Scaling of Anisotropy in Hydromagnetic Turbulence

Evidence accumulated over the past several decades indicates that a large-scale applied (dc) magnetic field imposes a preferred direction on turbulence, and thus plays an important role in plasma diffusion [1], energetic particle scattering [2], and plasma heating [3–5]. Each of these in turn may significantly influence large-scale flows and structure [6–8]. The interplay between turbulence and large-scale magnetic field suggests a crucial role of rotational symmetry or “geometry” of the fluctuations in many astrophysical plasma settings. There has been considerable recent interest in detection and understanding of anisotropy of fluctuations in solar, interplanetary, and galactic plasmas, and thus it would appear to be of importance to understand mechanisms that can produce and regulate anisotropy in fluid-scale plasma turbulence. In this Letter we show, using numerical solutions of magnetohydrodynamics (MHD), that anisotropy produced by spectral transfer scales in a systematic way with applied field strength. In particular, an angular measure of the anisotropy of the spectrum varies linearly with field strength over a useful range of applied field magnitudes. A simple argument, based upon the physics of reduced MHD [9–11], explains this scaling property as well as its saturation. Within the MHD framework, anisotropy associated with a (uniform) dc magnetic field sB0d may take a number of forms [12–14]. Here we are concerned specifically with dynamical development of spectral anisotropy due to asymmetry of nonlinear spectral transfer relative to the mean field direction [14,15]. This anisotropy is characterized by gradients across the mean magnetic field that are relatively larger than gradients along the field. Such features can be readily observed in fluctuations of plasma fluid velocity, magnetic field, and density, and have been observed in the solar wind [16–18], the solar corona [19], the interstellar medium [20,21], and in various laboratory plasma devices [22,23]. The limiting case, when all variations are perpendicular to the mean field, and the parallel coordinate is ignorable, is known as two-dimensional (2D) turbulence. The opposite limit, with perpendicular coordinates ignorable, often called “slab” symmetry, is traditionally employed in linear wave theory [2,16]. Turbulence