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Partial invariants, large-scale dynamo action, and the inverse transfer of magnetic helicity

The existence of partially conserved enstrophy-like quantities is conjectured to cause inverse energy transfers to develop embedded in magnetohydrodynamical (MHD) turbulence, in analogy to the influence of enstrophy in two-dimensional nonconducting turbulence. By decomposing the velocity and magnetic fields in spectral space onto helical modes, we identify subsets of three-wave (triad) interactions conserving two new enstrophy-like quantities which can be mapped to triad interactions recently identified with facilitating large-scale $α$-type dynamo action and the inverse transfer of magnetic helicity. Due to their dependence on interaction scale locality, the invariants suggest that the inverse transfer of magnetic helicity might be facilitated by both local- and nonlocal-scale interactions, and is a process more local than the $α$-dynamo. We test the predicted embedded (partial) energy fluxes by constructing a shell model (reduced wave-space model) of the minimal set of triad interactions (MTI) required to conserve the ideal MHD invariants. Numerically simulated MTIs demonstrate that, for a range of forcing configurations, the partial invariants are, with some exceptions, indeed useful for understanding the embedded contributions to the total spectral energy flux. Furthermore, we demonstrate that strictly inverse energy transfers may develop if enstrophy-like conserving interactions are favoured, a mechanism recently attributed to the energy cascade reversals found in nonconducting three-dimensional turbulence subject to strong rotation or confinement. The presented results have implications for the understanding of the physical mechanisms behind large-scale dynamo action and the inverse transfer of magnetic helicity, processes thought to be central to large-scale magnetic structure formation.