pressure has an important contribution to electron acceleration allowing highly parallel energization. In contrast, no significant effect of these additional terms is observed for the protons., Comment: 10 pages

Employing a simple ideal magnetohydrodynamic model in spherical geometry,we show that the presence of either rotation or finite magnetic helicity is sufficient to induce dynamical reversals of the magnetic dipole moment. The statistical character of the model is similar to that of terrestrial magnetic field reversals, with the similarity being stronger when rotation is present.The connection between long time correlations, $1/f$ noise, and statistics of reversals is supported, consistent with earlier suggestions., Comment: accepted in Physical Review E

We study the stability of shear flows in a fully ionized plasma. Kelvin-Helmholtz is a well known, macroscopic and ideal shear-driven instability. In sufficiently low density plasmas, also the microscopic Hall magneto-shear instability can take place. We performed three-dimensional simulations of the Hall-MHD equations where these two instabilities are present, and carried out a comparative study. We find that when the shear flow is so intense that its vorticity surpasses the ion-cyclotron frequency of the plasma, the Hall magneto-shear instability is not only non-negligible, but it actually displays growth rates larger than those of the Kelvin-Helmholtz instability.

We present a detailed study of intermittency in the velocity and magnetic field fluctuations of compressible Hall-magnetohydrodynamic turbulence with an external guide field. To solve the equations numerically, a reduced model valid when a strong guide field is present is used. Different values for the ion skin depth are considered in the simulations. The resulting data is analyzed computing field increments in several directions perpendicular to the guide field, and building structure functions and probability density functions. In the magnetohydrodynamic limit we recover the usual results with the magnetic field being more intermittent than the velocity field. In the presence of the Hall effect, field fluctuations at scales smaller than the ion skin depth show a substantial decrease in the level of intermittency, with close to monofractal scaling., Comment: 10 pages, 8 figures

We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the four-fold symmetries of the Taylor-Green vortex generalized to MHD, leading to substantial computer time and memory savings at a given resolution; we also use a re-gridding method that allows for lower-resolution runs at early times, with no loss of spectral accuracy. One magnetic configuration is examined at an equivalent resolution of $6144^3$ points, and three different configurations on grids of $4096^3$ points. At the highest resolution, two different current and vorticity sheet systems are found to collide, producing two successive accelerations in the development of small scales. At the latest time, a convergence of magnetic field lines to the location of maximum current is probably leading locally to a strong bending and directional variability of such lines. A novel analytical method, based on sharp analysis inequalities, is used to assess the validity of the finite-time singularity scenario. This method allows one to rule out spurious singularities by evaluating the rate at which the logarithmic decrement of the analyticity-strip method goes to zero. The result is that the finite-time singularity scenario cannot be ruled out, and the singularity time could be somewhere between $t=2.33$ and $t=2.70.$ More robust conclusions will require higher resolution runs and grid-point interpolation measurements of maximum current and vorticity., Comment: 18 pages, 13 figures, 2 tables; submitted to Physical Review E

Understanding the in situ amplification of large scale magnetic fields in turbulent astrophysical rotators has been a core subject of dynamo theory. When turbulent velocities are helical, large scale dynamos that substantially amplify fields on scales that exceed the turbulent forcing scale arise, but the minimum sufficient fractional kinetic helicity f_h,C has not been previously well quantified. Using direct numerical simulations for a simple helical dynamo, we show that f_h,C decreases as the ratio of forcing to large scale wave numbers k_F/k_min increases. From the condition that a large scale helical dynamo must overcome the backreaction from any non-helical field on the large scales, we develop a theory that can explain the simulations. For k_F/k_min>8 we find f_h,C< 3%, implying that very small helicity fractions strongly influence magnetic spectra for even moderate scale separation., Comment: 5 pages, 4 figures

