http://arxiv.org/abs/1903.10725
The existence of partially conserved enstrophy-like quantities is conjectured to cause embedded, inverse magnetic energy cascades to develop in magnetohydrodynamical (MHD) turbulence. By decomposing the velocity and magnetic fields in spectral space onto helical modes, we show that two new quantities exist which are partially conserved among a set of three-wave (triad) interactions in MHD turbulence. In a subset of these helical triad interactions, the quantities become enstrophy-like, which, by analogy to enstrophy-conserving triad interactions in two-dimensional, nonconducting hydrodynamical turbulence, are conjectured to cause embedded, inverse magnetic energy cascades to develop. We test the resulting predictions by constructing a nonlocal helical MHD shell model (reduced wave-space numerical model) of the minimal set of triad interactions (MTIs) required to conserve the ideal MHD invariants, energy, magnetic helicity, and cross-helicity. The numerically simulated MTIs demonstrate that, for a range of forcing configurations, the partial invariants are indeed useful for understanding the embedded energy cascade contributions to the total spectral energy flux, which has potential implications for the turbulent dynamo action, central to the evolution of astrophysical magnetic fields.
N. Rathmann and P. Ditlevsen
Wed, 27 Mar 19
72/74
Comments: 11 pages, 6 figures
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