On the parallel spectrum in MHD Turbulence

TL;DR

This paper explores the origin of anisotropic spectra in MHD turbulence, linking the parallel spectrum to Alfvén wave propagation and challenging the necessity of the critical balance hypothesis, supported by high-resolution simulations.

Contribution

It demonstrates that the $k^{-2}$ parallel spectrum arises from Alfvén wave dynamics, independent of the critical balance assumption, and verifies this through high-resolution MHD turbulence simulations.

Findings

Parallel spectrum cutoff scales with Kolmogorov timescale.

Steeper $k^{-2}$ spectrum is linked to Alfvén wave propagation.

Anisotropy can be explained without critical balance.

Abstract

Anisotropy of MHD turbulence has been studied extensively for many years, most prominently by measurements in the solar wind and high resolution simulations. The spectrum parallel to the local magnetic field was observed to be steeper than perpendicular spectrum, typically $k^{-2}$, consistent with the widely accepted Goldreich-Sridhar (1995) model. In this Letter I looked deeper into the nature of the relation between parallel and perpendicular spectra and argue that this $k^{-2}$ scaling has the same origin as the $\omega^{-2}$ scaling of Lagrangian frequency spectrum in strong hydrodynamic turbulence. This follows from the fact that Alfv\'en waves propagate along magnetic field lines. It is now became clear that the observed anisotropy can be argued without invocation of the "critical balance" argument and is more robust that was previously thought. The relation between parallel (Lagrangian) and perpendicular (Eulerian) spectra is inevitable consequence of strong turbulence of Alfven waves, rather than a conjecture based on the uncertainty relation. I tested this using high-resolution simulations of MHD turbulence, in particular I verified that the cutoff of the parallel spectrum scales as Kolmogorov timescale, not lengthscale.