Reply to Comment on "Spectra of strong magnetohydrodynamic turbulence from high-resolution simulations"

TL;DR

This paper refutes claims that previous high-resolution MHD turbulence simulations were underresolved or lacked error estimates, clarifying the actual resolution criteria and error assessments used in the original study.

Contribution

It clarifies misconceptions about the resolution and error estimation in Beresnyak (2014)'s MHD turbulence simulations, reaffirming their validity.

Findings

Beresnyak (2014) used a higher resolution criterion ($k_{max}\eta_{41}$=1.06) than Perez et al (0.8).

Beresnyak (2014) estimated numerical error below 0.003.

The comment by Perez et al lacks numerical evidence against Beresnyak (2014).

Abstract

In a Comment by Perez et al (2014) it is claimed that recently published simulations of Beresnyak (2014) are grossly underresolved, compared to theirs, and that Beresnyak (2014) failed to estimate numerical error. Both claims are contrary to the fact. Firstly, as far as numerical resolution is concerned, Beresnyak (2014) was using $k_{\rm max}\eta_{41}$=1.06 resolution criterion, while Perez et al has been using $k_{\rm max}\eta_{41}$=0.8. Obviously, $1.06>0.8$. Secondly, Beresnyak (2014) have estimated numerical error and found it to be below $3\times 10^{-3}$, which is properly explained in the paper. On close inspection of the Comment I have not found a single numerical value or parameter pertaining to the criticized paper, Beresnyak (2014), and it is completely unclear how the Authors came to their conclusions.