[Paper Review] Isotropization and Evolution of Energy-Containing Eddies in Solar Wind Turbulence: Parker Solar Probe, Helios 1, ACE, WIND, and Voyager 1

M. E. Cuesta, Rohit Chhiber+7 more|arXiv (Cornell University)|May 1, 2022

Solar and Space Plasma Dynamics52 references39 citations

TL;DR

This study analyzes radial evolution of energy-containing eddy correlation lengths in solar wind turbulence using magnetic field data from Parker Solar Probe, Helios 1, ACE, WIND, and Voyager 1. It finds that perpendicular (λ⊥C) and parallel (λ∥C) correlation lengths isotropize near 1 au, with λ∥C/λ⊥C ≈ 0.75 at 0.10 au and ≈1.29 at 1 au, indicating a reversal of anisotropy with heliocentric distance, while emphasizing the importance of accounting for changing sampling directions in PSP data for accurate turbulence interpretation.

ABSTRACT

We examine the radial evolution of correlation lengths perpendicular (\(\lambda_C^{\perp}\)) and parallel (\(\lambda_C^{\parallel}\)) to the magnetic-field direction, computed from solar wind magnetic-field data measured by Parker Solar Probe (PSP) during its first eight orbits, Helios 1, Advanced Composition Explorer (ACE), WIND, and Voyager 1 spacecraft. Correlation lengths are grouped by an interval's alignment angle; the angle between the magnetic-field and solar wind velocity vectors (\(\Theta_{ m BV}\)). Parallel and perpendicular angular channels correspond to angles \(0^{\circ}~<~\Theta_{ m BV}~<~40^{\circ}\) and \(50^{\circ}~<~\Theta_{ m BV}~<~90^{\circ}\), respectively. We observe an anisotropy in the inner heliosphere within 0.40~au, with \(\lambda_C^{\parallel} / \lambda_C^{\perp} \approx 0.75\) at 0.10~au. This anisotropy reduces with increasing heliocentric distance and the correlation lengths roughly isotropize within 1~au. Results from ACE and WIND support a reversal of the anisotropy, such that \(\lambda_C^{\parallel} /\lambda_C^{\perp} \approx 1.29\) at 1~au. The ratio does not appear to change significantly beyond 1~au, although the small number of parallel intervals in the Voyager dataset precludes unambiguous conclusions from being drawn. This study provides insights regarding the radial evolution of the large, most energetic interacting turbulent fluctuations in the heliosphere. We also emphasize the importance of tracking the changes in sampling direction in PSP measurements as the spacecraft approaches the Sun, when using these data to study the radial evolution of turbulence. This can prove to be vital in understanding the more complex dynamics of the solar wind in the inner heliosphere and can assist in improving related simulations.

Motivation & Objective

• Examine the radial evolution of correlation lengths perpendicular (λ⊥C) and parallel (λ∥C) to the magnetic field in solar wind turbulence.
• Assess how anisotropy in energy-containing eddies changes with heliocentric distance using multi-spacecraft data.
• Address the challenge of sampling direction bias in Parker Solar Probe measurements due to radial flow and magnetic field alignment near perihelion.
• Provide a comprehensive view of turbulence evolution from 0.1 au to 10 au using data from PSP, Helios 1, ACE, WIND, and Voyager 1.
• Highlight the importance of accounting for changing spacecraft frame sampling directions when interpreting PSP data for turbulence studies.

Proposed method

• Compute two-time autocorrelation functions RC(τ) of magnetic field fluctuations b(t) = B(t) − ⟨B⟩ over time intervals.
• Identify the e-folding correlation time τe from RC(τe) = 1/e, representing the characteristic timescale of energy-containing eddies.
• Apply the Taylor frozen-in hypothesis (ℓ = VSWτ) to convert τe into spatial correlation scales λC = VSWτe.
• Group intervals by alignment angle ΘBV between solar wind velocity and magnetic field vectors: 0° < ΘBV < 40° (parallel) and 50° < ΘBV < 90° (perpendicular).
• Use 1-hour intervals for PSP at R < 0.30 au and 3-hour intervals for R > 0.30 au to maintain adequate sampling of decreasing correlation scales.
• Validate the Taylor hypothesis by checking VA/VSW ratios; only ~1% of PSP intervals at R < 0.20 au show poor validity (VA/VSW > 0.66).

Experimental results

Research questions

• RQ1 How does the ratio λ∥C/λ⊥C evolve with heliocentric distance in the inner heliosphere?
• RQ2 Does the anisotropy of energy-containing eddies in solar wind turbulence isotropize near 1 au, and if so, what is the magnitude of the ratio?
• RQ3 How does the sampling direction bias in Parker Solar Probe data—driven by radial flow and magnetic field alignment—affect the measurement of perpendicular correlation lengths?
• RQ4 Is there a reversal in the anisotropy trend from λ∥C < λ⊥C in the inner heliosphere to λ∥C > λ⊥C at 1 au, as suggested by ACE and WIND data?
• RQ5 What is the statistical reliability of correlation length measurements beyond 1 au, particularly from Voyager 1, given limited parallel alignment intervals?

Key findings

• At 0.10 au, the ratio of parallel to perpendicular correlation lengths is λ∥C/λ⊥C ≈ 0.75, indicating a strong anisotropy with shorter scales along the magnetic field.
• Within 1 au, the correlation lengths isotropize, with λ∥C/λ⊥C approaching unity, suggesting a reduction in directional preference of turbulent eddies.
• ACE and WIND data show a reversal of anisotropy at 1 au, with λ∥C/λ⊥C ≈ 1.29, indicating longer parallel correlation scales than perpendicular ones.
• Beyond 1 au, the ratio λ∥C/λ⊥C does not change significantly, though statistical uncertainty limits definitive conclusions due to few parallel intervals in Voyager 1 data.
• The study confirms that the Taylor hypothesis remains valid for ~99% of PSP intervals, with only ~1% showing poor validity (VA/VSW > 0.66) near perihelion.
• Proper accounting for changing sampling directions in PSP data is critical for accurate interpretation of radial turbulence evolution, especially near the Sun.