Theory and Transport of Nearly Incompressible Magnetohydrodynamics Turbulence. III. Evolution of Power Anistropy in Magnetic Field Fluctuations throughout the Heliosphere

Abstract

Abstract A theoretical model that describes the evolution of the power anisotropy in the energy-containing and inertial ranges throughout the heliosphere is developed for three possibilities: (i) no in situ sources of turbulence; (ii) stream-shear sources of 2D and slab turbulence; and (iii) a fully driven turbulence model that includes both stream-shear driving and a pickup ion source of slab turbulence. At the inner boundary (1 au), we assume that the ratios of the 2D to slab fluctuating magnetic energy variances in the energy-containing range are 80:20, 70:30, 60:40, and 55:45. For case (i), in the energy-containing range increases monotonically throughout the heliosphere, whereas the inertial range ratio increases until ∼20 au and then decreases. For case (ii), the energy-containing range ratio increases initially and then remains approximately constant and ordered beyond ∼2 au, according to the inner boundary assumptions. The inertial range ratio for the 80:20 case increases with heliocentric distance, whereas for the 70:30, 60:40, and 55:45 cases, the rations increase between ∼2 to ∼10–20 au, and then generally decrease at larger heliocentric distances. For case (iii), the energy-containing and inertial range ratios increase initially, remain approximately constant and increase slightly, respectively, and then decrease more rapidly between ∼8 and 30 au, and more gradually thereafter, approaching a ratio of ∼1 at 75 au. We present preliminary results that show the power anisotropy in magnetic field fluctuations observed by Ulysses spacecraft increasing with heliocentric distance from ∼1.5 to 4.5 au.