# Triad interactions and the bidirectional turbulent cascade of magnetic helicity

## TL;DR

This paper uses simulations and theoretical analysis to show that magnetic helicity undergoes a bidirectional cascade in turbulent flows, with opposite signs at different scales, influenced by finite magnetic Reynolds numbers.

## Contribution

It reveals the bidirectional cascade of magnetic helicity and explains the underlying triad interactions through a combined numerical and analytical approach.

## Key findings

- Magnetic helicity exhibits a bidirectional cascade at finite Rm.
- Opposite signs of magnetic helicity are generated at different scales.
- The direct cascade of positive magnetic helicity diminishes as Rm approaches infinity.

## Abstract

Using direct numerical simulations we demonstrate that magnetic helicity exhibits a bidirectional turbulent cascade at high but finite magnetic Reynolds numbers. Despite the injection of positive magnetic helicity in the flow, we observe that magnetic helicity of opposite signs is generated between large and small scales. We explain these observations by carrying out an analysis of the magnetohydrodynamic equations reduced to triad interactions using the Fourier helical decomposition. Within this framework, the direct cascade of positive magnetic helicity arises through triad interactions that are associated with small scale dynamo action, while the occurrence of negative magnetic helicity at large scales is explained through triad interactions that are related to stretch-twist-fold dynamics and small scale dynamo action, which compete with the inverse cascade of positive magnetic helicity. Our analytical and numerical results suggest that the direct cascade of magnetic helicity is a finite magnetic Reynolds number $Rm$ effect that will vanish in the limit $Rm \to \infty$.