Two-dimensional magnetohydrodynamics and interstellar plasma turbulence

This paper is concerned with a physical understanding of the main features of interstellar plasma turbulence. Our observational knowledge of this turb ulence is provided by radio-wave propagation observations, generically refe rred to as interstellar scintillations. Distinctive features of the observa tions are the nearly omnipresent anisotropy of scattering, revealed by elli ptical rather than circular scattering disks, drastic differences in the ma gnitude of scattering between closely spaced lines of sight through the int erstellar medium, evidence from Faraday rotation observations that the inte rstellar vector magnetic field changes markedly on small spatial scales, an d the existence of a power-law spectrum of density irregularities over a wi de range of spatial scales. This power-law density spectrum strongly sugges ts the existence of similar spatial power spectra for the other magnetohydr odynamic (MHD) variables such as flow velocity and magnetic held. In this p aper, it is pointed out that the aforementioned features arise or may natur ally be explained by an approximate theory of magnetohydrodynamic turbulenc e, two-dimensional magnetohydrodynamics. In this theory, the plasma turbule nce is described by two scalar functions (a velocity stream function and on e 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 presen ted. Although obviously an incomplete description of the interstellar plasm a, these equations provide plausible explanations for the observational fea tures described above. Anisotropy of scattering arises as an obvious conseq uence 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-dimensi onal MHD predict the formation of intense electrical current and vorticity sheets from broad classes of initial conditions. It is highly plausible tha t 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 interste llar magnetic held. Finally, the equations of two-dimensional MHD produce s pectral flattening of initial conditions with steep spatial power spectra. The calculations presented here, as well as elsewhere in the literature, in dicate that the equilibrium magnetic field and velocity spectra may be powe r laws with indices close to those observed for the density fluctuations. I n summary, the equations of two-dimensional magnetohydrodynamics are propos ed as a simplified theoretical tool for use in understanding interstellar p lasma turbulence.