The radial evolution of the amplitudes of “dissipationless” turbulent solar wind fluctuations

Abstract

We examine the evolution with heliocentric distance of the amplitude of fluctuations in the interplanetary magnetic and velocity fields assuming a model of homogeneous, steady state turbulence. Based on observations and recent results, both the Alfvén ratio and the normalized cross helicity are taken to be constant compared to other variations, and the turbulence is assumed to be nearly incompressive. The fluctuation amplitudes are found by taking the heating of the plasma by the fluctuations to be negligible; quasi-steady state turbulence with damping balanced by large-scale energy input will lead to the same conclusions for inertial range fluctuations. While the assumptions of this model contrast sharply with those for purely Alfvénic fluctuations, we find that the radial dependence of the amplitude of the fluctuations for reasonable parameters is very nearly that found from both WKB analysis and recent turbulence modeling. The robustness of this result suggests why some predictions of WKB theory are apparently correct in solar wind conditions where the theory is not expected to be valid.