Anisotropic form of thirdorder moments and relationship to the cascade rate in axisymmetric magnetohydrodynamic turbulence
Abstract
Laws governing the behavior of statistical thirdorder 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 thirdorder 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 crosshelicity {epsilon}{sub C} from experimental data is described. The results show that the measurement of the cascade rates goes handinhand with the measurement of the spatial anisotropy of the thirdorder moments F and F{sub C}. The theory developed here can be applied to measure the turbulent cascade rates of energy and crosshelicity in laboratory plasmamore »
 Authors:

 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 1070664X
 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 thirdorder 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 thirdorder 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 thirdorder 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 thirdorder 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 thirdorder 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 thirdorder 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 crosshelicity {epsilon}{sub C} from experimental data is described. The results show that the measurement of the cascade rates goes handinhand with the measurement of the spatial anisotropy of the thirdorder moments F and F{sub C}. The theory developed here can be applied to measure the turbulent cascade rates of energy and crosshelicity 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 = {1070664X},
number = 9,
volume = 14,
place = {United States},
year = {2007},
month = {9}
}