Characterization of Flow-Magnetic Field Interactions in Magneto-Hydrodynamic Turbulence (original) (raw)

Kinetic-magnetic energy exchanges in rotating magnetohydrodynamic turbulence

Journal of Turbulence, 2019

We use direct numerical simulations to study the dynamics of incompressible homogeneous turbulence subjected to a uniform magnetic field B (the Alfvén velocity) in a rotating frame with rotation vector Ω. We consider two cases: Ω B and Ω ⊥ B. The initial flow state is homogeneous isotropic hydrodynamic turbulence with kinetic Reynolds number Re = u l l/ν 170. The magnetic Prandtl number is Pm = ν/η = 1 and the Elsasser number Λ = B 2 /(2Ωη) = 0.5, 0.9 or 2. Both for Ω B and Ω ⊥ B, the total (kinetic + magnetic) energy E decays as ∼ t −5/7 for Λ = 0.5 and 0.9, and as ∼ t −6/7 for Λ = 2. In the spectral range 2 < k < 20, the radial (spherically averaged) spectrum of kinetic energy scales as ∼ k −p where the index p increases with time (2 ≤ p ≤ 4.2), or equivalently, with the interaction parameter N = B 2 l/(ηu l). This time-dependent scaling is similar to that observed in quasi-static MHD. The two rotating MHD flow cases differ mainly in how kinetic and magnetic fluctuations exchange energy, with a mechanism mostly driven by the dynamics of the spectral buffer layer around k Ω = |Ω•k|/Ω ≈ 0. At k Ω = 0, both the frequencies of inertial and Alfvén waves vanish when Ω B, but only the frequency of inertial waves vanishes for the case when Ω ⊥ B. When Ω B, rotation results in an increased reduction of magnetic fluctuations generation. In terms of anisotropy, we show that the elongated structures occurring in rapidly non-magnetized rotating flows are distorted or inhibited for Ω ⊥ B, and their intensity is weakened for Ω B.

Quasi-static magnetohydrodynamic turbulence at high Reynolds number

Journal of Fluid Mechanics, 2011

We analyse the anisotropy of homogeneous turbulence in an electrically conducting fluid submitted to a uniform magnetic field, for low magnetic Reynolds number, in the quasistatic approximation. We interpret disagreeing previous predictions between linearized theory and simulations: in the linear limit, the kinetic energy of transverse velocity components, normal to the magnetic field, decays faster than the kinetic energy of the axial component, along the magnetic field (Moffatt (1967)); whereas many numerical studies predict a final state characterised by dominant energy of transverse velocity components. We investigate the corresponding nonlinear phenomenon using Direct Numerical Simulations of freely-decaying turbulence, and a two-point statistical spectral closure based on the Eddy Damped Quasi-Normal Markovian model. The transition from the three-dimensional turbulent flow to a "two-and-a-half-dimensional" flow (Montgomery & Turner ) is a result of the combined effects of short-time linear Joule dissipation and longer time nonlinear creation of polarisation anisotropy. It is this combination of linear and nonlinear effects which explains the disagreement between predictions from linearized theory and results from numerical simulations. The transition is characterized by the elongation of turbulent structures along the applied magnetic field, and by the strong anisotropy of directional two-point correlation spectra, in agreement with experimental evidence. Inertial equatorial transfers in both DNS and the model are presented to describe in detail the most important equilibrium dynamics. Spectral scalings are maintained in high Reynolds number turbulence attainable only with the EDQNM model, which also provides simplified modelling of the asymptotic state of quasi-static MHD turbulence.

Probing Physics of Magnetohydrodynamic Turbulence Using Direct Numerical Simulation

1998

The energy spectrum and the nolinear cascade rates of MHD turbulence is not clearly understood. We have addressed this problem using direct numerical simulation and analytical calculations. Our numerical simulations indicate that Kolmogorov-like phenomenology with k −5/3 energy spectrum, rather than Kraichnan's k −3/2 , appears to be applicable in MHD turbulence. Here, we also construct a self-consistent renomalization group procedure in which the mean magnetic field gets renormalized, which in turns yields k −5/3 energy spectrum. The numerical simulations also show that the fluid energy is transferred to magnetic energy. This result could shed light on the generation magnetic field as in dynamo mechanism.

High Reynolds number magnetohydrodynamic turbulence using a Lagrangian model

Physical Review E, 2011

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 Alfvén 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.

Rapid Alignment of Velocity and Magnetic Field in Magnetohydrodynamic Turbulence

Physical Review Letters, 2008

We show that local directional alignment of the velocity and magnetic field fluctuations occurs rapidly in magnetohydrodynamics for a variety of parameters. This is observed both in direct numerical simulations and in solar wind data. The phenomenon is due to an alignment between the magnetic field and either pressure gradients or shear-associated kinetic energy gradients. A similar alignment, of velocity and vorticity, occurs in the Navier Stokes fluid case. This may be the most rapid and robust relaxation process in turbulent flows, and leads to a local weakening of the nonlinear terms in the small scale vorticity and current structures where alignment takes place.

