Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1999-03-19
Nonlinear Sciences
Chaotic Dynamics
A sign in previous formula (28) has been changed. Previous perturbative expressions (29) and (30) (relative to (28)) are thus
Scientific paper
10.1103/PhysRevE.60.R3483
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{\zeta_j=j-2+ \xi (2j^3 +j^2 -5 j - 4)/[2(4 j^2 - 1)]} $ where $j$ ($j\geq 2$) 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.
Lanotte Alessandra
Mazzino Andrea
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