Triad interactions and the bidirectional turbulent cascade of magnetic helicity

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 $Rm\to \infty$.

postprint version

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Cited by in corpus (8)

• Cascades and transitions in turbulent flows
• Regime Transition in the Energy Cascade of Rotating Turbulence
• The nature of triad interactions in active turbulence
• Inverse cascade and magnetic vortices in kinetic Alfvén-wave turbulence
• Inverse cascade of hybrid helicity in $B\Omega$-MHD turbulence
• Partial invariants, large-scale dynamo action, and the inverse transfer of magnetic helicity
• Inverse transfer of magnetic helicity in direct numerical simulations of compressible isothermal turbulence: helical transfers
• Helicity dynamics, inverse and bi-directional cascades in fluid and MHD turbulence: A brief review