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Title: Anisotropic form of third-order moments and relationship to the cascade rate in axisymmetric magnetohydrodynamic turbulence

Abstract

Laws governing the behavior of statistical third-order moments in the inertial range are among the few rigorous results in the theory of statistically homogeneous incompressible magnetohydrodynamic turbulence. These fundamental laws apply to both isotropic and anisotropic turbulence. Assuming that the turbulence is stationary in time and statistically axisymmetric under proper rotations about the direction of the mean magnetic field, it is shown that the general mathematical form of the tensor quantities appearing in these laws is constrained by symmetry to have a particular form. Using these forms, the general solutions of the law for the vector and pseudovector third-order moments F and F{sub C} are obtained in the limit of large kinetic Reynolds number and large magnetic Reynolds number. The physical meaning of the different terms in F and F{sub C} are investigated and a method for obtaining the cascade rates of energy {epsilon} and cross-helicity {epsilon}{sub C} from experimental data is described. The results show that the measurement of the cascade rates goes hand-in-hand with the measurement of the spatial anisotropy of the third-order moments F and F{sub C}. The theory developed here can be applied to measure the turbulent cascade rates of energy and cross-helicity in laboratory plasmamore » experiments, numerical simulations, and the solar wind.« less

Authors:
; ;  [1]
  1. Space Science Center, University of New Hampshire, Durham, New Hampshire 03824 (United States)
Publication Date:
OSTI Identifier:
21069828
Resource Type:
Journal Article
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 14; Journal Issue: 9; Other Information: DOI: 10.1063/1.2783224; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANISOTROPY; AXIAL SYMMETRY; COMPUTERIZED SIMULATION; HELICITY; MAGNETIC FIELDS; MAGNETIC REYNOLDS NUMBER; MAGNETOHYDRODYNAMICS; MATHEMATICAL SOLUTIONS; PLASMA; PLASMA SIMULATION; ROTATION; SOLAR WIND; TURBULENCE; VECTORS

Citation Formats

Podesta, J J, Forman, M A, Smith, C W, Department of Physics and Astronomy, State University of New York, Stony Brook, New York 11794, and Space Science Center, University of New Hampshire, Durham, New Hampshire 03824. Anisotropic form of third-order moments and relationship to the cascade rate in axisymmetric magnetohydrodynamic turbulence. United States: N. p., 2007. Web. doi:10.1063/1.2783224.
Podesta, J J, Forman, M A, Smith, C W, Department of Physics and Astronomy, State University of New York, Stony Brook, New York 11794, & Space Science Center, University of New Hampshire, Durham, New Hampshire 03824. Anisotropic form of third-order moments and relationship to the cascade rate in axisymmetric magnetohydrodynamic turbulence. United States. https://doi.org/10.1063/1.2783224
Podesta, J J, Forman, M A, Smith, C W, Department of Physics and Astronomy, State University of New York, Stony Brook, New York 11794, and Space Science Center, University of New Hampshire, Durham, New Hampshire 03824. Sat . "Anisotropic form of third-order moments and relationship to the cascade rate in axisymmetric magnetohydrodynamic turbulence". United States. https://doi.org/10.1063/1.2783224.
@article{osti_21069828,
title = {Anisotropic form of third-order moments and relationship to the cascade rate in axisymmetric magnetohydrodynamic turbulence},
author = {Podesta, J J and Forman, M A and Smith, C W and Department of Physics and Astronomy, State University of New York, Stony Brook, New York 11794 and Space Science Center, University of New Hampshire, Durham, New Hampshire 03824},
abstractNote = {Laws governing the behavior of statistical third-order moments in the inertial range are among the few rigorous results in the theory of statistically homogeneous incompressible magnetohydrodynamic turbulence. These fundamental laws apply to both isotropic and anisotropic turbulence. Assuming that the turbulence is stationary in time and statistically axisymmetric under proper rotations about the direction of the mean magnetic field, it is shown that the general mathematical form of the tensor quantities appearing in these laws is constrained by symmetry to have a particular form. Using these forms, the general solutions of the law for the vector and pseudovector third-order moments F and F{sub C} are obtained in the limit of large kinetic Reynolds number and large magnetic Reynolds number. The physical meaning of the different terms in F and F{sub C} are investigated and a method for obtaining the cascade rates of energy {epsilon} and cross-helicity {epsilon}{sub C} from experimental data is described. The results show that the measurement of the cascade rates goes hand-in-hand with the measurement of the spatial anisotropy of the third-order moments F and F{sub C}. The theory developed here can be applied to measure the turbulent cascade rates of energy and cross-helicity in laboratory plasma experiments, numerical simulations, and the solar wind.},
doi = {10.1063/1.2783224},
url = {https://www.osti.gov/biblio/21069828}, journal = {Physics of Plasmas},
issn = {1070-664X},
number = 9,
volume = 14,
place = {United States},
year = {2007},
month = {9}
}