The Anisotropy of Magnetohydrodynamic Alfvenic Turbulence (original) (raw)
Related papers
On spectral scaling laws for incompressible anisotropic magnetohydrodynamic turbulence
Physics of Plasmas, 2005
A heuristic model is given for anisotropic magnetohydrodynamics (MHD) turbulence in the presence of a uniform external magnetic field B 0ê . The model is valid for both moderate and strong B 0 and is able to describe both the strong and weak wave turbulence regimes as well as the transition between them. The main ingredient of the model is the assumption of constant ratio at all scales between the linear wave period and the nonlinear turnover timescale. Contrary to the model of critical balance introduced by Goldreich and Sridhar [P. Goldreich and S. Sridhar, ApJ 438, 763 (1995)], it is not assumed in addition that this ratio be equal to unity at all scales which allows us to use the Iroshnikov-Kraichnan phenomenology. It is then possible to recover the widely observed anisotropic scaling law k ∝ k 2/3 ⊥ between parallel and perpendicular wavenumbers (with reference to B 0ê ) and to obtain the universal prediction, 3α + 2β = 7, for the total energy spectrum
Physical Review Fluids
We studied the anisotropization of homogeneous magnetohydrodynamic turbulence at low magnetic Reynolds numbers. Flows of this type are not only important for different engineering applications, but also provide an appealing framework for studies of quasi-two-dimensional turbulence with strongly modified transport properties. The results of large-scale forced, direct numerical simulations are presented and compared with those obtained with the quasi-normal scale elimination theory. For a weak magnetic field, the simulations validated the theoretical predictions, including the generation of the k −7/3 range of the energy spectra and its propagation toward higher wave numbers with increasing magnetic field strength. In a strong magnetic field, the turbulence attains a quasi-two-dimensional state with an enstrophy cascade inertial range of the normal flow components in the normal plane and a passive scalar inertial-convective range of the parallel component. The corresponding energy spectra are in a good agreement with logarithmically corrected k −3 and k −1 theoretical predictions. With increasing Reynolds number at constant magnetic field the enstrophy cascade becomes unstable and is replaced by helicity cascade with k −7/3 energy spectrum. The enstrophy cascade is restored with an increasing magnetic field. An investigation of the mechanism of energy injection into the parallel component in a strong magnetic field revealed that the energy is supplied directly by an external force. The spectrum of the parallel component depends on the isotropy of external forcing and is, thus, not universal.
Incompressible Homogeneous Anisotropic Turbulence: Magnetohydrodynamic Turbulence
Homogeneous Turbulence Dynamics, 2018
Magnetohydrodynamic (MHD) turbulence is present in electrically-conducting fluids, both in industrial devices and in the core of the earth, and is ubiquitous in heliophysics and astrophysics. MHD is also the first step to address the physics of plasmas, with recent studies motivated by the ITER project. Interactions of velocity and magnetic (or induction) fields yield new coupled effects. These effects can be mainly described and modelled in our context of homogeneous turbulence, because the Lorentz (or Laplace) force is a body force, as are the Coriolis force (Chap. 7) and the buoyancy force (Chap. 10). Limits of our incompressible and "homogenized" approach are touched upon at the end of this chapter. Incompressibility is not questioned in a turbulent liquid metal, but it is not suited in many astrophysical situations, so that we will explore the limits of this approximation as well, and look at some extensions using the anelastic approximation, or magnetosonic modes. Analogies and differences with the "hydro" (hydrodynamic hereinafter) case can be first discussed in the presence of a mean magnetic field, which can appear as a mean Alfvén velocity using a simple rescaling. Without strong diffusion and in the presence of a dominant mean field B 0 , Alfvén waves are easily identified from background coupled equations, observations, experiments and numerical simulations. With respect to the other wave régimes presented in this book in the "hydro" case, these plane waves are not dispersive (sometime called semi-dispersive), the dispersion law displays a typical mean-velocity-scale (the Alfvén velocity) and not a typical frequency (Coriolis parameter, stratification frequency). In contrast with the Coriolis force and the buoyancy force (at least within the Boussinesq approximation), that are linear, the Lorentz force is quadratic, so that it yields cubic correlations in the equations for kinetic energy and total energy, as for nonlinear transfer terms. Accordingly, Alfvén waves are well identified in the presence of a dominant external magnetic field, when the Lorentz force is linearized, but they do exist without mean magnetic field.
