Global invariants in ideal magnetohydrodynamic turbulence

2013 ◽  
Vol 20 (10) ◽  
pp. 102305 ◽  
Author(s):  
John V. Shebalin
Keyword(s):  
Magnetohydrodynamic Turbulence ◽  
Global Invariants ◽  
Ideal Magnetohydrodynamic

Temperature and Entropy in Ideal Magnetohydrodynamic Turbulence

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
John V. Shebalin
Keyword(s):  
Dynamical System ◽  
Probability Density Function ◽  
Fourier Analysis ◽  
Numerical Experiments ◽  
Magnetic Energy ◽  
Fourier Mode ◽  
Mhd Turbulence ◽  
Magnetohydrodynamic Turbulence ◽  
Ideal Mhd ◽  
Ideal Magnetohydrodynamic

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.

Magnetohydrodynamic Turbulence of Coronal Active Regions and the Distribution of Nanoflares

1998 ◽  
Vol 505 (2) ◽  
pp. 974-983 ◽  
Author(s):  
Pablo Dmitruk ◽  
Daniel O. Gomez ◽  
Edward E. DeLuca
Keyword(s):  
Active Regions ◽  
Magnetohydrodynamic Turbulence

A compact exact law for compressible isothermal Hall magnetohydrodynamic turbulence

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Renaud Ferrand ◽  
Sébastien Galtier ◽  
Fouad Sahraoui
Keyword(s):  
Source Term ◽  
Reynolds Numbers ◽  
Space Plasmas ◽  
Order Structure ◽  
Magnetohydrodynamic Turbulence ◽  
Statistical Homogeneity ◽  
Background Magnetic Field ◽  
Taylor Hypothesis ◽  
Spacecraft Data

Using mixed second-order structure functions, a compact exact law is derived for isothermal compressible Hall magnetohydrodynamic turbulence with the assumptions of statistical homogeneity, time stationarity and infinite kinetic/magnetic Reynolds numbers. The resulting law is written as the sum of a Yaglom-like flux term, with an overall expression strongly reminiscent of the incompressible law, and a pure compressible source. Being mainly a function of the increments, the compact law is Galilean invariant but is dependent on the background magnetic field if one is present. Only the magnetohydrodynamic source term requires multi-spacecraft data to be estimated whereas the other components, which include those introduced by the Hall term, can be fully computed with single-spacecraft data using the Taylor hypothesis. These properties make this compact law more appropriate for analysing both numerical simulations and in situ data gathered in space plasmas, in particular when only single-spacecraft data are available.

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