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Title: On the nature of incompressible magnetohydrodynamic turbulence

Abstract

A novel model of incompressible magnetohydrodynamic turbulence in the presence of a strong external magnetic field is proposed for the explanation of recent numerical results. According to the proposed model, in the presence of the strong external magnetic field, incompressible magnetohydrodynamic turbulence becomes nonlocal in the sense that low-frequency modes cause decorrelation of interacting high-frequency modes from the inertial interval. It is shown that the obtained nonlocal spectrum of the inertial range of incompressible magnetohydrodynamic turbulence represents an anisotropic analogue of Kraichnan's nonlocal spectrum of hydrodynamic turbulence. Based on the analysis performed in the framework of the weak-coupling approximation, which represents one of the equivalent formulations of the direct interaction approximation, it is shown that incompressible magnetohydrodynamic turbulence could be both local and nonlocal, and therefore anisotropic analogues of both the Kolmogorov and Kraichnan spectra are realizable in incompressible magnetohydrodynamic turbulence.

Authors:
 [1]
  1. Georgian National Astrophysical Observatory, 2a Kazbegi Avenue, 0160 Tbilisi (Georgia)
Publication Date:
OSTI Identifier:
20974827
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 2; Other Information: DOI: 10.1063/1.2437753; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANISOTROPY; APPROXIMATIONS; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; PLASMA; PLASMA INSTABILITY; SPECTRA; TURBULENCE

Citation Formats

Gogoberidze, G. On the nature of incompressible magnetohydrodynamic turbulence. United States: N. p., 2007. Web. doi:10.1063/1.2437753.
Gogoberidze, G. On the nature of incompressible magnetohydrodynamic turbulence. United States. doi:10.1063/1.2437753.
Gogoberidze, G. Thu . "On the nature of incompressible magnetohydrodynamic turbulence". United States. doi:10.1063/1.2437753.
@article{osti_20974827,
title = {On the nature of incompressible magnetohydrodynamic turbulence},
author = {Gogoberidze, G.},
abstractNote = {A novel model of incompressible magnetohydrodynamic turbulence in the presence of a strong external magnetic field is proposed for the explanation of recent numerical results. According to the proposed model, in the presence of the strong external magnetic field, incompressible magnetohydrodynamic turbulence becomes nonlocal in the sense that low-frequency modes cause decorrelation of interacting high-frequency modes from the inertial interval. It is shown that the obtained nonlocal spectrum of the inertial range of incompressible magnetohydrodynamic turbulence represents an anisotropic analogue of Kraichnan's nonlocal spectrum of hydrodynamic turbulence. Based on the analysis performed in the framework of the weak-coupling approximation, which represents one of the equivalent formulations of the direct interaction approximation, it is shown that incompressible magnetohydrodynamic turbulence could be both local and nonlocal, and therefore anisotropic analogues of both the Kolmogorov and Kraichnan spectra are realizable in incompressible magnetohydrodynamic turbulence.},
doi = {10.1063/1.2437753},
journal = {Physics of Plasmas},
number = 2,
volume = 14,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}
  • Numerical solutions of decaying two-dimensional incompressible magnetohydrodynamic turbulence reach a long-lived self-similar state which is described in terms of a turbulent enstrophy cascade. The ratio of kinetic to magnetic enstrophy remains approximately constant, while the ratio of energies decreases steadily. Although the enstrophy is not an inviscid invariant, the rates of enstrophy production, dissipation, and conversion from magnetic to kinetic enstrophy are very evenly balanced, resulting in smooth power law decay. Energy spectra have a {ital k}{sup {minus}3/2} dependence at early times, but steepen to {ital k}{sup {minus}5/2}. Local alignment of the intermediate and small-scale fields grows, but global correlationmore » coefficients do not. The spatial kurtosis of current grows and is always greater than the vorticity kurtosis. Axisymmetric monopole patterns in the current (magnetic vortices) are dominant structures; they typically have a weaker concentric, nonmonotonic vorticity component. Fast reconnection or coalescence events occur on advective and Alfven time scales between close vortices of like sign. Current sheets created during these coalescence events are local sites of enstrophy production, conversion, and dissipation. The number of vortices decreases until the fluid reaches a magnetic dipole as its nonlinear evolutionary end-state. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.« less
  • The statistical properties of the dissipation process constrain the analysis of large scale numerical simulations of three-dimensional incompressible magnetohydrodynamic (MHD) turbulence, such as those of Biskamp and Mueller [Phys. Plasmas 7, 4889 (2000)]. The structure functions of the turbulent flow are expected to display statistical self-similarity, but the relatively low Reynolds numbers attainable by direct numerical simulation, combined with the finite size of the system, make this difficult to measure directly. However, it is known that extended self-similarity, which constrains the ratio of scaling exponents of structure functions of different orders, is well satisfied. This implies the extension of physicalmore » scaling arguments beyond the inertial range into the dissipation range. The present work focuses on the scaling properties of the dissipation process itself. This provides an important consistency check in that we find that the ratio of dissipation structure function exponents is that predicted by the She and Leveque [Phys. Rev. Lett 72, 336 (1994)] theory proposed by Biskamp and Mueller. This supplies further evidence that the cascade mechanism in three-dimensional MHD turbulence is nonlinear random eddy scrambling, with the level of intermittency determined by dissipation through the formation of current sheets.« less
  • A heuristic model is given for anisotropic magnetohydrodynamics turbulence in the presence of a uniform external magnetic field B{sub 0}e{sub parallel}. The model is valid for both moderate and strong B{sub 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 time scale. Contrary to the model of critical balance introduced by Goldreich and Sridhar [Astrophys. J. 438, 763 (1995)], it is not assumed, inmore » addition, that this ratio be equal to unity at all scales. This allows us to make use of the Iroshnikov-Kraichnan phenomenology; it is then possible to recover the widely observed anisotropic scaling law k{sub parallel}{proportional_to}k{sub perpendicular}{sup 2/3} between parallel and perpendicular wave numbers (with reference to B{sub 0}e{sub parallel} and to obtain for the total-energy spectrum E(k{sub perpendicular},k{sub parallel}){approx}k{sub perpendicu=} l{sub ar}{sup -{alpha}}k{sub parallel}{sup -{beta}} the universal prediction, 3{alpha}+2{beta}=7. In particular, with such a prediction, the weak Alfven wave turbulence constant-flux solution is recovered and, for the first time, a possible explanation to its precursor found numerically by Galtier et al. [J. Plasma Phys. 63, 447 (2000)] is given.« less
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