Spatial scales and temporal scales in the theory of magnetohydrodynamic turbulence
Abstract
In the study of incompressible magnetohydrodynamic (MHD) turbulence the correlation lengths along the directions parallel and perpendicular to the local mean magnetic field may be defined by isoenergy surfaces derived from second order structure functions. The correlation time of the turbulence may be defined in a similar manner by means of a temporal second order structure function. Moreover, there is a natural correspondence between the lengthscales of fluctuations with a given energy and the timescale of fluctuations of the same energy so that each isoenergy surface is associated with a unique pair of parallel and perpendicular correlation lengths and a unique correlation time. In the case when the magnetic Prandtl number is unity, Pr{sub m{identical_to}{nu}}/{eta}=1, it is shown that the correlation time {tau} associated with an isoenergy contour of energy E is equal to the energy cascade time of the turbulence in the sense that E/{tau}{approx}{epsilon}, where {epsilon} is the energy cascade rate. For balanced MHD turbulence, turbulence with vanishing crosshelicity, both the Goldreich and Sridhar theory and Boldyrev's theory are shown to have this same property. An attempt is made to generalize these ideas to imbalanced MHD turbulence, turbulence with nonvanishing crosshelicity. It is shown that if the normalizedmore »
 Authors:

 Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
 Publication Date:
 OSTI Identifier:
 21532188
 Resource Type:
 Journal Article
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 18; Journal Issue: 1; Other Information: DOI: 10.1063/1.3534824; (c) 2011 American Institute of Physics; Journal ID: ISSN 1070664X
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FLUCTUATIONS; MAGNETOHYDRODYNAMICS; PLASMA; PLASMA SIMULATION; TURBULENCE; FLUID MECHANICS; HYDRODYNAMICS; MECHANICS; SIMULATION; VARIATIONS
Citation Formats
Podesta, J J. Spatial scales and temporal scales in the theory of magnetohydrodynamic turbulence. United States: N. p., 2011.
Web. doi:10.1063/1.3534824.
Podesta, J J. Spatial scales and temporal scales in the theory of magnetohydrodynamic turbulence. United States. https://doi.org/10.1063/1.3534824
Podesta, J J. Sat .
"Spatial scales and temporal scales in the theory of magnetohydrodynamic turbulence". United States. https://doi.org/10.1063/1.3534824.
@article{osti_21532188,
title = {Spatial scales and temporal scales in the theory of magnetohydrodynamic turbulence},
author = {Podesta, J J},
abstractNote = {In the study of incompressible magnetohydrodynamic (MHD) turbulence the correlation lengths along the directions parallel and perpendicular to the local mean magnetic field may be defined by isoenergy surfaces derived from second order structure functions. The correlation time of the turbulence may be defined in a similar manner by means of a temporal second order structure function. Moreover, there is a natural correspondence between the lengthscales of fluctuations with a given energy and the timescale of fluctuations of the same energy so that each isoenergy surface is associated with a unique pair of parallel and perpendicular correlation lengths and a unique correlation time. In the case when the magnetic Prandtl number is unity, Pr{sub m{identical_to}{nu}}/{eta}=1, it is shown that the correlation time {tau} associated with an isoenergy contour of energy E is equal to the energy cascade time of the turbulence in the sense that E/{tau}{approx}{epsilon}, where {epsilon} is the energy cascade rate. For balanced MHD turbulence, turbulence with vanishing crosshelicity, both the Goldreich and Sridhar theory and Boldyrev's theory are shown to have this same property. An attempt is made to generalize these ideas to imbalanced MHD turbulence, turbulence with nonvanishing crosshelicity. It is shown that if the normalized crosshelicity {sigma}{sub c} is a constant in the inertial range, independent of wavenumber, then one obtains a model in which the energy cascade times of the two Elsasser fields are equal throughout the inertial range, that is, {tau}{sup +}/{tau}{sup }=1. This result appears to be contradicted by numerical simulations and, therefore, the generalization to imbalanced turbulence discussed here requires further development; this is an important unsolved problem.},
doi = {10.1063/1.3534824},
url = {https://www.osti.gov/biblio/21532188},
journal = {Physics of Plasmas},
issn = {1070664X},
number = 1,
volume = 18,
place = {United States},
year = {2011},
month = {1}
}