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Title: A two-component phenomenology for homogeneous magnetohydrodynamic turbulence

Abstract

A one-point closure model for energy decay in three-dimensional magnetohydrodynamic (MHD) turbulence is developed. The model allows for influence of a large-scale magnetic field that may be of strength sufficient to induce Alfven wave propagation effects, and takes into account components of turbulence in which either the wave-like character is negligible or is dominant. This two-component model evolves energy and characteristic length scales, and may be useful as a simple description of homogeneous MHD turbulent decay. In concert with spatial transport models, it can form the basis for approximate treatment of low-frequency plasma turbulence in a variety of solar, space, and astrophysical contexts.

Authors:
; ;  [1];  [2]
  1. Department of Mathematics, University of Waikato, Private Bag 3105, Hamilton (New Zealand)
  2. (United States)
Publication Date:
OSTI Identifier:
20782734
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 13; Journal Issue: 4; Other Information: DOI: 10.1063/1.2188088; (c) 2006 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; ALFVEN WAVES; DECAY; LENGTH; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; PLASMA; RADIATION TRANSPORT; THREE-DIMENSIONAL CALCULATIONS; TRANSPORT THEORY; TURBULENCE

Citation Formats

Oughton, S., Dmitruk, P., Matthaeus, W. H., and Bartol Research Institute, University of Delaware, Newark, Delaware 19716. A two-component phenomenology for homogeneous magnetohydrodynamic turbulence. United States: N. p., 2006. Web. doi:10.1063/1.2188088.
Oughton, S., Dmitruk, P., Matthaeus, W. H., & Bartol Research Institute, University of Delaware, Newark, Delaware 19716. A two-component phenomenology for homogeneous magnetohydrodynamic turbulence. United States. doi:10.1063/1.2188088.
Oughton, S., Dmitruk, P., Matthaeus, W. H., and Bartol Research Institute, University of Delaware, Newark, Delaware 19716. Sat . "A two-component phenomenology for homogeneous magnetohydrodynamic turbulence". United States. doi:10.1063/1.2188088.
@article{osti_20782734,
title = {A two-component phenomenology for homogeneous magnetohydrodynamic turbulence},
author = {Oughton, S. and Dmitruk, P. and Matthaeus, W. H. and Bartol Research Institute, University of Delaware, Newark, Delaware 19716},
abstractNote = {A one-point closure model for energy decay in three-dimensional magnetohydrodynamic (MHD) turbulence is developed. The model allows for influence of a large-scale magnetic field that may be of strength sufficient to induce Alfven wave propagation effects, and takes into account components of turbulence in which either the wave-like character is negligible or is dominant. This two-component model evolves energy and characteristic length scales, and may be useful as a simple description of homogeneous MHD turbulent decay. In concert with spatial transport models, it can form the basis for approximate treatment of low-frequency plasma turbulence in a variety of solar, space, and astrophysical contexts.},
doi = {10.1063/1.2188088},
journal = {Physics of Plasmas},
number = 4,
volume = 13,
place = {United States},
year = {Sat Apr 15 00:00:00 EDT 2006},
month = {Sat Apr 15 00:00:00 EDT 2006}
}
  • Two-dimensional (2D) homogeneous magnetohydrodynamic (MHD) turbulence has many of the same qualitative features as three-dimensional (3D) homogeneous MHD turbulence. These features include several ideal (i.e., nondissipative) invariants along with the phenomenon of broken ergodicity (defined as nonergodic behavior over a very long time). Broken ergodicity appears when certain modes act like random variables with mean values that are large compared to their standard deviations, indicating a coherent structure or dynamo. Recently, the origin of broken ergodicity in 3D MHD turbulence that is manifest in the lowest wavenumbers was found. Here, we study the origin of broken ergodicity in 2D MHDmore » turbulence. It will be seen that broken ergodicity in ideal 2D MHD turbulence can be manifest in the lowest wavenumbers of a finite numerical model for certain initial conditions or in the highest wavenumbers for another set of initial conditions. The origins of broken ergodicity in an ideal 2D homogeneous MHD turbulence are found through an eigenanalysis of the covariance matrices of the probability density function and by an examination of the associated entropy functional. When the values of ideal invariants are kept fixed and grid size increases, it will be shown that the energy in a few large modes remains constant, while the energy in any other mode is inversely proportional to grid size. Also, as grid size increases, we find that broken ergodicity becomes manifest at more and more wavenumbers.« less
  • Magnetohydrodynamics (MHD) turbulence theory, often employed satisfactorily in astrophysical applications, has often focused on parameter ranges that imply nearly equal values of kinetic and magnetic energies and length scales. However, MHD flow may have disparity magnetic Prandtl number, dissimilar kinetic and magnetic Reynolds number, different kinetic and magnetic outer length scales, and strong anisotropy. Here a phenomenology for such ''non-equipartitioned'' MHD flow is discussed. Two conditions are proposed for a MHD flow to transition to strong turbulent flow, extensions of (1) Taylor's constant flux in an inertial range, and (2) Kolmogorov's scale separation between the large and small scale boundariesmore » of an inertial range. For this analysis, the detailed information on turbulence structure is not needed. These two conditions for MHD transition are expected to provide consistent predictions and should be applicable to anisotropic MHD flows, after the length scales are replaced by their corresponding perpendicular components. Second, it is stressed that the dynamics and anisotropy of MHD fluctuations is controlled by the relative strength between the straining effects between eddies of similar size and the sweeping action by the large-eddies, or propagation effect of the large-scale magnetic fields, on the small scales, and analysis of this balance in principle also requires consideration of non-equipartition effects.« less
  • Magnetohydrodynamics (MHD) turbulence theory, often employed satisfactorily in astrophysical applications, has often focused on parameter ranges that imply nearly equal values of kinetic and magnetic energies and length scales. However, MHD flow may have disparity magnetic Prandtl number, dissimilar kinetic and magnetic Reynolds number, different kinetic and magnetic outer length scales, and strong anisotropy. Here a phenomenology for such 'nonequipartitioned' MHD flow is discussed. Two conditions are proposed for a MHD flow to transition to strong turbulent flow, which are extensions of (i) Taylor's constant flux in an inertial range and (ii) Kolmogorov's scale separation between the large and smallmore » scale boundaries of an inertial range. For this analysis, the detailed information on turbulence structure is not needed. These two conditions for MHD transition are expected to provide consistent predictions and should be applicable to anisotropic MHD flows, after the length scales are replaced by their corresponding perpendicular components. Second, it is stressed that the dynamics and anisotropy of MHD fluctuations are controlled by the relative strength between the straining effects between eddies of similar size and the sweeping action by the large eddies, or propagation effect of the large-scale magnetic fields, on the small scales, and analysis of this balance, in principle, also requires consideration of nonequipartition effects.« less
  • MHD turbulence in a conducting liquid subjected to a strong magnetic field is studied by reducing the problem to that encountered in the absence of the field. (AIP)
  • Results are presented for three-dimensional direct numerical simulations of nonhelical magnetohydrodynamic (MHD) 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{sub {lambda}}{approx_equal}30. 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 themore » 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 {open_quote}{open_quote}flux tubes{close_quote}{close_quote} and magnetic {open_quote}{open_quote}sheets.{close_quote}{close_quote} 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 {open_quote}{open_quote}structural{close_quote}{close_quote} description of turbulence. {copyright} {ital 1996 American Institute of Physics.}« less