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Special Section Articles

Temperature and Entropy in Ideal Magnetohydrodynamic Turbulence

[+] Author and Article Information
John V. Shebalin

Astrophysicist
Astromaterials Research Office,
NASA Johnson Space Center,
Houston, TX 77058
e-mail: john.v.shebalin@nasa.gov

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 27, 2012; final manuscript received July 24, 2013; published online April 28, 2014. Assoc. Editor: Ye Zhou.This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

J. Fluids Eng 136(6), 060901 (Apr 28, 2014) (5 pages) Paper No: FE-12-1479; doi: 10.1115/1.4025674 History: Received September 27, 2012; Revised July 24, 2013

Fourier analysis of incompressible, homogeneous magnetohydrodynamic (MHD) turbulence produces a model dynamical system on which to perform numerical experiments. Statistical methods are used to understand the results of ideal (i.e., nondissipative) MHD turbulence simulations, with the goal of finding those aspects that survive the introduction of dissipation. This statistical mechanics is based on a Boltzmannlike probability density function containing three “inverse temperatures,” one associated with each of the three ideal invariants: energy, cross helicity, and magnetic helicity. However, these inverse temperatures are seen to be functions of a single parameter that may defined as the “temperature” in a statistical and thermodynamic sense: the average magnetic energy per Fourier mode. Here, we discuss temperature and entropy in ideal MHD turbulence and their use in understanding numerical experiments and physical observations.

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References

Figures

Grahic Jump Location
Fig. 1

Phase plots of (a) u˜1,2(1,0,0) and (b) b˜1,2(1,0,0) for 643 MHD run 1a from Ref. [19] (• represents an initial point and + represents the origin; trajectories run from t=0 to 200)

Grahic Jump Location
Fig. 2

Phase path for (a) v˜1,2(1,0,0) and (b) v˜3,4(1,0,0) for 643 ideal MHD run 1a from Ref. [19]. These curves come from applying Eqs. (22)–(25) to data shown in Fig. 1.

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