This study shows the connection between three previously observed but seemingly unrelated phenomena in hydrodynamic (HD) and magnetohydrodynamic (MHD) turbulent flows, involving the emergence of fluctuations occurring on very long time scales: the low-frequency 1/f noise in the power frequency spectrum, the delayed ergodicity of complex valued amplitude fluctuations in wavenumber space, and the spontaneous flippings or reversals of large scale fields. Direct numerical simulations of ideal MHD and HD are employed in three space dimensions, at low resolution, for long periods of time, and with high accuracy to study several cases: Different geometries, presence of rotation and/or a uniform magnetic field, and different values of the associated conserved global quantities. It is conjectured that the origin of all these long-time phenomena is rooted in the interaction of the longest wavelength fluctuations available to the system with fluctuations at much smaller scales. The strength of this non-local interaction is controlled either by the existence of conserved global quantities with a back-transfer in Fourier space, or by the presence of a slow manifold in the dynamics., Comment: 17 pages, 21 figures, accepted for publication in Physical Review E

With the help of a model of magnetohydrodynamic (MHD) turbulence tested previously, we explore high Reynolds number regimes up to equivalent resolutions of 6000^3 grid points in the absence of forcing and with no imposed uniform magnetic field. For the given initial condition chosen here, with equal kinetic and magnetic energy, the flow ends up being dominated by the magnetic field, and the dynamics leads to an isotropic Iroshnikov-Kraichnan energy spectrum. However, the locally anisotropic magnetic field fluctuations perpendicular to the local mean field follow a Kolmogorov law. We find that the ratio of the eddy turnover time to the Alfven time increases with wavenumber, contrary to the so-called critical balance hypothesis. Residual energy and helicity spectra are also considered; the role played by the conservation of magnetic helicity is studied, and scaling laws are found for the magnetic helicity and residual helicity spectra. We put these results in the context of the dynamics of a globally isotropic MHD flow which is locally anisotropic because of the influence of the strong large-scale magnetic field, leading to a partial equilibration between kinetic and magnetic modes for the energy and the helicity., Comment: 11 pages, 7 figures, submitted to Phys. Rev. E

We present a systematic analysis of statistical properties of turbulent current and vorticity structures at a given time using cluster analysis. The data stems from numerical simulations of decaying three-dimensional (3D) magnetohydrodynamic turbulence in the absence of an imposed uniform magnetic field; the magnetic Prandtl number is taken equal to unity, and we use a periodic box with grids of up to 1536^3 points, and with Taylor Reynolds numbers up to 1100. The initial conditions are either an X-point configuration embedded in 3D, the so-called Orszag-Tang vortex, or an Arn'old-Beltrami-Childress configuration with a fully helical velocity and magnetic field. In each case two snapshots are analyzed, separated by one turn-over time, starting just after the peak of dissipation. We show that the algorithm is able to select a large number of structures (in excess of 8,000) for each snapshot and that the statistical properties of these clusters are remarkably similar for the two snapshots as well as for the two flows under study in terms of scaling laws for the cluster characteristics, with the structures in the vorticity and in the current behaving in the same way. We also study the effect of Reynolds number on cluster statistics, and we finally analyze the properties of these clusters in terms of their velocity-magnetic field correlation. Self-organized criticality features have been identified in the dissipative range of scales. A different scaling arises in the inertial range, which cannot be identified for the moment with a known self-organized criticality class consistent with MHD. We suggest that this range can be governed by turbulence dynamics as opposed to criticality, and propose an interpretation of intermittency in terms of propagation of local instabilities., Comment: 17 pages, 9 figures, 5 tables

This article reviews recent studies of scale interactions in magnetohydrodynamic turbulence. The present day increase of computing power, which allows for the exploration of different configurations of turbulence in conducting flows, and the development of shell-to-shell transfer functions, has led to detailed studies of interactions between the velocity and the magnetic field and between scales. In particular, processes such as induction and dynamo action, the damping of velocity fluctuations by the Lorentz force, or the development of anisotropies, can be characterized at different scales. In this context we consider three different configurations often studied in the literature: mechanically forced turbulence, freely decaying turbulence, and turbulence in the presence of a uniform magnetic field. Each configuration is of interest for different geophysical and astrophysical applications. Local and non-local transfers are discussed for each case. While the transfer between scales of solely kinetic or solely magnetic energy is local, transfers between kinetic and magnetic fields are observed to be local or non-local depending on the configuration. Scale interactions in the cascade of magnetic helicity are also reviewed. Based on the results, the validity of several usual assumptions in hydrodynamic turbulence, such as isotropy of the small scales or universality, is discussed., Comment: Posted with permission from the Annual Review of Fluid Mechanics, Volume 43 (c) 2011 by Annual Reviews, http://www.annualreviews.org