Anisotropy in Quasi-Static Magnetohydrodynamic Turbulence
Reports on progress in physics. Physical Society (Great Britain), 2017
In this review we summarise the current status of the quasi-static magnetohydrodynamic turbulence. The energy spectrum is steeper than Kolmogorov's k (-5/3) spectrum due to the decrease of the kinetic energy flux with wavenumber k as a result of Joule dissipation. The spectral index decreases with the increase of interaction parameter. The flow is quasi two-dimensional with strong [Formula: see text] at small k and weak [Formula: see text] at large k, where [Formula: see text] and [Formula: see text] are the perpendicular and parallel components of velocity relative to the external magnetic field. For small k, the energy flux of [Formula: see text] is negative, but for large k, the energy flux of [Formula: see text] is positive. Pressure mediates the energy transfer from [Formula: see text] to [Formula: see text].
The Anisotropy of Electron Magnetohydrodynamic Turbulence
The Astrophysical Journal, 2004
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 ∝ k 1/3 ⊥ , where k and k ⊥ are wave numbers parallel and perpendicular to (local) mean magnetic field, respectively.
Spectral study of anisotropic magnetohydrodynamic turbulence
2009
A spectral analysis of anisotropic magneto-hydrodynamic turbulence, in presence of a constant magnetic field, is presented using direct numerical simulations. A method of decomposing the spectral space into ring structures is presented and the energy transfers between such rings are studied. This decomposition method takes into account the angular dependency of transfer functions in anisotropic systems, while it allows to recover easily the known shell-to-shell transfers in the limit of isotropic turbulence. For large values of the constant magnetic field, the dominant energy transfers appear to be in the direction perpendicular to the mean magnetic field. The linear transfer due to the constant magnetic also appear to be important in redistributing the energy between the velocity and the magnetic fields.
Scale Interactions in Magnetohydrodynamic Turbulence
Annual Review of Fluid Mechanics, 2011
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-toshell 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
Physical Review E, 2014
Small-scale anisotropic intermittency is examined in three-dimensional incompressible magnetohydrodynamic turbulence subjected to a uniformly imposed magnetic field. Orthonormal wavelet analyses are applied to direct numerical simulation data at moderate Reynolds number and for different interaction parameters. The magnetic Reynolds number is sufficiently low such that the quasistatic approximation can be applied. Scale-dependent statistical measures are introduced to quantify anisotropy in terms of the flow components, either parallel or perpendicular to the imposed magnetic field, and in terms of the different directions. Moreover, the flow intermittency is shown to increase with increasing values of the interaction parameter, which is reflected in strongly growing flatness values when the scale decreases. The scale-dependent anisotropy of energy is found to be independent of scale for all considered values of the interaction parameter. The strength of the imposed magnetic field does amplify the anisotropy of the flow.
Scale Locality of Magnetohydrodynamic Turbulence
Physical Review Letters, 2010
We investigate the scale-locality of cascades of conserved invariants at high kinetic and magnetic Reynolds numbers in the "inertial-inductive range" of magnetohydrodynamic (MHD) turbulence, where velocity and magnetic field increments exhibit suitable power-law scaling. We prove that fluxes of total energy and cross-helicity-or, equivalently, fluxes of Elsässer energies-are dominated by the contributions of local triads. Corresponding spectral transfers are also scale-local when defined using octave wavenumber bands. Flux and transfer of magnetic helicity may be dominated by nonlocal triads. The magnetic stretching term also may be dominated by non-local triads but we prove that it can convert energy only between velocity and magnetic modes at comparable scales. We explain the disagreement with numerical studies that have claimed conversion nonlocally between disparate scales. We present supporting data from a 1024 3 simulation of forced MHD turbulence.
Structure of homogeneous nonhelical magnetohydrodynamic turbulence
Physics of Plasmas, 1996
Results are presented for three-dimensional direct numerical simulations of nonhelical magnetohydrodynamic ͑MHD͒ turbulence for both stationary isotropic and homogeneous shear flow configurations with zero mean induction and unity magnetic Prandtl number. Small scale dynamo action is observed in both flows, and stationary values for the ratio of magnetic to kinetic energy are shown to scale nearly linearly with the Taylor microscale Reynolds numbers above a critical value of Re Ϸ30. The presence of the magnetic field has the effect of decreasing the kinetic energy of the flow, while simultaneously increasing the Taylor microscale Reynolds number due to enlargement of the hydrodynamic length scales. For shear flows, both the velocity and the magnetic fields become increasingly anisotropic with increasing initial magnetic field strength. The kinetic energy spectra show a relative increase in high wave-number energy in the presence of a magnetic field. The magnetic field is found to portray an intermittent behavior, with peak values of the flatness near the critical Reynolds number. The magnetic field of both flows is organized in the form of ''flux tubes'' and magnetic ''sheets.'' These regions of large magnetic field strength show a small correlation with moderate vorticity regions, while the electric current structures are correlated with large amplitude strain regions of the turbulence. Some of the characteristics of small scale MHD turbulence are explained via the ''structural'' description of turbulence.