The Spectral Slope and Kolmogorov Constant of MHD turbulence

TL;DR

This study confirms the -5/3 spectral slope in strong MHD turbulence through high-resolution simulations, measures the Kolmogorov constant, and clarifies previous discrepancies caused by numerical effects and energy transfer locality.

Contribution

The paper provides the first high-resolution simulation evidence for the asymptotic -5/3 slope in MHD turbulence and measures the Kolmogorov constant, clarifying previous conflicting results.

Findings

Confirmed the -5/3 spectral slope in high-resolution MHD turbulence.

Measured Kolmogorov constants for Alfvénic and full MHD turbulence.

Identified the impact of energy transfer locality and simulation resolution on spectral slope.

Abstract

The spectral slope of strong MHD turbulence has recently been a matter of controversy. While Goldreich-Sridhar model (1995) predicts Kolmogorov's -5/3 slope of turbulence, shallower slopes were often reported by numerical studies. We argue that earlier numerics was affected by driving due to a diffuse locality of energy transfer in MHD case. Our highest-resolution simulation (3072^2x1024) has been able to reach the asymptotic -5/3 regime of the energy slope. Additionally, we found that so-called dynamic alignment, proposed in the model with -3/2 slope, saturates and therefore can not affect asymptotic slope. The observation of the asymptotic regime allowed us to measure Kolmogorov constant C_KA=3.2+-0.2 for purely Alfv\'enic turbulence and C_K=4.1+-0.3 for full MHD turbulence. These values are much higher than the hydrodynamic value of 1.64. The larger value of Kolmogorov constant is an indication of a fairly inefficient energy transfer and, as we show in this Letter, is in theoretical agreement with our observation of diffuse locality. We also explain what has been missing in numerical studies that reported shallower slopes.