Scaling of spectral anisotropy with magnetic field strength in decaying magnetohydrodynamic turbulence

Abstract

Space plasma measurements, laboratory experiments, and simulations have shown that magnetohydrodynamic ͑MHD͒ turbulence exhibits a dynamical tendency towards spectral anisotropy given a sufficiently strong background magnetic field. Here the undriven decaying initial-value problem for homogeneous MHD turbulence is examined with the purpose of characterizing the variation of spectral anisotropy of the turbulent fluctuations with magnetic field strength. Numerical results for both incompressible and compressible MHD are presented. A simple model for the scaling of this spectral anisotropy as a function of the fluctuating magnetic field over total magnetic field is offered. The arguments are based on ideas from reduced MHD ͑RMHD͒ dynamics and resonant driving of certain non-RMHD modes. The results suggest physical bases for explaining variations of the anisotropy with compressibility, Reynolds numbers, and spectral width of the ͑isotropic͒ initial conditions.

A two-component phenomenology for homogeneous magnetohydrodynamic turbulence

“…[12][13][14][15] In terms of these time scales, the condition nl ͑k͒ Ͻ A ͑k͒ serves to define the quasi-2D, or low-frequency fluctuations. 10,[16][17][18][19][20][21] For the H c = 0 case, this is equivalent to k ʈ V A Ͻ ku k . Conversely, the wave-like fluctuations are defined by the opposite inequality: k ʈ V A Ͼ ku k .…”

Reduced magnetohydrodynamics and parallel spectral transfer

“…This justifies at least partially the use of RMHD models by some authors [9][10][11][12] to investigate theoretical issues in general MHD theory. By investigating in some detail the structure of RMHD in the context of full MHD, we will provide here a context for understanding the generality and limitations of such conclusions.…”

“…Moreover, the strength of the interaction depends on the partitioning of energy between the H and N modes. 9,12,25 Under the condition that the quasi-two-dimensional part of the spectrum ͑the H modes͒ is sufficiently strong, it seems likely that the perpendicular spectrum of the N modes will be determined by the N -H interactions, and that this would lead to an expected k Ќ Ϫ5/3 spectrum in the N range of k ʈ . The weak turbulence contribution of k Ќ Ϫ2 would be masked.…”

“…The ratio 19 of these two timescales yields a parameter central to RMHD-and indeed MHD turbulence in general: 3,9,12,13,[20][21][22][23] …”

Collisionless Isotropization of the Solar-Wind Protons by Compressive Fluctuations and Plasma Instabilities

“…A background magnetic field B 0 can lead to an anisotropic cascade (Goldreich & Sridhar 1995), and, in fact, most astrophysical plasmas are permeated by such a magnetic field. Theoretical considerations, numerical simulations, and solar-wind observations indicate that the turbulent cascadeespecially for large-scale noncompressive fluctuations-preferentially transfers energy to large k ⊥ , and to a lesser extent to large k P in a magnetized plasma, where k ⊥ (k P ) is the wavenumber in the direction perpendicular (parallel) to B 0 (Montgomery & Turner 1981;Oughton et al 1994Oughton et al , 1998Cho & Vishniac 2000;Sahraoui et al 2010;Chen et al 2011;Narita et al 2011;He et al 2012;Salem et al 2012;Verscharen et al 2012). We focus our treatment on the outer scales of the turbulence at which the frequencies (linear and nonlinear) are W p , where W º q B m c p p 0 p is the proton gyrofrequency, q p and m p are the charge and the mass of a proton, and c is the speed of light.…”