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The existence of partially conserved enstrophy-like quantities is conjecturedto cause inverse energy transfers to develop embedded in magnetohydrodynamical(MHD) turbulence, in analogy to the influence of enstrophy in two-dimensionalnonconducting turbulence. By decomposing the velocity and magnetic fields inspectral space onto helical modes, we identify subsets of three-wave (triad)interactions conserving two new enstrophy-like quantities which can be mappedto triad interactions recently identified with facilitating large-scale$\alpha$-type dynamo action and the inverse transfer of magnetic helicity. Dueto their dependence on interaction scale locality, the invariants suggest thatthe inverse transfer of magnetic helicity might be facilitated by both local-and nonlocal-scale interactions, and is a process more local than the$\alpha$-dynamo. We test the predicted embedded (partial) energy fluxes byconstructing a shell model (reduced wave-space model) of the minimal set oftriad interactions (MTI) required to conserve the ideal MHD invariants.Numerically simulated MTIs demonstrate that, for a range of forcingconfigurations, the partial invariants are, with some exceptions, indeed usefulfor understanding the embedded contributions to the total spectral energy flux.Furthermore, we demonstrate that strictly inverse energy transfers may developif enstrophy-like conserving interactions are favoured, a mechanism recentlyattributed to the energy cascade reversals found in nonconductingthree-dimensional turbulence subject to strong rotation or confinement. Thepresented results have implications for the understanding of the physicalmechanisms behind large-scale dynamo action and the inverse transfer ofmagnetic helicity, processes thought to be central to large-scale magneticstructure formation.

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