On weak and strong magnetohydrodynamic turbulence

TL;DR

This paper investigates the transition between weak and strong magnetohydrodynamic turbulence using numerical simulations, clarifying how the energy spectrum depends on the balance of linear and nonlinear interactions.

Contribution

It introduces a numerical framework to study the anisotropic MHD turbulence transition and characterizes the energy spectrum scaling in different turbulent regimes.

Findings

Strong turbulence exhibits a $k_{ot}^{-3/2}$ spectrum under critical balance.

Weaker turbulence approaches a $k_{ot}^{-2}$ spectrum as linear effects dominate.

Spectrum sensitivity explains conflicting observational and numerical results.

Abstract

Recent numerical and observational studies contain conflicting reports on the spectrum of magnetohydrodynamic turbulence. In an attempt to clarify the issue we investigate anisotropic incompressible magnetohydrodynamic turbulence with a strong guide field $B_0$. We perform numerical simulations of the reduced MHD equations in a special setting that allows us to elucidate the transition between weak and strong turbulent regimes. Denote $k_{\|}$, $k_\perp$ characteristic field-parallel and field-perpendicular wavenumbers of the fluctuations, and $b_{\lambda}$ the fluctuating field at the scale $\lambda\sim 1/k_{\perp}$. We find that when the critical balance condition, $k_{\|}B_0\sim k_{\perp} b_{\lambda}$, is satisfied, the turbulence is strong, and the energy spectrum is $E(k_{\perp})\propto k^{-3/2}_{\perp}$. As the $k_{\|}$ width of the spectrum increases, the turbulence rapidly becomes weaker, and in the limit $k_{\|}B_0\gg k_{\perp} b_{\lambda}$, the spectrum approaches $E(k_{\perp})\propto k_{\perp}^{-2}$. The observed sensitivity of the spectrum to the balance of linear and nonlinear interactions may explain the conflicting numerical and observational findings where this balance condition is not well controlled.