Kolmogorov Scaling for Total Energy and Cross Helicity in Magnetohydrodynamic Turbulence

TL;DR

This study uses high-resolution simulations to resolve the longstanding debate on the energy scaling laws in isotropic magnetohydrodynamic turbulence, providing evidence favoring Kolmogorov's $k^{-5/3}$ spectrum for total energy.

Contribution

The paper demonstrates through extensive simulations that total energy and cross helicity follow Kolmogorov scaling, clarifying the energy transfer mechanisms in MHD turbulence.

Findings

Total energy and cross helicity spectra are closer to $k^{-5/3}$.

Magnetic energy follows a $k^{-5/3}$ spectrum, while kinetic energy exhibits a $k^{-3/2}$ spectrum.

Energy transfer from magnetic to velocity field explains the kinetic energy spectrum.

Abstract

The problem of scaling in isotropic magnetohydrodynamic (MHD) turbulence has remained unresolved, with competing predictions of $k^{-5/3}$ (Kolmogorov) and $k^{-3/2}$ (Iroshnikov-Kraichnan) scalings. In this paper, we address this long-standing controversy using high-resolution numerical simulations on $8192^2$ and $1536^3$ grids. We show that the total energy and cross helicity spectra are closer to $k^{-5/3}$ than $k^{-3/2}$. The fluxes and structure functions of the total energy and cross helicity also demonstrate robust support for Kolmogorov scaling. The magnetic energy shows $k^{-5/3}$ spectrum, but the kinetic energy exhibits $k^{-3/2}$ spectrum; the latter spectrum is due to the energy transfers from the magnetic field to the velocity field.