Much of the progress in our understanding of dynamo mechanisms has been made within the theoretical framework of magnetohydrodynamics (MHD). However, for sufficiently diffuse media, the Hall effect eventually becomes non-negligible. We present results from three dimensional simulations of the Hall-MHD equations subjected to random non-helical forcing. We study the role of the Hall effect in the dynamo efficiency for different values of the Hall parameter, using a pseudospectral code to achieve exponentially fast convergence. We also study energy transfer rates among spatial scales to determine the relative importance of the various nonlinear effects in the dynamo process and in the energy cascade. The Hall effect produces a reduction of the direct energy cascade at scales larger than the Hall scale, and therefore leads to smaller energy dissipation rates. Finally, we present results stemming from simulations at large magnetic Prandtl numbers, which is the relevant regime in hot and diffuse media such a the interstellar medium., Comment: 11 pages and 11 figures

We demonstrate that, for the case of quasi-equipartition between the velocity and the magnetic field, the Lagrangian-averaged magnetohydrodynamics alpha-model (LAMHD) reproduces well both the large-scale and small-scale properties of turbulent flows; in particular, it displays no increased (super-filter) bottleneck effect with its ensuing enhanced energy spectrum at the onset of the sub-filter-scales. This is in contrast to the case of the neutral fluid in which the Lagrangian-averaged Navier-Stokes alpha-model is somewhat limited in its applications because of the formation of spatial regions with no internal degrees of freedom and subsequent contamination of super-filter-scale spectral properties. No such regions are found in LAMHD, making this method capable of large reductions in required numerical degrees of freedom; specifically, we find a reduction factor of 200 when compared to a direct numerical simulation on a large grid of 1536^3 points at the same Reynolds number., Comment: 22 pages, 9 figures; accepted Phys.Rev.E

We propose two sets of initial conditions for magnetohydrodynamics (MHD) in which both the velocity and the magnetic fields have spatial symmetries that are preserved by the dynamical equations as the system evolves. When implemented numerically they allow for substantial savings in CPU time and memory storage requirements for a given resolved scale separation. Basic properties of these Taylor-Green flows generalized to MHD are given, and the ideal non-dissipative case is studied up to the equivalent of 2048^3 grid points for one of these flows. The temporal evolution of the logarithmic decrements, delta, of the energy spectrum remains exponential at the highest spatial resolution considered, for which an acceleration is observed briefly before the grid resolution is reached. Up to the end of the exponential decay of delta, the behavior is consistent with a regular flow with no appearance of a singularity. The subsequent short acceleration in the formation of small magnetic scales can be associated with a near collision of two current sheets driven together by magnetic pressure. It leads to strong gradients with a fast rotation of the direction of the magnetic field, a feature also observed in the solar wind., Comment: 8 pages, 4 figures

We examine the effect of accuracy of high-order spectral element methods, with or without adaptive mesh refinement (AMR), in the context of a classical configuration of magnetic reconnection in two space dimensions, the so-called Orszag-Tang vortex made up of a magnetic X-point centered on a stagnation point of the velocity. A recently developed spectral-element adaptive refinement incompressible magnetohydrodynamic (MHD) code is applied to simulate this problem. The MHD solver is explicit, and uses the Elsasser formulation on high-order elements. It automatically takes advantage of the adaptive grid mechanics that have been described elsewhere in the fluid context [Rosenberg, Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)]; the code allows both statically refined and dynamically refined grids. Tests of the algorithm using analytic solutions are described, and comparisons of the Orszag-Tang solutions with pseudo-spectral computations are performed. We demonstrate for moderate Reynolds numbers that the algorithms using both static and refined grids reproduce the pseudo--spectral solutions quite well. We show that low-order truncation--even with a comparable number of global degrees of freedom--fails to correctly model some strong (sup--norm) quantities in this problem, even though it satisfies adequately the weak (integrated) balance diagnostics., Comment: 19 pages, 10 figures, 1 table. Submitted to New Journal of Physics

