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Title: Global invariants in ideal magnetohydrodynamic turbulence

Magnetohydrodynamic (MHD) turbulence is an important though incompletely understood factor affecting the dynamics of many astrophysical, geophysical, and technological plasmas. As an approximation, viscosity and resistivity may be ignored, and ideal MHD turbulence may be investigated by statistical methods. Incompressibility is also assumed and finite Fourier series are used to represent the turbulent velocity and magnetic field. The resulting model dynamical system consists of a set of independent Fourier coefficients that form a canonical ensemble described by a Gaussian probability density function (PDF). This PDF is similar in form to that of Boltzmann, except that its argument may contain not just the energy multiplied by an inverse temperature, but also two other invariant integrals, the cross helicity and magnetic helicity, each multiplied by its own inverse temperature. However, the cross and magnetic helicities, as usually defined, are not invariant in the presence of overall rotation or a mean magnetic field, respectively. Although the generalized form of the magnetic helicity is known, a generalized cross helicity may also be found, by adding terms that are linear in the mean magnetic field and angular rotation vectors, respectively. These general forms are invariant even in the presence of overall rotation and a meanmore » magnetic field. We derive these general forms, explore their properties, examine how they extend the statistical theory of ideal MHD turbulence, and discuss how our results may be affected by dissipation and forcing.« less
Authors:
 [1]
  1. Astromaterials Research Office, NASA Johnson Space Center, Houston, Texas 77058-3696 (United States)
Publication Date:
OSTI Identifier:
22218520
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 20; Journal Issue: 10; Other Information: (c) 2013 U.S. Government; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; GAUSSIAN PROCESSES; HELICITY; INTEGRALS; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; PLASMA; PROBABILITY DENSITY FUNCTIONS; STATISTICAL MODELS; TURBULENCE; VECTORS; VISCOSITY