On the energy spectrum of strong magnetohydrodynamic turbulence

TL;DR

This paper presents high-resolution simulations of strong magnetohydrodynamic turbulence, revealing a consistent -3/2 power-law energy spectrum in both balanced and imbalanced cases at high Reynolds numbers.

Contribution

It provides the largest statistical sample to date of steady-state MHD turbulence spectra, demonstrating convergence to a -3/2 power law and exploring spectral behavior in balanced and imbalanced turbulence.

Findings

Energy spectrum converges to a -3/2 power law at high Reynolds numbers.

In imbalanced turbulence, E^- scales as k^{-3/2} while E^+ flattens with increasing Re.

Both spectra are pinned at dissipation and driving scales, suggesting parallel spectra at high Re.

Abstract

The energy spectrum of magnetohydrodynamic turbulence attracts interest due to its fundamental importance and its relevance for interpreting astrophysical data. Here we present measurements of the energy spectra from a series of high-resolution direct numerical simulations of MHD turbulence with a strong guide field and for increasing Reynolds number. The presented simulations, with numerical resolutions up to 2048^3 mesh points and statistics accumulated over 30 to 150 eddy turnover times, constitute, to the best of our knowledge, the largest statistical sample of steady state MHD turbulence to date. We study both the balanced case, where the energies associated with Alfv\'en modes propagating in opposite directions along the guide field, E^+ and $E^-, are equal, and the imbalanced case where the energies are different. In the balanced case, we find that the energy spectrum converges to a power law with exponent -3/2 as the Reynolds number is increased, consistent with phenomenological models that include scale-dependent dynamic alignment. For the imbalanced case, with E^+>E^-, the simulations show that E^- ~ k_{\perp}^{-3/2} for all Reynolds numbers considered, while E^+ has a slightly steeper spectrum at small Re. As the Reynolds number increases, E^+ flattens. Since both E^+ and E^- are pinned at the dissipation scale and anchored at the driving scales, we postulate that at sufficiently high Re the spectra will become parallel in the inertial range and scale as E^+ ~ E^- ~ k_{\perp}^{-3/2}. Questions regarding the universality of the spectrum and the value of the "Kolmogorov constant" are discussed.