Dynamo action in a fully helical Beltrami (ABC) flow is studied using both direct numerical simulations and subgrid modeling. Sufficient scale separation is given in order to allow for large-scale magnetic energy build-up. Growth of magnetic energy obtains down to a magnetic Prandtl number PM=RM/RV close to 0.005, where RV and RM are the kinetic and magnetic Reynolds numbers. The critical magnetic Reynolds number for dynamo action RMc seems to saturate at values close to 20. Detailed studies of the dependence of the amplitude of the saturated magnetic energy with PM are presented. In order to decrease PM, numerical experiments are conducted with either RV or RM kept constant. In the former case, the ratio of magnetic to kinetic energy saturates to a value slightly below unity as PM decreases. Examination of energy spectra and structures in real space both reveal that quenching of the velocity by the large-scale magnetic field takes place, with an inverse cascade of magnetic helicity and a force-free field at large scale in the saturated regime., Comment: 10 pages, 15 figures

Numerical solutions of the incompressible magnetohydrodynamic (MHD) equations are reported for the interior of a rotating, perfectly-conducting, rigid spherical shell that is insulator-coated on the inside. A previously-reported spectral method is used which relies on a Galerkin expansion in Chandrasekhar-Kendall vector eigenfunctions of the curl. The new ingredient in this set of computations is the rigid rotation of the sphere. After a few purely hydrodynamic examples are sampled (spin down, Ekman pumping, inertial waves), attention is focused on selective decay and the MHD dynamo problem. In dynamo runs, prescribed mechanical forcing excites a persistent velocity field, usually turbulent at modest Reynolds numbers, which in turn amplifies a small seed magnetic field that is introduced. A wide variety of dynamo activity is observed, all at unit magnetic Prandtl number. The code lacks the resolution to probe high Reynolds numbers, but nevertheless interesting dynamo regimes turn out to be plentiful in those parts of parameter space in which the code is accurate. The key control parameters seem to be mechanical and magnetic Reynolds numbers, the Rossby and Ekman numbers (which in our computations are varied mostly by varying the rate of rotation of the sphere) and the amount of mechanical helicity injected. Magnetic energy levels and magnetic dipole behavior are exhibited which fluctuate strongly on a time scale of a few eddy turnover times. These seem to stabilize as the rotation rate is increased until the limit of the code resolution is reached., Comment: 26 pages, 17 figures, submitted to New Journal of Physics

We investigate using direct numerical simulations with grids up to 1536^3 points, the rate at which small scales develop in a decaying three-dimensional MHD flow both for deterministic and random initial conditions. Parallel current and vorticity sheets form at the same spatial locations, and further destabilize and fold or roll-up after an initial exponential phase. At high Reynolds numbers, a self-similar evolution of the current and vorticity maxima is found, in which they grow as a cubic power of time; the flow then reaches a finite dissipation rate independent of Reynolds number., Comment: 4 pages, 3 figures

We present a computational method to solve the magnetohydrodynamic equations in spherical geometry. The technique is fully nonlinear and wholly spectral, and uses an expansion basis that is adapted to the geometry: Chandrasekhar-Kendall vector eigenfunctions of the curl. The resulting lower spatial resolution is somewhat offset by being able to build all the boundary conditions into each of the orthogonal expansion functions and by the disappearance of any difficulties caused by singularities at the center of the sphere. The results reported here are for mechanically and magnetically isolated spheres, although different boundary conditions could be studied by adapting the same method. The intent is to be able to study the nonlinear dynamical evolution of those aspects that are peculiar to the spherical geometry at only moderate Reynolds numbers. The code is parallelized, and will preserve to high accuracy the ideal magnetohydrodynamic (MHD) invariants of the system (global energy, magnetic helicity, cross helicity). Examples of results for selective decay and mechanically-driven dynamo simulations are discussed. In the dynamo cases, spontaneous flips of the dipole orientation are observed., Comment: 15 pages, 19 figures. Improved figures, in press in Physics of Fluids

