Anisotropic fluid turbulence in the interstellar medium and solar wind

Abstract

The interstellar medium and solar wind is permeated by a magnetic field that renders magnetohydrodynamic turbulence anisotropic. In the classic work of Iroshnikov [Astron. Zh. 40, 742 (1963)] and Kraichnan [Phys. Fluids 8, 1385 (1965)], it is assumed that the turbulence is isotropic, and an inertial range energy spectrum that scales as k−3/2 is deduced based on the nonlinear interaction of Alfvén wave packets. Much insight can be gained by analysis and high-resolution numerical simulations of such interactions. In the weak-turbulence limit in which three-wave interactions dominate, analytical and high-resolution numerical results based on random scattering of shear-Alfvén waves propagating parallel to a large-scale magnetic field demonstrate an anisotropic energy spectrum that scales as k⊥−2. Even in the absence of a background magnetic field, when the energy spectrum is globally isotropic, anisotropy is found to develop with respect to the local magnetic field. The two-dimensional case is studied by means of simulations and phenomenological arguments. Despite the presence of local anisotropy, we obtain the Iroshnikov–Kraichnan spectrum, rather than the Kolmogorov spectrum. The same techniques are used to study turbulence in electron magnetohydrodynamics where whistler waves mediate the energy cascade, and comparisons are made with turbulence in magnetohydrodynamics.

Fast Magnetic Reconnection and Spontaneous Stochasticity

“…Absolute equilibrium spectra in 3D suggest that energy and cross-helicity cascade to high wavenumbers and magnetic helicity to low wavenumbers (Frisch et al 1975), while the same argument in 2D leads to an identical conclusion, with an inverse cascade of magnetic potential replacing that of magnetic helicity (Fyfe & Montgomery 1976). Numerical simulations have corroborated these predictions, with the most recent 2D MHD simulations giving energy spectra close to k −5/3 or k −3/2 in the forward cascade range (Gomez et al 1999;Biskamp & Schwarz 2001;Ng et al 2003). On the other hand, from the point of view of GS95 theory, 2D MHD turbulence appears as a very degenerate case.…”

Spectrum of Kinetic-Alfvén Turbulence

“…Previous simulations of electron MHD were conducted mostly for two-dimensional cases and/or for relatively weak guide fields and/or decaying cases, and the spectrum close to k −7/3 ⊥ was observed (e.g., Biskamp et al 1999;Cho & Lazarian 2004, 2009Ng et al 2003;Dastgeer & Zank 2003). Due to the limited extent of the inertial interval, however, simulations with weak guide field may not reach the universal scaling regime that we address in this work.…”

“…The scaling of strong kinetic-Alfvén turbulence was addressed in a number of works (e.g., Howes et al 2008;Schekochihin et al 2009); see also Biskamp et al (1999), Ng et al (2003), and Cho & Lazarian (2004, 2009. It was argued that in strong turbulence, the critical balance condition, which ensures that both linear and nonlinear terms in (3) are of the same order, should be satisfied at all scales.…”

Parallel electric field generation by Alfvén wave turbulence

“…Its linear modes are the whistler waves with ω ± = ±k d i k ⊥ . Some key properties of the EMHD turbulence have been investigated both numerically and theoretically, suggesting that the Kolmogorov type arguments work fine (Biskamp et al 1999;Ng et al 2003;Cho & Lazarian 2004. A calculation along the lines of the one below for KAWs, shows that the energy spectrum for whistler wave turbulence is…”