Compressible magnetohydrodynamic turbulence: mode coupling, scaling relations, anisotropy, viscosity-damped regime and astrophysical implications

Abstract

We present numerical simulations and explore scalings and anisotropy of compressible magnetohydrodynamic (MHD) turbulence. Our study covers both gas‐pressure‐dominated (high β) and magnetic‐pressure‐dominated (low β) plasmas at different Mach numbers. In addition, we present results for super‐Alfvénic turbulence and discuss in what way it is similar to sub‐Alfvénic turbulence. We describe a technique of separating different magnetohydrodynamic modes (slow, fast and Alfvén) and apply it to our simulations. We show that, for both high‐ and low‐β cases, Alfvén and slow modes reveal a Kolmogorov k−5/3 spectrum and scale‐dependent Goldreich–Sridhar anisotropy, while fast modes exhibit a k−3/2 spectrum and isotropy. We discuss the statistics of density fluctuations arising from MHD turbulence in different regimes. Our findings entail numerous astrophysical implications ranging from cosmic ray propagation to gamma ray bursts and star formation. In particular, we show that the rapid decay of turbulence reported by earlier researchers is not related to compressibility and mode coupling in MHD turbulence. In addition, we show that magnetic field enhancements and density enhancements are marginally correlated. Addressing the density structure of partially ionized interstellar gas on astronomical‐unit scales, we show that the viscosity‐damped regime of MHD turbulence that we reported earlier for incompressible flows persists for compressible turbulence and therefore may provide an explanation for these mysterious structures.

The dynamics of charged dust in magnetized molecular clouds

“…This scaling assumes that the influence of the magnetic field on the flow should be relatively unimportant until at, or below, the subsonic scales (λ ≤ Rsonic). 8 Otherwise -i.e., in the case of strong mean fields -the turbulence would be Alfvénic in character and anisotropic at large scales (Lithwick & Goldreich 2001;Cho & Lazarian 2003). Our analysis is thus restricted to turbulence where MA > 1 and the field is tangled on supersonic scales (this is the opposite regime to Yan et al 2004).…”

Cosmic Ray propagation in magneto-hydrodynamic turbulence

“…The local magnetic field is not unique, its direction in fact depends on the scale 1/k under consideration as explained in [10]. In the compressible limit, using direct numerical MHD simulations (DNS), [11] confirmed that Alfvénic turbulence follows a GS spectrum and show that fast-magnetosonic turbulence follows an isotropic Kraichnan spectrum. In this work we perform DNS MHD simulations and couple them to the Lorentz force by upgrading the RAMSES MHD code [12,13] with a turbulence forcing module (see §2.1) and a kinetic module (see §2.2).…”

“…Here, we found typical ratios λ (χ = 1)/λ (χ = 0) < 100 which are not as small as predicted by these analytical models. This is likely because both compressible and incompressible modes are produced in the two forcing geometries [11]. Any more quantitative discussion would require to isolate the effects of each mode that composes the turbulent spectrum in the different forcing limits.…”

The Phase Coherence of Interstellar Density Fluctuations

“…We use the isothermal MHD code detailed in Cho & Lazarian (2003) . Nonlinear wave-wave interactions take place more strongly in compressible and magnetized flows, and in that case we can have ¹ k k 1 2 .…”

“…Studies of power spectra have played a crucial role for our modern understanding of MHD turbulence (see Goldreich & Sridhar 1995;Lazarian & Vishniac 1999;Cho, Lazarian & Vishniac 2002;Lithwick, Goldreich & Sridhar 2007;Cho & Lazarian 2003;Kowal, Lazarian & Beresnyak 2010). 3 However, such studies have their limitations.…”