Abstract
Some of the consequences of the conservation of magnetic helicity$\int \rm{a.b}\it{d}^{\rm{3}}\rm{r\qquad (a\; =\; vector\; potential\; of\; magnetic\; field\; b)}$for incompressible three-dimensional turbulent MHD flows are investigated. Absolute equilibrium spectra for inviscid infinitely conducting flows truncated at lower and upper wavenumberskminandkmaxare obtained. When the total magnetic helicity approaches an upper limit given by the total energy (kinetic plus magnetic) divided bykmin, the spectra of magnetic energy and helicity are strongly peaked nearkmin; in addition, when the cross-correlations between the velocity and magnetic fields are small, the magnetic energy density nearkmingreatly exceeds the kinetic energy density. Several arguments are presented in favour of the existence of inverse cascades of magnetic helicity towards small wavenumbers leading to the generation of large-scale magnetic energy.
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