Two‐dimensional Magnetohydrodynamics and Interstellar Plasma Turbulence

Abstract

This paper is concerned with a physical understanding of the main features of interstellar plasma turbulence. Our observational knowledge of this turbulence is provided by radio-wave propagation observations, generically referred to as interstellar scintillations. Distinctive features of the observations are the nearly omnipresent anisotropy of scattering, revealed by elliptical rather than circular scattering disks, drastic differences in the magnitude of scattering between closely spaced lines of sight through the interstellar medium, evidence from Faraday rotation observations that the interstellar vector magnetic field changes markedly on small spatial scales, and the existence of a power-law spectrum of density irregularities over a wide range of spatial scales. This power-law density spectrum strongly suggests the existence of similar spatial power spectra for the other magnetohydrodynamic (MHD) variables such as flow velocity and magnetic field. In this paper, it is pointed out that the aforementioned features arise or may naturally be explained by an approximate theory of magnetohydrodynamic turbulence, two-dimensional magnetohydrodynamics. In this theory, the plasma turbulence is described by two scalar functions (a velocity stream function and one component of the magnetic vector potential) that are coupled by nonlinear partial differential equations. These equations are physically transparent, possess some relevant analytic results, and are easily solved numerically. Arguments for the relevance of this reduced plasma description are presented. Although obviously an incomplete description of the interstellar plasma, these equations provide plausible explanations for the observational features described above. Anisotropy of scattering arises as an obvious consequence of the conditions for validity of the two-dimensional MHD description, i.e., that spatial gradients along a large-scale magnetic field are much smaller than those perpendicular to the field. The equations of two-dimensional MHD predict the formation of intense electrical current and vorticity sheets from broad classes of initial conditions. It is highly plausible that these sheets are the loci of elevated turbulence, which could explain the variations of radio-wave scattering and provide a physical explanation for intermittency in interstellar turbulence. The strong current sheets would also produce localized reversals in the turbulent component of the interstellar magnetic field. Finally, the equations of two-dimensional MHD produce spectral flattening of initial conditions with steep spatial power spectra. The calculations presented here, as well as elsewhere in the literature, indicate that the equilibrium magnetic field and velocity spectra may be power laws with indices close to those observed for the density fluctuations. In summary, the equations of two-dimensional magnetohydrodynamics are proposed as a simplified theoretical tool for use in understanding interstellar plasma turbulence.