On the Parallel Spectrum in Magnetohydrodynamic Turbulence

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 the perpendicular spectrum, typically , consistent with the widely accepted Goldreich & Sridhar model. In this Letter, I looked deeper into the nature of the relation between parallel and perpendicular spectra and argue that this scaling has the same origin as the scaling of the Lagrangian frequency spectrum in strong hydrodynamic turbulence. This follows from the fact that Alfvén waves propagate along magnetic field lines. It has 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 an inevitable consequence of strong turbulence of Alfvén 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 a Kolmogorov timescale, not lengthscale.