The Anisotropy of Electron Magnetohydrodynamic Turbulence (original) (raw)
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Electron magnetohydrodynamic turbulence
Physics of Plasmas, 1999
Electron magnetohydrodynamic ͑EMHD͒ turbulence is studied in two-and three-dimensional ͑2D and 3D͒ systems. Results in 2D are particularly noteworthy. Energy dissipation rates are found to be independent of the diffusion coefficients. The energy spectrum follows a k Ϫ5/3 law for kd e Ͼ1 and k Ϫ7/3 for kd e Ͻ1, which is consistent with a local spectral energy transfer independent of the linear wave properties, contrary to magnetohydrodynamic ͑MHD͒ turbulence, where the Alfvén effect dominates the transfer dynamics. In 3D spectral properties are similar to those in 2D.
Anisotropic three-dimensional MHD turbulence
Journal of Geophysical Research: Space Physics, 1996
Direct spectral method simulation of the three-dimensional magnetohydrodynamics (MHD) equations is used to explore anisotropy that develops from initially isotropic fluctuations as a consequence of a uniform applied magnetic field. Spectral and variance anisotropies are investigated in both compressible and incompressible MHD. The nature of the spectral anisotropy is consistent with the model of Shebalin et al. [1983] in which the spectrum broadens in the perpendicular wavenumber direction, the anisotropy being greater for smaller wavenumbers. Here this effect is seen for both incompressible and polytropic compressible MHD. In contrast, the longitudinal (compressive) velocity fluctuations remain isotropic. Variance anisotropy is observed for low plasma beta compressible MHD but not for incompressible MHD. Solar wind observations are qualitatively consistent with both variance and spectral anisotropies of the type discussed here. gested the presence of spectral anisotropy in laboratory plasma devices [e.g., Robinson and Rusbridge, 1971; Zweben et al., 1979]. Anisotropy is inherent in the "reduced" MHD description [Strauss, 1976; Montgomery and Turner, 1981; Montgomery, 1982], which nevertheless must appeal to dynamical theory for its justification. Variance anisotropy has also been observed by many in situ spacecraft observations [Belcher and Davis, 1971; Klein et al., 1991]. In addition, there is direct evidence of spectral anisotropy in solar wind magnetic field observations [
Whistlerization and anisotropy in two-dimensional electron magnetohydrodynamic turbulence
Physics of Plasmas, 2000
A detailed numerical simulation to understand the turbulent state of the decaying two-dimensional electron magnetohydrodynamics is presented. It is observed that the evolved spectrum is comprised of a collection of random eddies and a gas of whistler waves, the latter constituting the normal oscillatory modes of such a model. The whistlerization of the turbulent spectra has been quantified by novel diagnostics. In this work, results are presented only in the regime where the spatial excitation scales are longer than the electron skin depth. Simulations suggest that spectra at short scales are comparatively more whistlerized. The long scale field merely acts as the ambient field along which whistler waves propagate. It is also observed that, in the presence of an external magnetic field, the power spectrum acquires a distinct directional dependence. This anisotropy is dominant at short scales. It is shown that such an anisotropy at short scales results from a cascade mechanism governed by the interacting whistlers waves.
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.
The Anisotropy of Magnetohydrodynamic Alfvenic Turbulence
The Astrophysical Journal, 2000
We perform direct 3-dimensional numerical simulations for magnetohydrodynamic (MHD) turbulence in a periodic box of size 2π threaded by strong uniform magnetic fields. We use a pseudo-spectral code with hyperviscosity and hyperdiffusivity to solve the incompressible MHD equations. We analyze the structure of the eddies as a function of scale. A straightforward calculation of anisotropy in wavevector space shows that the anisotropy is scale-independent. We discuss why this is not the true scaling law and how the curvature of large-scale magnetic fields affects the power spectrum and leads to the wrong conclusion. When we correct for this effect, we find that the anisotropy of eddies depends on their size: smaller eddies are more elongated than larger ones along local magnetic field lines. The results are consistent with the scaling lawk ∼k 2/3 ⊥ proposed by Sridhar (1995, 1997). Herek (andk ⊥ ) are wavenumbers measured relative to the local magnetic field direction. However, we see some systematic deviations which may be a sign of limitations to the model, or our inability to fully resolve the inertial range of turbulence in our simulations.
Two-Dimensional Electron Magnetohydrodynamic Turbulence
Physical Review Letters, 1996
A novel type of turbulence, which arises in 2D electron magnetohydrodynamics, is studied by numerical simulation. Energy dissipation rates are found to be independent of the dissipation coefficients. The energy spectrum E k follows the basic Kolmogorov-type predictions, k 25͞3 for kd e. 1 and k 27͞3 for kd e , 1 (d e is the electron inertial length) and is hence independent of the linear wave properties. Results are compared with other 2D turbulent systems.
AIP Conference Proceedings, 2007
The solar wind and the interstellar medium are permeated by large-scale magnetic fields that render magnetohydrodynamic (MHD) turbulence anisotropic. In the weak-turbulence limit in which three-wave interactions dominate, analytical and high-resolution numerical results based on random scattering of shear-Alfvén waves propagating parallel to a large-scale magnetic field, as well as direct simulations demonstrate rigorously an anisotropic energy spectrum that scales as ! k " #2 , instead of the famous Iroshnikov-Kraichnan (IK) spectrum of ! k "3 / 2 for the isotropic case. Even in the absence of a background magnetic field, anisotropy is found to develop with respect to the local magnetic field, although the energy spectrum is globally isotropic and is found to be consistent with a ! k "3 / 2 scaling. It is also found in direct numerical simulations that the energy cascade rate is much closer to IK scaling than a Kolmogorov scaling. Recent observations in the solar wind on cascade rates (as functions of the proton temperature and solar wind speed at 1 AU) seem to support this result [Vasquez et al. 2007].
Dynamic anisotropy in MHD turbulence induced by mean magnetic field
Physics of Plasmas, 2017
In this paper, we study the development of anisotropy in strong MHD turbulence in the presence of a large scale magnetic field B 0 by analyzing the results of direct numerical simulations. Our results show that the developed anisotropy among the different components of the velocity and magnetic field is a direct outcome of the inverse cascade of energy of the perpendicular velocity components u ? and a forward cascade of the energy of the parallel component u k. The inverse cascade develops for a strong B 0 , where the flow exhibits a strong vortical structure by the suppression of fluctuations along the magnetic field. Both the inverse and the forward cascade are examined in detail by investigating the anisotropic energy spectra, the energy fluxes, and the shell to shell energy transfers among different scales. Published by AIP Publishing.
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].
On triple correlations in isotropic electron magnetohydrodynamic turbulence
2003
The evolution of the correlation characteristics in three-dimensional isotropic electron magnetohydrodynamic turbulence is investigated. Universal exact relations between the longitudinal and transverse two-point triple correlations of the components of the fluctuational magnetic fields and the rates of dissipation of the magnetic helicity and energy are obtained in the inertial range.