Scale-dependent angle of alignment between velocity and magnetic field fluctuations in solar wind turbulence

Abstract

Under certain conditions, freely decaying magnetohydrodynamic (MHD) turbulence evolves in such a way that velocity and magnetic field fluctuations δv and δB approach a state of alignment in which δv ∝ δB. This process is called dynamic alignment. Boldyrev has suggested that a similar kind of alignment process occurs as energy cascades from large to small scales through the inertial range in strong incompressible MHD turbulence. In this study, plasma and magnetic field data from the Wind spacecraft, data acquired in the ecliptic plane near 1 AU, are employed to investigate the angle θ(τ) between velocity and magnetic field fluctuations in the solar wind as a function of the time scale τ of the fluctuations and to look for the scaling relation 〈θ(τ)〉 ∼ τ¹/⁴ predicted by Boldyrev. We find that the angle 〈θ(τ)〉 appears to scale like a power law at large inertial range scales, but then deviates from power law behavior at medium to small inertial range scales. We also find that small errors in the velocity vector measurements can lead to large errors in the angle measurements at small time scales. As a result, we cannot rule out the possibility that the observed deviations from power law behavior arise from errors in the velocity measurements. When we fit the data from 2 × 10³ s to 2 × 10⁴ s with a power law of the form 〈θ(τ)〉 ∝ τᵖ, our best fit values for p are in the range 0.27–0.36.