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A weak turbulence theory for incompressible magnetohydrodynamics

Published online by Cambridge University Press:  01 June 2000

S. GALTIER ,
S. V. NAZARENKO ,
A. C. NEWELL  and
A. POUQUET
S. GALTIER
Affiliation:
Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK Observatoire de la Côte d'Azur, CNRS UMR 6529, BP 4229, 06304 Nice Cedex 4, France
S. V. NAZARENKO
Affiliation:
Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK
A. C. NEWELL
Affiliation:
Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK
A. POUQUET
Affiliation:
Observatoire de la Côte d'Azur, CNRS UMR 6529, BP 4229, 06304 Nice Cedex 4, France
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Abstract

We derive a weak turbulence formalism for incompressible magnetohydrodynamics. Three-wave interactions lead to a system of kinetic equations for the spectral densities of energy and helicity. The kinetic equations conserve energy in all wavevector planes normal to the applied magnetic field B0ê∥. Numerically and analytically, we find energy spectra E± ∼ kn±⊥, such that n+ + n− = −4, where E± are the spectra of the Elsässer variables z± = v ± b in the two-dimensional case (k∥ = 0). The constants of the spectra are computed exactly and found to depend on the amount of correlation between the velocity and the magnetic field. Comparison with several numerical simulations and models is also made.

Type
Research Article
Information
Journal of Plasma Physics , Volume 63 , Issue 5 , June 2000 , pp. 447 - 488
Copyright
2000 Cambridge University Press

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