Comment on the numerical measurements of the magnetohydrodynamic turbulence spectrum by A. Beresnyak (Phys. Rev. Lett. 106 (2011) 075001; MNRAS 422 (2012) 3495; ApJ 784 (2014) L20)

TL;DR

This paper critiques Beresnyak's numerical simulations of MHD turbulence spectra, arguing they are unresolved and do not accurately represent the physical phenomena, supporting the $k^{-3/2}$ scaling over $k^{-5/3}$.

Contribution

The paper provides a clear critique of previous numerical methods used to measure MHD turbulence spectra, emphasizing the importance of resolution for accurate results.

Findings

Beresnyak's simulations are critically unresolved.

The $k^{-3/2}$ spectral scaling is supported.

Previous claims of $k^{-5/3}$ scaling are challenged.

Abstract

The inertial-interval energy spectrum of strong magnetohydrodynamic (MHD) turbulence with a uniform background magnetic field was observed numerically to be close to $k^{-3/2}$ by a number of independent groups. A dissenting opinion has been voiced by Beresnyak, A. 2011, PRL, 106, 075001-. 2012, MNRAS, 422, 3495-. 2014, ApJ, 784, L20 that the spectral scaling is close to $k^{-5/3}$. The conclusions of these papers are however incorrect as they are based on numerical simulations that are drastically unresolved, so that the discrete numerical scheme does not approximate the physical solution at the scales where the measurements are performed. These results have been rebutted in our more detailed papers Perez, J. C., Mason, J., Boldyrev, S., & Cattaneo, F. 2012, PRX, 2, 041005-. 2014, ApJL, 793, L13; here, by popular demand, we present a brief and simple explanation of our major criticism of Beresnyak's work.