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
ξ
. Inertial-range anisotropic contributions to the scaling exponents,
ζ
j
, of second-order magnetic correlations are associated to zero modes and have been calculated non-perturbatively. For
d=3
, the limit
ξ↦0
yields $\protect{\zeta_j=j-2+ \xi (2j^3 +j^2 -5 j - 4)/[2(4 j^2 - 1)]}$ where
j
(
j≥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.