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Possibility of an inverse cascade of magnetic helicity in magnetohydrodynamic turbulence

Published online by Cambridge University Press:  29 March 2006

U. Frisch
Affiliation:
Centre National de la Recherche Scientifique, Observatoire de Nice, France
A. Pouquet
Affiliation:
Centre National de la Recherche Scientifique, Observatoire de Nice, France
J. LÉOrat
Affiliation:
Université Paris VII, Observatoire de Meudon, France
A. Mazure
Affiliation:
Université Paris VII, Observatoire de Meudon, France

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 wavenumbers kmin and kmax are obtained. When the total magnetic helicity approaches an upper limit given by the total energy (kinetic plus magnetic) divided by kmin, the spectra of magnetic energy and helicity are strongly peaked near kmin; in addition, when the cross-correlations between the velocity and magnetic fields are small, the magnetic energy density near kmin greatly 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.

Type
Research Article
Copyright
© 1975 Cambridge University Press

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Possibility of an inverse cascade of magnetic helicity in magnetohydrodynamic turbulence
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