INHOMOGENEOUS NEARLY INCOMPRESSIBLE DESCRIPTION OF MAGNETOHYDRODYNAMIC TURBULENCE

Journal Article · Tue Jul 20 00:00:00 EDT 2010 · Astrophysical Journal

DOI:https://doi.org/10.1088/0004-637X/718/1/148· OSTI ID:21455161

Hunana, P; Zank, G P ^[1]

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1. Center for Space Plasma and Aeronomic Research (CSPAR), University of Alabama, Huntsville, AL 35805 (United States)

The nearly incompressible theory of magnetohydrodynamics (MHD) is formulated in the presence of a static large-scale inhomogeneous background. The theory is an inhomogeneous generalization of the homogeneous nearly incompressible MHD description of Zank and Matthaeus and a polytropic equation of state is assumed. The theory is primarily developed to describe solar wind turbulence where the assumption of a composition of two-dimensional (2D) and slab turbulence with the dominance of the 2D component has been used for some time. It was however unclear, if in the presence of a large-scale inhomogeneous background, the dominant component will also be mainly 2D and we consider three distinct MHD regimes for the plasma beta {beta} << 1, {beta} {approx} 1, and{beta} >> 1. For regimes appropriate to the solar wind ({beta} << 1, {beta} {approx} 1), compared to the homogeneous description of Zank and Matthaeus, the reduction of dimensionality for the leading-order description from three dimensional (3D) to 2D is only weak, with the parallel component of the velocity field proportional to the large-scale gradients in density and the magnetic field. Close to the Sun, however, where the large-scale magnetic field can be considered as purely radial, the collapse of dimensionality to 2D is complete. Leading-order density fluctuations are shown to be of the order of the sonic Mach number O(M) and evolve as a passive scalar mixed by the turbulent velocity field. It is emphasized that the usual 'pseudosound' relation used to relate density and pressure fluctuations through the sound speed as {delta}{rho} = c {sup 2} {sub s{delta}}p is not valid for the leading-order O(M) density fluctuations, and therefore in observational studies, the density fluctuations should not be analyzed through the pressure fluctuations. The pseudosound relation is valid only for higher order O(M{sup 2}) density fluctuations, and then only for short-length scales and fast timescales. The spectrum of the leading-order density fluctuations should be modeled as k {sup -5/3} in the inertial range, followed by a Bessel function solution K {sub {nu}}(k), where for stationary turbulence {nu} = 1, in the viscous-convective and diffusion range. Other implications for solar wind turbulence with an emphasis on the evolution of density fluctuations are also discussed.

• OSTI ID: 21455161
• Journal Information: Astrophysical Journal, Journal Name: Astrophysical Journal Journal Issue: 1 Vol. 718; ISSN ASJOAB; ISSN 0004-637X
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
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FLUID MECHANICS
FUNCTIONS
HYDRODYNAMICS
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STELLAR ACTIVITY
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THREE-DIMENSIONAL CALCULATIONS
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