Quantifying energetics and dissipation in magnetohydrodynamic turbulence

Monthly Notices of the Royal Astronomical Society, 2014

We perform a suite of two-and three-dimensional magnetohydrodynamic (MHD) simulations with the Athena code of the non-driven Kelvin-Helmholtz instability in the subsonic, weak magnetic field limit. Focusing the analysis on the non-linear turbulent regime, we quantify energy transfer on a scale-by-scale basis and identify the physical mechanisms responsible for energy exchange by developing the diagnostic known as spectral energy transfer function analysis. At late times when the fluid is in a state of MHD turbulence, magnetic tension mediates the dominant mode of energy injection into the magnetic reservoir, whereby turbulent fluid motions twist and stretch the magnetic field lines. This generated magnetic energy turbulently cascades to smaller scales, while being exchanged backwards and forwards with the kinetic energy reservoir, until finally being dissipated. Incorporating explicit dissipation pushes the dissipation scale to larger scales than if the dissipation were entirely numerical. For scales larger than the dissipation scale, we show that the physics of energy transfer in decaying MHD turbulence is robust to numerical effects.

Depletion of nonlinearity in magnetohydrodynamic turbulence: Insights from analysis and simulations

Physical Review E

It is shown how suitably scaled, order-m moments, D ± m , of the Elsässer vorticity fields in threedimensional magnetohydrodynamics (MHD) can be used to identify three possible regimes for solutions of the MHD equations with magnetic Prandtl number PM = 1. These vorticity fields are defined by ω ± = curl z ± = ω ± j, where z ± are Elsässer variables, and where ω and j are, respectively, the fluid vorticity and current density. This study follows recent developments in the study of three-dimensional Navier-Stokes fluid turbulence [Gibbon et al. Nonlinearity 27, 2605]. Our mathematical results are then compared with those from a variety of direct numerical simulations (DNSs) which demonstrate that all solutions that have been investigated remain in only one of these regimes which has depleted nonlinearity. The exponents q ± that characterize the inertial range power-law dependencies of the z ± energy spectra, E ± (k), are then examined, and bounds are obtained. Comments are also made on : (a) the generalization of our results to the case PM = 1 and (b) the relation between D ± m and the order-m moments of gradients of magnetohydrodynamic fields, which are used to characterize intermittency in turbulent flows.

Energy transfers in magnetohydrodynamic turbulence in presence of an ambient imposed magnetic field

2009

The purpose of this study is to explore the energy exchange mechanisms in magnetohydrodynamic (MHD) turbulence. A spectral analysis of isotropic and anisotropic MHD turbulence is performed using direct numerical simulations. The anisotropy is generated due to the presence of the ambient magnetic field and the turbulence level is maintained by a mechanical force. In the statistically stationary regime, the energy spectra and the energy transfer functions are studied for different values of the ambient magnetic field. In the direction parallel to this magnetic field, we observe suppression of the energy transfer when compared to the isotropic case. Also the energy tends to accumulate around the direction perpendicular to the constant magnetic field. These effects are stronger with the increase of the constant magnetic field value. Since the use of shell-to-shell transfer functions is inadequate for describing anisotropic effects, a ring decomposition of the spectral space is used.

The Generation of Magnetic Fields through Driven Turbulence

The Astrophysical Journal, 2000

We have tested the ability of driven turbulence to generate magnetic field structure from a weak uniform field using three dimensional numerical simulations of incompressible turbulence. We used a pseudo-spectral code with a numerical resolution of up to 144 3 collocation points. We find that the magnetic fields are amplified through field line stretching at a rate proportional to the difference between the velocity and the magnetic field strength times a constant. Equipartition between the kinetic and magnetic energy densities occurs at a scale somewhat smaller than the kinetic energy peak. Above the equipartition scale the velocity structure is, as expected, nearly isotropic. The magnetic field structure at these scales is uncertain, but the field correlation function is very weak. At the equipartition scale the magnetic fields show only a moderate degree of anisotropy, so that the typical radius of curvature of field lines is comparable to the typical perpendicular scale for field reversal. In other words, there are few field reversals within eddies at the equipartition scale, and no fine-grained series of reversals at smaller scales. At scales below the equipartition scale, both velocity and magnetic structures are anisotropic; the eddies are stretched along the local magnetic field lines, and the magnetic energy dominates the kinetic energy on the same scale by a factor which increases at higher wavenumbers. We do not show a scale-free inertial range, but the power spectra are a function of resolution and/or the imposed viscosity and resistivity. Our results are consistent with the emergence of a scale-free inertial range at higher Reynolds numbers.