Scale interactions in Hall MHD are studied using both the mean field theory derivation of transport coefficients, and direct numerical simulations in three space dimensions. In the magnetically dominated regime, the eddy resistivity is found to be negative definite, leading to large scale instabilities. A direct cascade of the total energy is observed, although as the amplitude of the Hall effect is increased, backscatter of magnetic energy to large scales is found, a feature not present in MHD flows. The coupling between the magnetic and velocity fields is different than in the MHD case, and backscatter of energy from small scale magnetic fields to large scale flows is also observed. For the magnetic helicity, a strong quenching of its transfer is found. We also discuss non-helical magnetically forced Hall-MHD simulations where growth of a large scale magnetic field is observed., Comment: 25 pages, 16 figures

We present direct numerical simulations and Lagrangian averaged (also known as alpha-model) simulations of forced and free decaying magnetohydrodynamic turbulence in two dimensions. The statistics of sign cancellations of the current at small scales is studied using both the cancellation exponent and the fractal dimension of the structures. The alpha-model is found to have the same scaling behavior between positive and negative contributions as the direct numerical simulations. The alpha-model is also able to reproduce the time evolution of these quantities in free decaying turbulence. At large Reynolds numbers, an independence of the cancellation exponent with the Reynolds numbers is observed., Comment: Finite size box effects have been taken into account in the definition of the partition function. This has resulted in a more clear scaling in all figures. Several points are clarified in the text

We study the transfer of energy between different scales for forced three-dimensional MHD turbulent flows in the kinematic dynamo regime. Two different forces are examined: a non-helical Taylor Green flow with magnetic Prandtl number P_M=0.4, and a helical ABC flow with P_M=1. This analysis allows us to examine which scales of the velocity flow are responsible for dynamo action, and identify which scales of the magnetic field receive energy directly from the velocity field and which scales receive magnetic energy through the cascade of the magnetic field from large to small scales. Our results show that the turbulent velocity fluctuations are responsible for the magnetic field amplification in the small scales (small scale dynamo) while the large scale field is amplified mostly due to the large scale flow. A direct cascade of the magnetic field energy from large to small scales is also present and is a complementary mechanism for the increase of the magnetic field in the small scales. Input of energy from the velocity field in the small magnetic scales dominates over the energy that is cascaded down from the large scales until the large-scale peak of the magnetic energy spectrum is reached. At even smaller scales, most of the magnetic energy input is from the cascading process., Comment: Submitted to PRE

We investigate the transfer of energy from large scales to small scales in fully developed forced three-dimensional MHD-turbulence by analyzing the results of direct numerical simulations in the absence of an externally imposed uniform magnetic field. Our results show that the transfer of kinetic energy from the large scales to kinetic energy at smaller scales, and the transfer of magnetic energy from the large scales to magnetic energy at smaller scales, are local, as is also found in the case of neutral fluids, and in a way that is compatible with Kolmogorov (1941) theory of turbulence. However, the transfer of energy from the velocity field to the magnetic field is a highly non-local process in Fourier space. Energy from the velocity field at large scales can be transfered directly into small scale magnetic fields without the participation of intermediate scales. Some implications of our results to MHD turbulence modeling are also discussed., Comment: Submitted to PRE

We present direct numerical simulations of dynamo action in a forced Roberts flow. The behavior of the dynamo is followed as the mechanical Reynolds number is increased, starting from the laminar case until a turbulent regime is reached. The critical magnetic Reynolds for dynamo action is found, and in the turbulent flow it is observed to be nearly independent on the magnetic Prandtl number in the range from 0.3 to 0.1. Also the dependence of this threshold with the amount of mechanical helicity in the flow is studied. For the different regimes found, the configuration of the magnetic and velocity fields in the saturated steady state are discussed., Comment: 9 pages, 14 figures

We present direct numerical simulations and alpha-model simulations of four familiar three-dimensional magnetohydrodynamic (MHD) turbulence effects: selective decay, dynamic alignment, inverse cascade of magnetic helicity, and the helical dynamo effect. The MHD alpha-model is shown to capture the long-wavelength spectra in all these problems, allowing for a significant reduction of computer time and memory at the same kinetic and magnetic Reynolds numbers. In the helical dynamo, not only does the alpha-model correctly reproduce the growth rate of magnetic energy during the kinematic regime, but it also captures the nonlinear saturation level and the late generation of a large scale magnetic field by the helical turbulence., Comment: 12 pages, 19 figures

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 figures