Numerical Measurements of the Spectrum in Magnetohydrodynamic Turbulence

TL;DR

This paper presents high-resolution numerical simulations of magnetohydrodynamic turbulence with a strong guide field, conclusively supporting a -3/2 power law for the energy spectrum, resolving previous theoretical debates.

Contribution

The study provides definitive numerical evidence favoring the -3/2 spectral slope in strong MHD turbulence with a guide field, using advanced simulation techniques.

Findings

Spectrum follows E(k⊥) ∝ k⊥^{-3/2}

Supports the -3/2 spectral prediction over -5/3

Uses high-resolution (512^3) simulations with various forcing routines

Abstract

We report the results of an extensive set of direct numerical simulations of forced, incompressible, magnetohydrodynamic turbulence with a strong guide field. The aim is to resolve the controversy regarding the power law exponent (\alpha, say) of the field perpendicular energy spectrum E(k_\perp) \propto k_\perp ^ {\alpha}. The two main theoretical predictions, \alpha=-3/2 and \alpha=-5/3, have both received some support from numerical simulations carried out by different groups. Our simulations have a resolution of 512^3 mesh points, a strong guide field, an anisotropic simulation domain, and implement a broad range of large-scale forcing routines, including those previously reported in the literature. Our findings indicate that the spectrum of well developed, strong incompressible MHD turbulence with a strong guide field is E(k_{\perp})\propto k_{\perp}^{-3/2}.