Scale dependent alignment between velocity and magnetic field fluctuations in the solar wind and comparisons to Boldyrevs phenomenological theory

(Abridged abstract) A theory of incompressible MHD turbulence recently developed by Boldyrev predicts the existence of a scale dependent angle of alignment between velocity and magnetic field fluctuations that is proportional to the lengthscale of the fluctuations to the power 1/4. In this study, plasma and magnetic field data from the Wind spacecraft are used to investigate the angle between velocity and magnetic field fluctuations in the solar wind as a function of the timescale of the fluctuations and to look for the power law scaling predicted by Boldyrev.

💡 Research Summary

Background and Objective
Magnetohydrodynamic (MHD) turbulence governs the cascade of energy from large to small scales in space plasmas such as the solar wind. Classical Kolmogorov‑Kraichnan phenomenology predicts a –5/3 power‑law for the energy spectrum, assuming isotropic, incompressible fluctuations. In 2006, Boldyrev introduced a new picture for incompressible MHD turbulence: velocity fluctuations δv and magnetic‑field fluctuations δb tend to align with each other as the cascade proceeds. This “scale‑dependent alignment” weakens the nonlinear interaction, leading to a steeper energy spectrum (∝ k⁻³ᐟ²). The central quantitative prediction is that the alignment angle θ(ℓ) obeys a power law θ ∝ ℓ¹⁄⁴, where ℓ is the spatial scale of the fluctuations. The present paper tests this prediction using in‑situ measurements from the Wind spacecraft, focusing on the relationship between the alignment angle and the fluctuation timescale τ (via the Taylor hypothesis, τ ↔ ℓ/V_sw).

Data and Methodology

• Instrumentation: 3‑second plasma moments (velocity, density, temperature) from the Solar Wind Experiment (SWE) and high‑resolution magnetic field data (11 Hz) from the Magnetic Field Investigation (MFI) on board Wind.
• Interval Selection: Two long intervals (≈ 30 days each) in 2004‑2005 when the solar wind speed exceeded 400 km s⁻¹, density fluctuations were modest, and the flow was relatively steady, thereby minimizing compressive effects.
• Fluctuation Definition: For a given time lag τ, the increments are defined as δv(t,τ)=v(t+τ)−v(t) and δb(t,τ)=b(t+τ)−b(t). The mean solar‑wind flow is subtracted to isolate turbulent fluctuations.
• Alignment Angle: The angle between the two vectors is computed as
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