Inhomogeneous Nearly Incompressible Description of Magnetohydrodynamic Turbulence

Details Inhomogeneous Nearly Incompressible Description of Magnetohydrodynamic Turbulence Inhomogeneous Nearly Incompressible Description of Magnetohydrodynamic Turbulence

Jul 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010apj...718..148h&link_type=abstract

The Astrophysical Journal, Volume 718, Issue 1, pp. 148-167 (2010).

Astronomy and Astrophysics

Astronomy

5

Ism: General, Magnetohydrodynamics: Mhd, Solar Wind, Turbulence

Scientific paper

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 & 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 β Lt 1, β ~ 1, andβ Gt 1. For regimes appropriate to the solar wind (β Lt 1, β ~ 1), compared to the homogeneous description of Zank & 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 δρ = c 2 s δp 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^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 -5/3 in the inertial range, followed by a Bessel function solution K ν(k), where for stationary turbulence ν = 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.

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