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Title: On the cross-helicity dependence of the energy spectrum in magnetohydrodynamic turbulence

Abstract

Phenomenological theories of strong incompressible magnetohydrodynamic (MHD) turbulence derived by Goldreich and Sridhar (GS) in 1995 and by Boldyrev in 2006 are only applicable to turbulence with vanishing cross-helicity. In this study, these two theories are generalized to treat turbulence with nonvanishing cross-helicity in such a way that the relation (w{sup +}/w{sup -}){sup 2}=({epsilon}{sup +}/{epsilon}{sup -}){sup 2} observed in numerical simulations is satisfied. The average energy (second order structure function) in the generalized GS theory is E(r{sub perpendicular})={phi}{sub 1}({sigma}{sub c})({epsilon}r{sub perpendicular}){sup 2/3} and that in the generalized Boldyrev theory is E(r{sub perpendicular})={phi}{sub 2}({sigma}{sub c})(v{sub A{epsilon}}r{sub perpendicular}){sup 1/2}, where the function {phi}({sigma}{sub c}) describes the dependence on the normalized cross-helicity {sigma}{sub c}. The form of the function {phi}({sigma}{sub c}) is derived through a renormalization of the variable {sigma}{sub c} that yields a one parameter family of solutions. The theory derived by Lithwick, Goldreich, and Sridhar (LGS) in 2007 is a special case of the generalized GS theory derived here; however, other generalizations of the GS theory are obtained that have a different cross-helicity dependence than the LGS theory. This new class of solutions and similar generalizations of Boldyrev's theory are investigated to see how the energy cascade rate {epsilon} changes asmore » a function of {sigma}{sub c} when the energy at a given scale is held fixed. The generalization of Boldyrev's theory derived here is applicable to homogeneous MHD turbulence in the solar wind, for example, and can be used to obtain the turbulent dissipation rate {epsilon} from measurements of the energy spectrum and the normalized cross-helicity.« less

Authors:
 [1]
  1. Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
Publication Date:
OSTI Identifier:
21532189
Resource Type:
Journal Article
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 18; Journal Issue: 1; Other Information: DOI: 10.1063/1.3533671; (c) 2011 American Institute of Physics; Journal ID: ISSN 1070-664X
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ENERGY SPECTRA; HELICITY; MAGNETOHYDRODYNAMICS; NUMERICAL ANALYSIS; PLASMA SIMULATION; TURBULENCE; FLUID MECHANICS; HYDRODYNAMICS; MATHEMATICS; MECHANICS; PARTICLE PROPERTIES; SIMULATION; SPECTRA

Citation Formats

Podesta, J J. On the cross-helicity dependence of the energy spectrum in magnetohydrodynamic turbulence. United States: N. p., 2011. Web. doi:10.1063/1.3533671.
Podesta, J J. On the cross-helicity dependence of the energy spectrum in magnetohydrodynamic turbulence. United States. https://doi.org/10.1063/1.3533671
Podesta, J J. Sat . "On the cross-helicity dependence of the energy spectrum in magnetohydrodynamic turbulence". United States. https://doi.org/10.1063/1.3533671.
@article{osti_21532189,
title = {On the cross-helicity dependence of the energy spectrum in magnetohydrodynamic turbulence},
author = {Podesta, J J},
abstractNote = {Phenomenological theories of strong incompressible magnetohydrodynamic (MHD) turbulence derived by Goldreich and Sridhar (GS) in 1995 and by Boldyrev in 2006 are only applicable to turbulence with vanishing cross-helicity. In this study, these two theories are generalized to treat turbulence with nonvanishing cross-helicity in such a way that the relation (w{sup +}/w{sup -}){sup 2}=({epsilon}{sup +}/{epsilon}{sup -}){sup 2} observed in numerical simulations is satisfied. The average energy (second order structure function) in the generalized GS theory is E(r{sub perpendicular})={phi}{sub 1}({sigma}{sub c})({epsilon}r{sub perpendicular}){sup 2/3} and that in the generalized Boldyrev theory is E(r{sub perpendicular})={phi}{sub 2}({sigma}{sub c})(v{sub A{epsilon}}r{sub perpendicular}){sup 1/2}, where the function {phi}({sigma}{sub c}) describes the dependence on the normalized cross-helicity {sigma}{sub c}. The form of the function {phi}({sigma}{sub c}) is derived through a renormalization of the variable {sigma}{sub c} that yields a one parameter family of solutions. The theory derived by Lithwick, Goldreich, and Sridhar (LGS) in 2007 is a special case of the generalized GS theory derived here; however, other generalizations of the GS theory are obtained that have a different cross-helicity dependence than the LGS theory. This new class of solutions and similar generalizations of Boldyrev's theory are investigated to see how the energy cascade rate {epsilon} changes as a function of {sigma}{sub c} when the energy at a given scale is held fixed. The generalization of Boldyrev's theory derived here is applicable to homogeneous MHD turbulence in the solar wind, for example, and can be used to obtain the turbulent dissipation rate {epsilon} from measurements of the energy spectrum and the normalized cross-helicity.},
doi = {10.1063/1.3533671},
url = {https://www.osti.gov/biblio/21532189}, journal = {Physics of Plasmas},
issn = {1070-664X},
number = 1,
volume = 18,
place = {United States},
year = {2011},
month = {1}
}