Role of helicities for the dynamics of turbulent magnetic fields

TL;DR

This paper explores how helicities influence the inverse cascade of magnetic helicity in turbulent magnetohydrodynamics, revealing a universal relation between kinetic and magnetic helicities and suggesting a nonlinear quenching mechanism.

Contribution

It demonstrates the importance of nonlinear interactions in magnetic helicity dynamics and derives a universal relation linking kinetic and magnetic helicities using a quasi-normal Markovian approximation.

Findings

Self-similar scaling of magnetic helicity depends on nonlinear velocity-magnetic interactions.

Derived a universal relation between kinetic and magnetic helicities.

Identified a potential nonlinear quenching mechanism of the dynamo pseudoscalar.

Abstract

Investigations of the inverse cascade of magnetic helicity are conducted with pseudospectral, three-dimensional direct numerical simulations of forced and decaying incompressible magnetohydrodynamic turbulence. The high-resolution simulations which allow for the necessary scale-separation show that the observed self-similar scaling behavior of magnetic helicity and related quantities can only be understood by taking the full nonlinear interplay of velocity and magnetic fluctuations into account. With the help of the eddy-damped quasi-normal Markovian approximation a probably universal relation between kinetic and magnetic helicities is derived that closely resembles the extended definition of the prominent dynamo pseudoscalar $\alpha$. This unexpected similarity suggests an additional nonlinear quenching mechanism of the current-helicity contribution to $\alpha$.