Triad interactions and the bidirectional turbulent cascade of magnetic helicity

Using direct numerical simulations we demonstrate that magnetic helicity exhibits a bidirectionalturbulent cascade at high but finite magnetic Reynolds numbers. Despite the injection of positivemagnetic helicity in the flow, we observe that magnetic helicity of opposite signs is generated betweenlarge and small scales. We explain these observations by carrying out an analysis of the magnetohy-drodynamic equations reduced to triad interactions using the Fourier helical decomposition. Withinthis framework, the direct cascade of positive magnetic helicity arises through triad interactions thatare associated with small scale dynamo action, while the occurrence of negative magnetic helicityat large scales is explained through triad interactions that are related to stretch-twist-fold dynamicsand 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 finitemagnetic Reynolds numberRmeffect that will vanish in the limitRm→∞.