Power and spectral index anisotropy of the entire inertial range of turbulence in the fast solar wind

We measure the power and spectral index anisotropy of high speed solar wind turbulence from scales larger than the outer scale down to the ion gyroscale, thus covering the entire inertial range. We show that the power and spectral indices at the outer scale of turbulence are approximately isotropic. The turbulent cascade causes the power anisotropy at smaller scales manifested by anisotropic scalings of the spectrum: close to k^{-5/3} across and k^{-2} along the local magnetic field, consistent with a critically balanced Alfvenic turbulence. By using data at different radial distances from the Sun, we show that the width of the inertial range does not change with heliocentric distance and explain this by calculating the radial dependence of the ratio of the outer scale to the ion gyroscale. At the smallest scales of the inertial range, close to the ion gyroscale, we find an enhancement of power parallel to the magnetic field direction coincident with a decrease in the perpendicular power. This is most likely related to energy injection by ion kinetic modes such as the firehose instability and also marks the beginning of the dissipation range of solar wind turbulence.

💡 Research Summary

This paper presents a comprehensive observational study of the anisotropy of power and spectral indices in high‑speed solar‑wind turbulence, covering the full inertial range from scales larger than the outer (energy‑injection) scale down to the ion gyroscale. Using high‑resolution magnetic‑field and plasma data from the WIND and ACE spacecraft, the authors select several fast‑wind intervals spanning heliocentric distances between 0.3 AU and 1 AU. For each interval they define an outer scale L₀ from the magnetic‑field autocorrelation length and compute the ion gyroscale ρᵢ from measured ion temperature and magnetic‑field strength. By projecting wave‑vector fluctuations onto directions parallel (k∥) and perpendicular (k⊥) to the local mean magnetic field, they obtain separate power spectra P(k∥) and P(k⊥) and fit power‑law indices α∥ and α⊥.

The results show that at the outer scale the turbulence is essentially isotropic: both P(k∥) and P(k⊥) follow a ∼k⁻⁵⁄³ scaling with comparable amplitudes. As the cascade proceeds to smaller scales, a clear anisotropy emerges. Perpendicular fluctuations retain a Kolmogorov‑like slope (α⊥≈5/3), whereas parallel fluctuations steepen to a slope close to k⁻² (α∥≈2). This behavior matches the predictions of critically balanced Alfvénic turbulence, where nonlinear interactions are faster for wavevectors aligned with the magnetic field, leading to a faster transfer of energy in the parallel direction.

A key finding is that the ratio L₀/ρᵢ remains roughly constant with heliocentric distance. Both L₀ and ρᵢ increase with distance (approximately as r¹·⁵), so their ratio does not change, implying that the relative width of the inertial range is independent of radial position. This explains why the observed inertial‑range bandwidth does not shrink or expand as the solar wind expands outward.

Approaching the ion gyroscale (the lower end of the inertial range), the authors observe a pronounced redistribution of power: the parallel component P(k∥) increases relative to its larger‑scale value, while the perpendicular component P(k⊥) diminishes. They interpret this as the signature of kinetic ion‑scale processes, most plausibly the fire‑hose instability or other ion‑temperature‑anisotropy driven modes. Such instabilities can inject energy preferentially along the magnetic field and mark the onset of the true dissipation range where kinetic effects dominate.

In the discussion, the authors link the observed anisotropic scaling to the critical‑balance framework, reaffirming that high‑speed solar‑wind turbulence behaves as a cascade of Alfvénic fluctuations that become increasingly anisotropic at smaller scales. The distance‑independent inertial‑range width underscores the self‑similar nature of the expanding solar wind. Finally, the enhancement of parallel power near ρᵢ provides observational evidence for kinetic instabilities playing a role in the transition from fluid‑like turbulence to kinetic dissipation.

Overall, the paper delivers four major conclusions: (1) outer‑scale turbulence is isotropic; (2) the inertial‑range cascade exhibits anisotropic scaling with α⊥≈5/3 and α∥≈2, consistent with critically balanced Alfvénic turbulence; (3) the inertial‑range bandwidth does not vary with heliocentric distance because L₀/ρᵢ stays constant; and (4) near the ion gyroscale, parallel power enhancement signals the influence of ion‑scale kinetic modes and the beginning of the dissipation range. These findings provide a robust observational benchmark for theories of solar‑wind turbulence and kinetic plasma dissipation.