Asymptotic properties of turbulent magnetohydrodynamics

TL;DR

This paper uses the dynamic renormalization group to analyze the asymptotic behavior of turbulent magnetohydrodynamics, deriving scaling laws and spectral functions relevant to astrophysical and cosmological magnetic phenomena.

Contribution

It introduces a RG-based method to derive asymptotic scaling laws and spectral functions for turbulent MHD, including effects of magnetic helicity and energy cascade directions.

Findings

Derived scale-dependent viscosity and resistivity.

Obtained asymptotic energy spectra including Kolmogorov and Iroshnikov-Kraichnan.

Analyzed the impact of magnetic helicity on turbulence spectra.

Abstract

The dynamic renormalization group (RG) is used to study the large-distance and long-time limits of viscous and resistive incompressible magnetohydrodynamics subject to random forces and currents. The scale-dependent viscosity and magnetic resistivity are derived and used for carrying out RG-improved perturbation theory. This is applied to derive both the asymptotic scaling and the overall proportionality coefficients for both the velocity and magnetic field correlation functions as well as the kinetic and magnetic energy density spectral functions. The Kolmogorov, Iroshnikov-Kraichnan, as well as other energy spectra, formally can be obtained by suitable choice of injected noise, although the method limits the validity of these energy spectra only to the asymptotic regime . Injection of a random magnetic helicity is considered, its RG-improved spectral density derived, and its contribution to the velocity and magnetic field correlation functions determined. The RG scaling solutions are used to determine information at asymptotic scales about energy and helicity cascade directions and mixing between magnetic and kinetic energy. Some of the results found here also are shown to be valid for the Navier-Stokes hydrodynamic equation. The results have applicability to geomagnetism as well as cosmic magnetic fields at astrophysical and cosmological scales.