Abstract
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.
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