Anisotropic non-perturbative zero modes for passively advected magnetic fields

Abstract

A first analytic assessment of the role of anisotropic corrections to the isotropic anomalous scaling exponents is given for the $d$-dimensional kinematic magneto-hydrodynamics problem in the presence of a mean magnetic field. The velocity advecting the magnetic field changes very rapidly in time and scales with a positive exponent $\xi$. Inertial-range anisotropic contributions to the scaling exponents, ${\zeta }_j$, of second-order magnetic correlations are associated to zero modes and have been calculated non-perturbatively. For $d=3$, the limit $\xi \mapsto 0$ yields $\protect{ζ_j=j-2+ ξ(2j^3 +j^2 -5 j - 4)/[2(4 j^2 - 1)]} $ where $j$ ($j\ge 2$) is the order in the Legendre polynomial decomposition applied to correlation functions. Conjectures on the fact that anisotropic components cannot change the isotropic threshold to the dynamo effect are also made.

A sign in previous formula (28) has been changed. Previous perturbative expressions (29) and (30) (relative to (28)) are thus changed. Figure 1 has been modified. Minor changes in the notation have been made. New references have been added. Previous conclusions unchanged. Phys. Rev. E RC (1999) (to appear)

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